Wikipedia talk:WikiProject Mathematics/Archive/2006

Jan 2006 – Feb 2006

Help with Simple harmonic motion

A newbie, Itzchinoboi, rewrote Simple harmonic motion. The new article is more elementary, which is good. To me both the original version looks good, and the rewritten version looks good, although the latter is full of newbie mistakes. See the diff. Anybody knowledgeble willing to spend some time understanding the changes and see how to deal with all this matter? Note that a plain revert is not an option, it seems that the user spent half a day on that article. Oleg Alexandrov (talk) 22:31, 2 January 2006 (UTC)

Scalar (mathematics)

This newly created page is an abomination. Please help. Michael Hardy 02:41, 3 January 2006 (UTC)

I've had a go. Dysprosia 04:20, 3 January 2006 (UTC)

Nice one, D. This seems to be rather an uphill battle. It would be good to get the thoughts of others regarding the article introduction - see this bit of the talk page. Thanks!  — merge 04:14, 12 January 2006 (UTC)

Tensor wars

We may be in for more of the traditional troubles at Tensor. Category:Tensors now has 70 articles. I really think the main tensor article should reflect that (at least - some of the more algebraic pages are in Category:Multilinear algebra or elsewhere).

There is a sub-issue, rank of a tensor, which might be tractable on the basis of some sourced research.

Charles Matthews 17:02, 3 January 2006 (UTC)

Articles listed at Articles for deletion

• Set descriptions in colloquial English (AfD discussion)

Uncle G 01:03, 4 January 2006 (UTC)

Wikipedia talk:Stable versions#Certification gang

would you like to create certified articles in mathematics? -- Zondor 03:19, 5 January 2006 (UTC)

Hmmm ... I have major issues with this idea. How do you decide who can join your gang ? You wouldn't want to let just anyone in, would you ? They might start doing stuff that you disagreed with. It sounds awfully like a self-elected technocracy. I would be more worried if I didn't think that the chances of reaching critical mass on this idea are really, really small. Gandalf61 09:46, 5 January 2006 (UTC)

It will start out as a gang but eventually to something professional like a league. -- Zondor 13:35, 5 January 2006 (UTC)

Certification is an interesting idea, but its not yet completely fleshed out. Its primary utility is to handle articles where there have been significant edits wars, or get a lot of inappropriate edits from newbies, or even regular vandalism. This is maybe less than 1% of all math articles. The goal is to certify one particular version of the article, and then let anon hack on it. If one comes back in a month or two and its a horrid mess ... well, so what, at least the certified version is good. This is much better than the battle fatigue of having to defend an article on a daily basis. linas 15:20, 5 January 2006 (UTC)

But if you don't defend an article on a daily basis, then it will get messed up, and after a month or two you won't be able to sort out any good edits from the rubbish, so the only way forward will be to roll back to the "certified" version. In effect, you have frozen the article - no one will bother to make any serious contributions because they will all be lost in the next purge. Gandalf61 16:23, 5 January 2006 (UTC)

Our energy can be spent better in places other than in certifying articles. If you come back to an article months later and it's "messed up", you should take the time to go through the diff and find out what went wrong, and then either revert there or fix it by hand. Reverting to an outdated "stable" version is too crude a tool.

Meekohi 19:05, 5 January 2006 (UTC)

The energy is well spent if creating a Wikipedia:WikiReader project for Mathematics. -- Zondor 15:10, 7 January 2006 (UTC)

Yes, well, these points should be argued there, not here. My take is that I've seen too many good editors get wiki-fatigue and wikistress and have some of them leave, because they were unable to defend thousands of articles on a daily basis. If you can do this, great. Like many other "old-timers" (ok, I've been here a year), I now spend more time watching articles, trying to ward off decay, than I do on actually writing. That is wrong. It should not be a herculean effort to stave off wikirot. (See above, Wikipedia talk:WikiProject Mathematics#Help with Simple harmonic motion for a real-life example. Oleg watches a lot of these kinds articles, and can't keep up with the changes. The old version should have been declared "stable", and stay that way till the new one is done.) linas 21:25, 5 January 2006 (UTC)

This is getting offtopic, but I gave up watching articles by the thousands. After going under 1000 I actually found time to write new stuff every now and then. :) Yes, open acces is the biggest asset but also the biggest disadvantage of Wikipedia. But seems to work so far. :) Oleg Alexandrov (talk) 01:03, 6 January 2006 (UTC)

The single most important thing for stable versions is to have a guarantee of accuracy and reliability otherwise it is no different to the system we already have. So at any given time, we can demand a print edition of Wikipedia 1.0. Whereas, the wiki version serves as the playground for boldness, experimentation and to be cutting edge. Once you have made the published version, you can forget about it and concentrate on the wiki version. Eventually, it becomes better than the previous stable version, you then supplant it after it has been certified for accuracy. -- Zondor 01:02, 6 January 2006 (UTC)

Math Collaboration of the Week

I hope nobody is too opposed to the requets for nominations at the top of the page. I think we need it if we're going to get MCoW up and running again. Meekohi 20:06, 5 January 2006 (UTC)

Nevermind, apparently the big man minds. ;) Meekohi 20:07, 5 January 2006 (UTC)

Uhh, I've never really seen Oleg, but I would bet he's not really that big. Nevertheless as Fropuff suggested below it will get more attention here anyway. Paul August ☎ 03:46, 6 January 2006 (UTC)

What units do you want it in, feet, meters, edits per second? Oleg Alexandrov (talk) 18:59, 6 January 2006 (UTC)

It's alright, many people watch the discussion on this page. For those of you who don't know User:Meekohi is trying to get the Mathematics Collaboration of the Week going again (it has been dead for about four months now). If you are interested in participating please list nominations on that page. -- Fropuff 20:42, 5 January 2006 (UTC)

Perhaps that page should scale back to a less ambitious "Math Collaboration of the Month". Paul August ☎ 17:58, 6 January 2006 (UTC)

Well, is it flogging a dead horse? The discussions have always seemed to show up the way people here have rather disparate interests, within mathematics. We could have Algebra COTM, Geometry COTM etc., running in parallel.Charles Matthews 18:03, 6 January 2006 (UTC)

Honestly I feel it should be the Fortnightly collaboration since that is about how long it takes to get an article up to par, but it wouldn't fit in with all the other Weekly Collaborations we have in other subjects. Meekohi 15:45, 13 January 2006 (UTC)

A new project idea

I have an idea for a new math project that provides a somewhat concrete way of evaluating progress. I call it the "Let's Beat Mathworld" project; its goal is for every topic listed on Mathworld, to write a better article on the same topic. We've already done so for many of them, but I bet we can cover them all. We can make a project page listing all the topics in the Mathworld hierarchy with links. We have to watch out for copyvio, but I think it's a great source of useful topics that we may be failing to touch on or that may currently be stubs. Deco 04:25, 6 January 2006 (UTC)

For all that's worth, the mathworld articles already are listed at Wikipedia:Missing science topics (Math1 through Math7). Whoever did that seems to to have avoided copyvio by shuffling things and possibly mixing with entries from other places. Oleg Alexandrov (talk) 04:47, 6 January 2006 (UTC)

I was unaware of those lists. I've now added a link to them in the "Things to do" table on the main project page. (By the way Oleg, just how big are you?) Paul August ☎ 05:06, 6 January 2006 (UTC)

If you are asking how I got to know about that project, then the answer is that there was an announcement on this page a while ago, and actually Linas and Rick Norwood got there long before me. :)

Answered above. Oleg Alexandrov (talk) 04:17, 7 January 2006 (UTC)

By the way, there is also a User:Mathbot/List of mathematical redlinks, which I made at Fropuff's suggestion, containing 11,000 redlinks found in existing math articles. Oleg Alexandrov (talk) 07:38, 6 January 2006 (UTC)

Wow, 11k links. I wonder if it would be helpful to somehow categorize those missing links/ topics. I mean missing theorems, lemmas, formulas, problems, scientists... (Igny 14:45, 6 January 2006 (UTC))

A good chuck of those are nonmathematical. You would need artificial intelligence to sort out theorems from problems and from scientists. Yeah, I don't know how helpful that list is, but it exists. :) Oleg Alexandrov (talk) 15:01, 6 January 2006 (UTC)

Many of those 11K links are now blue. Oleg, do you plan on updating this list anytime? I don't know about other people, but I find it useful. Thanks again for doing it. -- Fropuff 15:26, 6 January 2006 (UTC)

I updated them now, and will do every couple of weeks or so. Oleg Alexandrov (talk) 04:17, 7 January 2006 (UTC)

I asked permission to used those list a few months ago, but received this reply

Rudy,

Thank you for your mail. We appreciate your effort to secure proper permission before using our material.

Our lists *do* represent original works of authorship and, as such, enjoy copyright protection. Further, the value of our editorial work is evidenced by your desire to incorporate the material into your project.

We understand your need for such a list, and we would very much like to support Wikipedia -- as I am sure you would like to support the continued development of MathWorld. It is worth noting the relative dearth of links to Mathworld from Wikipedia.

Regardless, it isn't obvious how reproducing MathWorld (which already offers unfettered, free access) furthers the goals of Wikipedia.

Are there other areas of mathematics/science that are in greater need of free web-based exposure that we could help Wikipedia develop?

Benson Dastrup Wolfram Research, Inc.

—Ruud 10:02, 6 January 2006 (UTC)

I really think we can set our own agenda now. Why not lead rather than follow? This is more likely to attract active research workers. Charles Matthews 15:22, 6 January 2006 (UTC)

I second Charles' opinion. MathWorld should be asking for our lists. If you see an article on MathWorld that doesn't have good coverage here, just post a request on Wikipedia:Requested articles/Mathematics. -- Fropuff 15:29, 6 January 2006 (UTC)

Well, that's if it's actually worth covering here. MathWorld's topic selection can be, to put it kindly, quirky (cf the Somer-Lucas pseudoprime article, which along with Somer pseudoprime probably ought to be deleted). --Trovatore 15:49, 6 January 2006 (UTC)

Trovatore, I don't understand you at all. Why would any article with substantiated content be deleted? Why would any topic not be worth covering? As for beating Mathworld, I do believe we already did, but in any case I think it will be much more efficient if every Math Wikipedian will, once in a while (or multiple times in a while), go to "random entry" in Mathworld, and make sure that Wikipedia has a better coverage of the encountered topic. If not, improve it or put a request for it. While this could create a little duplicate effort, it will solve many of the aforementioned problems (copyright issues, alleged statement that we are not as good as Mathworld, manageability of large lists of topics) as well as guarantee that changes to Mathworld will not be overlooked. --Meni Rosenfeld 17:01, 6 January 2006 (UTC)

Okay, perhaps those articles aren't as substantiated as I thought at first. Stil, I think the direction should be attempting to substantiate such articles, rather than delete them. --Meni Rosenfeld 19:50, 6 January 2006 (UTC)

I've noticed that while in many cases, we have better articles than mathworld, their articles will have a much larger section of raw often obscure formulas and identities. Those can detract from the quality of an article, as they're not very readable, but they're still important and useful, for any reference work. And remember, we're a reference, not a textbook. -lethe ^talk 04:25, 7 January 2006 (UTC)

The emphasis on formulas at MathWorld is surely to do with the Wolfram connection in the site's origins. Anyway I like classical formulae myself, but a more wordy style is indeed better for WP. Charles Matthews 08:01, 7 January 2006 (UTC)

It would probably be best to include such formulae, perhaps placing the less important ones near the end of the article so as not to be a distraction. --Meni Rosenfeld 15:09, 7 January 2006 (UTC)

While on one hand I agree that attempting to merely reproduce Mathworld's extensive quality entries might seem silly, on the other hand as the above e-mail demonstrates, their articles are not libre: we need to make the same information available to everyone to use, and update, in any way they please. Also, for the sake of our reputation, it would be neat to say that we unequivocably have even better coverage than a site as well-known as Mathworld. Deco 06:56, 10 January 2006 (UTC)

Mathematics Portal

I've been doing some work on the Mathematics Portal recently. It has been in fairly poor shape for most of the last year as very few people have bothered to maintain it. If you have any suggestions for improvement please mention them on Portal talk:Mathematics. I do need suggestions for future featured content. You can list these at Portal:Mathematics/Suggestions. Thanks. -- Fropuff 17:32, 6 January 2006 (UTC)

I think the new portal looks great. Paul August ☎ 17:45, 6 January 2006 (UTC)

Multivariable calculus help

If someone who remains div, grad, curl better than me would have a look at the van Hove singularity article I've just written, I'd be pleased. I can't recall the name of the series expansion $\mathrm {f(x)=f(0)+f'(0)x+1/2f''(0)x^{2}+\ldots }$. Probably there's a math article on this expansion that I could point to. Also, I have a feeling that the change of variable I'm doing where I go from a volume integral over k to a surface integral over E is the result of one of those fundamental theorems, (Gauss? Stokes? Green?) but I'm not sure which one. Perhaps in addition I have made an egregious notational faux pas. Thanks for any suggestions you have. Alison Chaiken 18:58, 8 January 2006 (UTC)

The series expansion you mentioned is the Taylor series. Unfortunately I don't remember multivariable calculus well enough to offer any additional help. --Meni Rosenfeld 19:28, 8 January 2006 (UTC)

The change of variable may have a more specific name, but "generalized Stokes theorem" would suffice. --KSmrq^T 20:31, 8 January 2006 (UTC)

Well, looks to me like this is about pushing forward a measure/density, and the only difficulty indeed would be at a critical point (mathematics). Not that that page is a great help. The thing about the square-root singularity comes out of the Morse lemma, and so is only generically true (true in practice ...)? That anyway is why you only get cases like the quadratic form cases to worry about. (Sorry Alison, this is hardly helpful, talking amongst ourselves here.) Charles Matthews 20:46, 8 January 2006 (UTC)]]

Thanks Charles for your editing. I added a link in the van Hove singularity article to critical point (mathematics) in the hope that it will improve eventually. I'm contemplating a link to the Morse lemma or Stokes theorem articles but need to think about it more. Alison Chaiken 03:23, 9 January 2006 (UTC)

The above expansion is, to be more specific, the Maclaurin series (the Taylor series about zero). Same article though. Deco 06:57, 10 January 2006 (UTC)

Formal calculation

During my studies, I have encountered the concept of a "formal calculation", in the sense of, roughly, a calculation for which the steps are not completely substantiated, and yet the result can give us insight about the true answer to the problem in question. I want to write an article about that concept, but I haven't found any references to it on the web, so I'm not sure how widely it is used and whether I understand the concept properly. Any ideas? --Meni Rosenfeld 18:34, 12 January 2006 (UTC)

On the contrary, I think of a "formal calculation" specifically as a calculation in which every step is very clear and verifiable. I'm not sure I know a name for what you're referring to. Meekohi 20:43, 12 January 2006 (UTC)

I think I know roughly what Meni is trying to say. I would have thought you might find it at heuristic or heuristic argument or something similar, but they seem to be run by philosophers. Dmharvey 20:47, 12 January 2006 (UTC)

A formal argument is when you just follow what the syntax seems to suggest your reasoning, without proving the reasoning is sound. Like when you prove that, in a ring, if (1+ab) is invertible, then so is (1+ba) by using power series. Power series don't exist in a ring, but but you can still make formal arguments using them. -lethe ^talk 21:58, 12 January 2006 (UTC)

Lethe's example is what I would call a heuristic inference. It seems very strange to me to call this "formal": it's good because of informal gut feeling experience, not in virtue of the formal structure of the problem. --- Charles Stewart 22:02, 12 January 2006 (UTC)

Lethe's reply coincides with my experience. I suspect that it may be hard to find good references, but I remember reading about it recently. Bear with me … -- Jitse Niesen (talk) 22:05, 12 January 2006 (UTC)

Here we are. Stuart S. Antman, Nonlinear Problems of Elasticity, Applied Mathematical Sciences vol. 107, Springer-Verlag, 1995. Page 1 contains the paragraph: "I follow the somewhat ambiguous mathematical usage of the adjective formal, which here means systematic, but without rigorous justification. A common exception to this usage is formal proof, which is not employed in this book because it smacks of redundancy." (his emphasis). -- Jitse Niesen (talk) 22:28, 12 January 2006 (UTC)

I think the term systematic calculation would be far more fitting nomenclature, but that doesn't really carry the connotation of being subtly incorrect that we're looking for. Meekohi 02:02, 13 January 2006 (UTC)

I wouldn't call it incorrect: it is, after all, an excellent heuristic. I'd rather say it was non-well-founded. --- Charles Stewart 02:13, 13 January 2006 (UTC)

Are all in favor of creating a stub, bearing the title "Formal calculation", based on the definition Jitse found, and beating it around until we reach something we can agree upon? --Meni Rosenfeld 13:40, 13 January 2006 (UTC)

I don't know, personally I'm fairly opposed. To me the term Formal Calculation distinctly implies that it is rigorously correct. The reference Jitse gave doesn't really give much support in my mind, seeing as he points out this is ambigous usage. If we are going to make an article on it, I think the main article should describe what it means to be rigorous/systematic, and then there should be a short section pointing out that it is possible to be apparently systematic, but still incorrect. Meekohi 14:05, 13 January 2006 (UTC)

I know that "formal calculation" seems to imply a rigorous one, and actually that did confuse me the first times I encountered the concept. But I got the impression that, while perhaps ambiguous, it is usually used in the sense I described - Much like in the probably more common term formal power series. In this sense, "formal" actually means of form, namely, the form of the objects matter and not their underlying meaning - making the calculation perhaps systematic, but not really rigorous because we are using properties without any justification to why these properties should hold. We could always delete the article later if we can't seem to rich any consensus. --Meni Rosenfeld 14:59, 13 January 2006 (UTC)

Formal power series are just sequences over a ring with convolution as multiplication. Since all sums involved are finite, this is a rigerous mathematical topic. Convergent power series is a different topic requiring the ring to be a Banach algebra. In france there is a state wide research association called "Calcul formel", which would probably translate as symbolic calculus or even symbolic algebra. The research and design of computer algebra systems is part of that.--LutzL 15:09, 13 January 2006 (UTC)

Of course formal power series are ultimately defined in a rigorous way, but the inspiration for this definition comes from a non-rigorous application of properties of convergent power series to arbitary power series. That's where the term "formal" comes from. --Meni Rosenfeld 15:12, 13 January 2006 (UTC)

I think the originally-proposed topic is a 'derivation', universal in (say) theoretical physics. It's not a particularly good topic for an article, though. Charles Matthews 16:20, 13 January 2006 (UTC)

I think that this is a good topic for an article, and it may well prove useful for my planned article on Boole's algebraic logic (to be carefully distinguished from Boolean algebra, since Boole's system allows terms that do not have set-valued denotations). They can be seen to be similar to the status of polynomials prior to the discovery of complex numbers: onbe can know the sum and product of the roots of a quadratic and know furthermore that those roots don't exist. If we are to resort to neologism, why not optimistic calculation? --- Charles Stewart^(talk) 16:29, 13 January 2006 (UTC)

I think "formal" in "formal calculation" has the same meaning as in "formal power series". In my experience, it is often used in the following context (for instance, in a talk on Kolmogorov-Arnold-Moser theory which I just attended): We want to prove that a function f_epsilon with a certain property exists for epsilon sufficiently small. We know f_0, so we expand f_epsilon in a power series in epsilon. If this is possible (i.e., if we can find all the coefficients in the power series), we have a "formal solution". To prove that this is actually a solution, we have to show that the power series has a positive radius of convergence.

So, formal is not just optimistic. And I don't think "formal" in this meaning is a neologism either, as Meni, Lethe and I have all heard of "formal" in this meaning. -- Jitse Niesen (talk) 18:08, 13 January 2006 (UTC)

Another example: formal group law. Dmharvey 21:16, 13 January 2006 (UTC)

It appears that the phrase is used in the proposed sense. It also appears to be understood in other ways, and it appears that some folks feel that the proposed sense is not a good sense. For an inclusionist (not necessarily me), Wikipedia should have an article. The article should note the opposition and provide disambiguation. However, a major unresolved question is: What is the primary meaning of "formal calculation"? The answer to that I do not know, but I'm inclined to think it's the "rigorous" sense, not the proposed sense. --KSmrq^T 01:23, 14 January 2006 (UTC)

I believe the phrase is commonly used in physics in the sense of "we know this can't possibly be right, but by shoving symbols around on a page, here's what you can come up with". For example, "formally", one has 1+2+3+...=-1/12, which is clearly both "right" and "wrong" in various deep ways. That is, its ambiguous without further clarification about how in the world this could possibly be a valid manipulation; but in physics, further clarification is often too hard to provide. A formal calculation is one step up from handwaving. linas 06:01, 14 January 2006 (UTC)

In a nutshell, I think my original proposition of creating a stub and beating it around is fair. I'll do that now. Be sure to check it out for any flaws\omissions\whatever as I am an inexperienced editor. Formal calculation. --Meni Rosenfeld 15:20, 15 January 2006 (UTC)

Yeah it seems that there is enough support for the idea now that we should have an article, even though I still don't like the terminology ;) Meekohi 15:28, 15 January 2006 (UTC)

Red links

Is there a handy way, given a red link, to figure out what articles link to it? Some of the red links we have seem like they just need to be reworded to link to something more appropriate. Meekohi 15:41, 13 January 2006 (UTC)

To find all articles linking to Magnus series, for instance, follow the red link and then click on "What links here". -- Jitse Niesen (talk) 15:59, 13 January 2006 (UTC)

Ha ha, hiding from me in the toolbox all this time. Thanks! Meekohi 18:29, 13 January 2006 (UTC)

70.22.128.220

Could an admin keep an eye on this IP? I've reverted two of their edits. They obviously know a little about the material they are editing, but are still make some pretty serious false claims and mistakes. I've put the details up on the Talk page. Meekohi 16:10, 13 January 2006 (UTC)

Well, you'd better explain your concern some more. Apart from the deletion of one reference, which is not explained, this looks like a technically proficient editor. Charles Matthews 16:16, 13 January 2006 (UTC)

For Scale-free networks he deleted the entire formal definition from the page, and for Complex networks he made claims that preferential attachment was the first generative model for power-law distribution graphs, which is false (and was stated as false in the article already). I'm not saying he's not technically proficient, but he's altering articles for the worst. Meekohi 16:35, 13 January 2006 (UTC)

The more you can document these points on the Talk pages of the articles, the easier it is for others to follow the changes, and contribute to the discussion. Charles Matthews 17:14, 13 January 2006 (UTC)

Math Will Rock Your World

Seems that math made it as the cover image at businessweek.com. See article. Admittedly this is not a Wikipedia related post, however, I found it interesting. The article ends with "Yes, it's a magnificent time to know math.". Oleg Alexandrov (talk) 20:05, 13 January 2006 (UTC)

That head is some kind of scary ;) Meekohi 20:22, 13 January 2006 (UTC)

History of Science WikiProject being formed

ragesoss is trying to start up a History of Science Wikiproject; add your name here and help him get started. linas 05:50, 14 January 2006 (UTC)

proof of impossibility

Someone's just started proof of impossibility, which seems like it could end up being quite nice. I've created a redirect from impossibility proof, which I think is a more common term. Perhaps we should move the original? Dmharvey 02:19, 15 January 2006 (UTC)

I chose the name. Either is fine for me. Deco 08:43, 15 January 2006 (UTC)

List of decimal expansions

Is there an article "List of decimal expansions of mathematical constants"?

• If so, where is it located?
• If not, does anyone think it would be a good idea to create one? Where should it be placed?

--Meni Rosenfeld 16:17, 15 January 2006 (UTC)

If you mean a list of mathematical constants sorted by magnitude, with 50 or so decimal places given, then sure, it would be a good idea. I started a Swedish such list a while back. Fredrik Johansson - talk - contribs 16:23, 15 January 2006 (UTC)

That seems like a potentially useful list, although I'm not sure if it's encyclopedic enough to be added. It would be better if rather than listing them bby magnitude (which is fairly meaningless) you catagorized them in some sensible way. Meekohi 16:58, 15 January 2006 (UTC)

Maybe I'll sort them by order of popularity or something like that. I'll try to see what I can put up... --Meni Rosenfeld 17:02, 15 January 2006 (UTC)

The page mathematical constant already provides such a list (for some definition of "popularity"...) Fredrik Johansson - talk - contribs 17:14, 15 January 2006 (UTC)

Well, this page will have to do for now - Although I do think a list with more digits per constant, perhaps without all the additional information, could be interesting. Perhaps we could also add binary expansions and factorial base expansions (which could be argued to be less arbitary than decimal). Maybe I'll try to compose something over the course of time. --Meni Rosenfeld 17:22, 15 January 2006 (UTC)

Decimal expansions of constants and other tables of numbers should go to Wikisource (see [1]). Samohyl Jan 18:42, 15 January 2006 (UTC)

Areas of mathematics article

To quote from the start of the article, "The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way." Although this has been done for some areas, others are most definately lacking. (All the Analysis, Non-physical sciences and General sections, plus about half the Algebra and Physical sciences sections). Due to the wide ranging nature of the topics in question, this needs contributions from plenty of people. Even if you are only able to expand on a bullet point or two, that would be a definate help. Tompw 11:38, 16 January 2006 (UTC)

Subset notation

As far as I can tell, the conventional notation for "subset" in most of mathematics and in WP is $\subseteq$. However, it has been argued that in probabilty theory the notation $\subset$ is used. Which one of the symbols should be used in the article shattering, which deals with a topic in probability theory? --Meni Rosenfeld 19:39, 16 January 2006 (UTC)

I believe that $\subset$ refers to a proper subset, while $\subseteq$ does not necessarily refer to a proper subset. NatusRoma 19:55, 16 January 2006 (UTC)

Unless the article specifically states that ⊂ may refer to nonproper subsets it seems wise to use ⊆ for the general case and ⊂ for proper subsets. I don't see why this should be any different in probability theory. -- Fropuff 20:16, 16 January 2006 (UTC)

To NatusRoma: Yes, that is the common convention - However it seems that in probability theory, a different convention is used, where $\subset$ means a not necessarily proper subset.

To Fropuff: That is what I also think, but it has been argued that probabilitists will be confused when they read an article in their field which uses a different convention than they. I would like to hear more opinions to make sure we have consensus on using ⊆. --Meni Rosenfeld 20:22, 16 January 2006 (UTC)

Probabilists use $\subset$ (⊂), to mean subset -- however they seem never to use $\subseteq$ (⊆), so the mathematically correct usage shouldn't confuse them. Arthur Rubin | (talk) 22:21, 16 January 2006 (UTC)

I have proposed a convention regarding this issue. Discuss it here. --Meni Rosenfeld 09:41, 17 January 2006 (UTC)

Chaos theory needs help

The Chaos theory page needs help. There is a Wikipedia user that insists in inserting comments about biotic motion into the page. Several contributers have tried to point out the problems with biotic motion to the contentious user, but to no avail. What should be done about this?

The long discussion in the Chaos theory talk page has brought up a series of difficulties with the published work in bios theory: lack of mathematical definitions, one common author in all the six papers in citation indices, no reference to a century of work in dynamical systems, simple analytical arguments not made, etc.

Despite the results being published, I find it hard to see how a topic that has failed to attract attention for seven years should be included as a major idea in the Chaos theory article.

XaosBits 03:08, 18 January 2006 (UTC)

Editors need help at function (mathematics)

There is a dispute going on at function (mathematics), where substantial rewriting (with reverts) has been going on, with the two editors unable yet to agree on how the article should be rewritten. Rich Norwood is requesting other editor's views. Please help out. (I will be away for a few days but I will try to lend a hand when I get back.) Thanks all. Paul August ☎ 15:20, 18 January 2006 (UTC)

Mathie

I nominated this for deletion. Votes (either way) welcome. :) Oleg Alexandrov (talk) 01:57, 19 January 2006 (UTC)

Shape or set?

I am having a dispute with Patrick over at shape. Here's the relevant diff to Patrick's version. I would argue that Patrick is a bit pedantic insisting on the word "set" instead of "object" and that it makes the article less clear for the general public. Patrick's explanation is in the edit summary to that edit, stating "object is undefined; e.g., there is unclarity about color". I would like some comments, on this page, which I will later move to talk:shape. Oleg Alexandrov (talk) 01:03, 21 January 2006 (UTC)

Yeah, it should be object. To talk about shape, there's already an implicit assumption made that the set has a metric. There's also an implcit assumption that there's a space so that rotations, translations, etc. are defined. By contrast, true "sets" don't have metrics and can't be rotated or translated. So insisting on "set" is kinda goofy. linas 01:25, 21 January 2006 (UTC)

Maybe we should use the word "object", and add a comment like "object here is taken to mean a subset of a metric space"? This will make it more or less accurate, while maintaining readability. -- Meni Rosenfeld (talk) 06:40, 21 January 2006 (UTC)

Real projective line

Hi everyone.

It seems that currently the only reference in Wikipedia on the real projective line ($\mathbb {R} \cup \{\infty \}$) is this 3-line subsection. I believe there is much more to be said about it, elegantly extending analytical properties of reals to it. The problem is that I've never really read about such definitions (I'm not very proficient in the mathematical literature), but it seems natural to me that these are things that should be defined. Examples are to say that $\lim _{x\to a}{f(x)}=\infty$ iff for every M > 0 there is ε > 0 such that $|f(x)|>M$ for every |x - a| < ε. In this way, $\lim _{x\to 0}{\frac {1}{x^{2}}}$, $\lim _{x\to 0}{\frac {1}{x}}$ and even $\lim _{x\to 0}{\frac {1}{xsin{1/x}}}$ are all equal to $\infty$. Since we don't want to use signed infinities, classical limits like $\lim _{x\to +\infty }{f(x)}$ and $\lim _{x\to -\infty }{f(x)}$ become $\lim _{x\to \infty {-}}{f(x)}$ and $\lim _{x\to \infty {+}}{f(x)}$ (approaching the point at infinity either from the left, through increasingly positive numbers, or from the right, through increasingly negative numbers). The concept of continuous function can be extended. The notion of intervals can be extended, for example if a > b, we define the open interval $(a,b)=(a,+\infty )\cup \{\infty \}\cup (-\infty ,b)$. This way, we have for example the nice propety: The image of the interval (a, b), under the funtion $f(x)={\frac {1}{x}}$, is $({\frac {1}{b}},{\frac {1}{a}})$, no matter what the values of a and b are.

I want to write an article on these topics (more specifically, turn real projective line from a redirect to an article). The questions are these:

1. Is there a place in WP where these concepts already appear?
2. Does anyone know a reference where these definitions appear, to make sure I'm not inventing anything?
3. Does anyone think this is not a good topic for an article?

I'll be grateful for any comments. -- Meni Rosenfeld (talk) 15:24, 22 January 2006 (UTC)

There are three more lines in a more abstract setting at compactification (mathematics) (look for the one-point compactification). It seems to me a good topic for an article if you can find some references and I expect these references to exist. -- Jitse Niesen (talk) 15:40, 22 January 2006 (UTC)

Have you heard about these concepts? That would be a good start. Unfortunately I do not know of any references. Would it be okay to create the article now, and add references as we find them? -- Meni Rosenfeld (talk) 16:11, 22 January 2006 (UTC)

No. I think you shouldn't write an article without consulting references. Personally, I even make mistakes if I know the stuff very well unless I have a book lying next to me. -- Jitse Niesen (talk) 00:50, 23 January 2006 (UTC)

It wasn't clear to me from your answer whether you have heard about these definitions. It is important to me to know, because if not I will have a mind to put this matter to rest. In either case, is there anyone who has heard about it, and preferrably, know of a reference to it? -- Meni Rosenfeld (talk) 06:34, 23 January 2006 (UTC)

Oh, and I've just found this. It doesn't address all of the above ideas, but it's a good start, no? Is it enough for starting an article with just what is mentioned there? But please do tell me if you've heard about the limits thing. -- Meni Rosenfeld (talk) 08:34, 23 January 2006 (UTC)

I have no definite recollection of the limit thing. On the other hand, I doubt I would remember it if I had read it somewhere as it seems quite natural to me and a consequence of general topology.

I'm quite sure I've seen the thing of how division of intervals might result in an interval containing infinity in a paper on interval arithmetic. This is also mentioned in the MathWorld link. -- Jitse Niesen (talk) 11:42, 23 January 2006 (UTC)

Yeah, I figured this is a special case of more general topologic spaces. But the reason I think these explicit definitions are of notable interest is because they are an elegant extension of the good old real numbers, a structure we all know and love. Also I don't know much topology so I'm not proficient in all the structures that exist.

I think we have sufficient grounds to at least start an article, which I will begin working on now. It will be called Real projective line. Everyone be sure to check back in a few hours and leave some feedback. -- Meni Rosenfeld (talk) 09:08, 24 January 2006 (UTC)

Hmm I don't like that name so much. Mostly because it's not a name that anyone uses. The space you're talking about is called (in my experience) the real projective line or else the one point compactification of the real line. -lethe ^talk 09:15, 24 January 2006 (UTC)

Okay, I thought it would be a good idea to call it this way because that's how it's called in Mathworld, but if you say it's uncommon I'll change that. -- Meni Rosenfeld (talk) 09:22, 24 January 2006 (UTC)

While we're at it, what is the most common notation for this space? -- Meni Rosenfeld (talk) 09:30, 24 January 2006 (UTC)

$\mathbf {P} ^{1}(\mathbf {R} )$ perhaps. Double-struck if you prefer. Dmharvey 13:33, 24 January 2006 (UTC)

Hmmm not so sure now. You seem to be talking about a set with certain arithmetic operations, and the notation I suggested doesn't really cover that. Dmharvey 13:48, 24 January 2006 (UTC)

Functions, partial, pre-, proto-, total, etc.

• JA: I'll be introducing some language under the heading of Relation (mathematics) to cover these cases and more, as they arise within the setting of relations in general. Stay tomed. Jon Awbrey 15:48, 22 January 2006 (UTC)

Notation for positive infinity

Another question on a loosely related subject: Is there a notational convention in WP regarding positive infinity? I think it is most commonly denoted $+\infty$ in the literature, but I've seen places in WP where it is denoted just $\infty$. Should the + sign be added for consistency and clarity? -- Meni Rosenfeld (talk) 16:40, 22 January 2006 (UTC)

As a rule the plus sign is used only if it is necessary to distinguish a positive infinity from a negative one. Also, some contexts require other ways of denoting infinities, such as ω or ℵ₀. --KSmrq^T 18:39, 22 January 2006 (UTC)

My experience is that it's referred to as $+\infty$ only where it is necessary to distinguish it explicitly from negative infinity, such as in the limit of some real-valued functions. In some contexts such as complex numbers there are an uncountable number of different kinds of infinity. Generally I think just $\infty$ is fine for most purposes. Deco 18:43, 22 January 2006 (UTC)

Maybe this example will clarify the question... Don't you agree that the + sign should be used there? These are statements about plain real numbers, not a projected line, a Riemann sphere, cardinalities, non-standard analysis and all the other stuff (which are all very nice but have little to do with my question). -- Meni Rosenfeld (talk) 18:47, 22 January 2006 (UTC)

I don't agree. For the same reason we don't need to write +1 to distinguish it from –1, we don't need +∞ to distinguish it from –∞. -lethe ^talk 00:15, 23 January 2006 (UTC)

I don't see any harm in using +∞, except that it seems maybe a little pedantic. It does serve a colorable purpose in distinguishing +∞, not from –∞, but from "unsigned infinity". --Trovatore 00:18, 23 January 2006 (UTC)

I like +&infinity;, especially when writing down an integral or sum. Also helps to distinguish from unsigned or complex infinity. —Ruud 00:28, 23 January 2006 (UTC)

I once thought like lethe, but have since come to realize that, like Trovatore and Ruud said, you don't need to distinguish +1 from an "unsigned one", but you do need to distinguish $+\infty$ from unsigned infinity. So what do you say? Should we use $+\infty$ consistently for this purpose? -- Meni Rosenfeld (talk) 06:30, 23 January 2006 (UTC)

OK, the point that infinity can be signed or unsigned while finite numbers are not is well-taken. I'm still not sure of the absolute necessity for adherence to this convention here. Seems to me that it will always be clear in context which is meant. In short, I think it's OK for you to use this convention, but I don't believe it's necessary to ask that everyone use it everywhere in the project. -lethe ^talk 06:40, 23 January 2006 (UTC)

I agree that no harm is done by not following such a convention, but I do believe that it can only improve things. I have proposed the convention, discuss it here. -- Meni Rosenfeld (talk) 07:54, 24 January 2006 (UTC)

Division by zero

I am having a dispute with Rick Norwood regarding division by zero. The problem is that I want to write about structures where division by zero is possible, while he systematically tries to prove that defining division by zero is "wrong" and that you mustn't do it, because it leads to problems. I will appreciate your comments (either way) on the issue.

And while you're at it, I would also like to hear your opinions regarding the size of inline fractions in the article. -- Meni Rosenfeld (talk) 06:41, 23 January 2006 (UTC)

Technically, you can come up with you own theory, which defines division by zero through axioms somehow. However, I think you will have a difficulty proving consistency of your theory. (Igny 13:36, 23 January 2006 (UTC))

We already have wheel theory, which purports to be such a theory. But such things are better structured as 'see alsos' to the main article. Charles Matthews 13:47, 23 January 2006 (UTC)

If I had to invent such a theory myself, I probably would have encountered difficulties formulating it; Fortunately, the theories are well developed and it is well known what is or is not true. About the wheel theory, I don't know much about it, but I think it may indeed be too advanced to be discussed thoroughly in this article. But things like the Riemann sphere are certainly more than mere curiosities, and should be discussed in such an article. -- Meni Rosenfeld (talk) 20:04, 23 January 2006 (UTC)

Not really. There are places like birational geometry, rational map and so on, where it can better be put into context. Charles Matthews 13:45, 24 January 2006 (UTC)

Sets of sets

A new but promising editor, User:MathStatWoman, has written an article called sets of sets, apparently in response to some talk-page discussion that I can't really remember where to locate at the moment. I think the article has two major problems. First, it seems to be more a personal essay than a verifiable encyclopedia article. Second, I don't think it's really correct: It claims, essentially, that locutions like "collection of sets" are preferred over "set of sets" because of the Russell paradox. I don't think that's the reason at all; when people discuss sets of reals and collections of sets of reals, the Russell paradox is not remotely in the same time zone as the objects being discussed, which can all be coded in V_ω+2. The reason for preferring the word "collection" is that it helps to keep the types straight in the reader's mind (and for that matter, in the author's mind).

I really think the article should go to AfD, hopefully without any prejudice to MathStatWoman. Any thoughts on the matter, or alternative suggestions? --Trovatore 04:36, 24 January 2006 (UTC)

AfD for sure -lethe ^talk 07:59, 24 January 2006 (UTC)

I agree that, at least in some contexts (possibly most), "collection of sets" is used for clarity rather than for accuracy. But I can't see why it looks to you like a personal essay. In any case, call me an inclusionist, but I think it's worth having an article with this name. Perhaps some of the content should be removed, some can be disambiguated (something like "'collection' is sometimes used for clarity, and sometimes because it really isn't a set"), and perhaps some words about the simple fact that an element of a set can be itself a set, a concept that is difficult for some first-year students. -- Meni Rosenfeld (talk) 08:03, 24 January 2006 (UTC)

The article is problematic. I saw the it late last night just before I went to bed, and was too tired to do anything about it then. I had planned to contact User:MathStatWoman and discuss it with her this morning. I don't really think we need such an article and as it stands it is misleading and inaccurate — but I had really hoped to avoid AfD. I hope we don't end up alienating the author. Paul August ☎ 13:22, 24 January 2006 (UTC)

No offense taken; no, you have not alienated the author. :-) But indeed there is a reason for not declaring certain collections sets. Some groups of things are not sets. Agreed, there are some sets of sets that are ok, when logical inconsistencies or incompleteness does not come into play. But we probabilists often run headlong into difficulties with certain particular peculiar collections, classes, or families of sets (and with AoC, and with measurability problems, too, by the way) My suggestion: let's keep the article sets of sets for now, discuss the issue, and clean it up together. with references and examples. Seem ok to all of you? Thanks for the input. I like a good debate like this one. You were all polite and kind, and I appreciate that. MathStatWoman 15:37, 24 January 2006 (UTC)

You said:

we probabilists often run headlong into difficulties with certain particular peculiar collections, classes, or families of sets

What are these problems, and how does this article address or resolve the problems? linas 16:23, 24 January 2006 (UTC)

First, please let me preface the answer: The article on empirical processes is under development; anyone else who works in this field is welcome to contribute, of course; that would be excellent, in fact. But I am struggling with the markup language, so it takes me a very long time to add very little information. Now the answer: Anyway, once the article is expanded,it will be evident that the study of empirical processes involves classes of sets, and also collections of functions related to those sets. It is well known that functions are related to families of subsets, since a particular function, (e.g. indicator functions, important in empirical processes and statistics), often can be viewed as a subset; hence we would end up using sets that could contain themselves, or not contain themselves; hence a paradox unless we use terminology such as families, collections, or classes of sets. See, for example, Vapnik and Chervonenkis, Pollard's, Wellner's, R. M. Dudley's, and R.S. Wenocur's works in V-C theory, empirical processes, and learning theory...they always use terms "classes of sets or collections of sets or functions to avoid these paradoxes. In some cases, a class" of sets cannot be a set itself, or we have inconsistency. Hope that clarifies the issue a bit for now. I would like us all to work more on the article sets of sets rather than delete it. I can add references soon, if that would help. MathStatWoman 17:00, 24 January 2006 (UTC)

MathStatWoman, I'm going to have to call you on this claim that the Russell paradox is relevant to anything that comes up in probability theory. I just don't see it happening. The Russell paradox fundamentally arises from a confusion between the intensional and extensional notions of set; no doubt one could code that confusion into probabilistic language, but only in an attempt to turn probability theory into foundations, and I've never heard that probabilists were into that. If you're going to stick to this claim, please find a minimal example and explain it here. --Trovatore 17:28, 24 January 2006 (UTC)

I have to go to work/schoool now, so just a few quick words; no time for markup language; please forgive my using plain typesetting here. Please understand that this is not a joke; it is serious mathematics; I am not trying to play games here. In probability theory, the probability space Omega and the sample space X can be anything; its elements can be sets (or, equivalently, functions, which can be viewed as sets, e.g. all functions from set Y to {0.1) is equivalent to the collection of all subsets of Y, i.e. its power set 2^Y. We use indicator functions in empirical processes. To show that we need to restrict sets under consideration to V-C classes of sets, or uniform Donsker classes of sets, or P-Glivenko-Cantelli sets, etc...we need counterexamples that involve e.g. X being the class of all sets. Cantor's Paradox and Von Neumann-Bernays-Gödel set theory (in which we do not speak of sets of sets apply here. When empirical process article develops, all this will become apparent. Let's just make the sets of sets article better, or, as an alternative put it (cleaned up and referenced) into Von Neumann-Bernays-Gödel set theory, how does that seem? Talk to you later. gtg now MathStatWoman 17:58, 24 January 2006 (UTC)

1. The notion of proper class is discussed in several places, I think; I don't see any need for a new article
2. If you really meant to say that NBG doesn't use sets of sets, that's wrong. In fact all sets in an interpretation of NBG are sets of sets. Yes, NBG also has collections of sets that are not themselves sets.
3. I'm still extremely skeptical that you're going to be able to show us how the Russell paradox attaches to VC theory or probability theory. Please give a minimal example. --Trovatore 21:33, 24 January 2006 (UTC)

I believe that this article should be deleted. If something needs to be said about sets and classes it should be said in proper class or class (mathematics) (the considerations here are too elementary for NBG, I think). "Set of sets" is the wrong title, because sets of sets per se are ubiquitous and unproblematic. There might be some issues here which should be moved to proper class or class (mathematics), though -- after being clarified; the existing text is confusing. Randall Holmes 03:59, 27 January 2006 (UTC)

On looking at these articles, I think the proper context for a discussion of these issues would as I said be class (set theory) (which is the same article as proper class, class (mathematics)); adding some informal examples with explanation to this article would be the right way to achieve the author's apparent purpose. There are some technical points: in most mathematics, a finite set which is one of its own members (used in one of the examples) will not arise; in the standard set theory ZFC, no set is an element of itself. And in the standard set theory ZFC all sets without exception are sets of sets; sets of sets is not the right title. Like Trovatore, I would be very interested in seeing any relevance of this topic to probability theory (though I wouldn't be surprised if there were some; mathematicians are ingenious :-) Randall Holmes 04:11, 27 January 2006 (UTC)

I should also add, lest I seem too encouraging, that the only real content in the article sets of sets seems to be a discussion of Russell's paradox, on which there is already an article. I do notice that class (set theory) might (or might not) benefit from an informal summary of reasons why certain classes (the Russell class, the class of all ordinals) actually are proper classes, and this might do what is wanted in sets of sets. If there are specific applications of the set/class distinction in probability theory, these might make a subject for an article. Randall Holmes 04:17, 27 January 2006 (UTC)

another point: the mere possibility of having sets which are elements of themselves does not in itself imply any danger of paradox. Aczel's theory of non-well-founded sets has this kind of circularity (and I suspect this may be all that is needed in the theory of empirical processes) and doesn't come anywhere near needing proper classes or risking Russell's paradox. Applications of hypersets may be the issue here. Randall Holmes 04:19, 27 January 2006 (UTC)

Lethe for admin

In case some of you don't follow Wikipedia:Requests for adminship, I nominated one uf us, Lethe, for administrator, which, in my opinion, was long overdue. If you are familiar enough with Lethe's work, you can vote at Wikipedia:Requests for adminship/Lethe. Oleg Alexandrov (talk) 17:06, 24 January 2006 (UTC)

Mediation needed in big dispute at relation (mathematics)

There is a big argument at talk:relation (mathematics), with Arthur Rubin and Randall Holmes on one side, and Jon Awbrey on the other side. I did not study the matter in a lot of detail (and am not an expert in the matter), but it seems that Jon Awbrey is making things more complicated than necessary and is rather pushy at enforcing his version (judging from the edit history. Anyway, help would be very much appreciated. Oleg Alexandrov (talk) 18:57, 24 January 2006 (UTC)

Proposed changes to mathematics

I've proposed some changes to the "Major themes in mathematics" section of the mathematics article, see: Talk:Mathematics#Proposed changes to "Major themes in mathematics" section. Paul August ☎ 21:35, 24 January 2006 (UTC)

Question about bases

Hi all, Base (mathematics) gets very little (if any) traffic so I'd like to ask this here. The question is on Talk:Base (mathematics), at the bottom, about integers vs. numbers (please respond there as I'm not watching this page). I'm not a mathematician, just an enthusiast, so this is me asking experts for (knowledge and) advice with the article (be warned, it is unreferenced and possibly inaccurate). Thanks :-) Neonumbers 10:02, 25 January 2006 (UTC)

another problematic article

The article SuperLeibniz law seems to be complete nonsense. I would have put it on AfD, but a search makes it look like a superLeibniz law might be something real (see e.g. Poisson superalgebra). However all the hits seem to be Wikipedia reflections, and Poisson superalgebra doesn't give any clue as to a definition for SuperLeibniz law. Poisson superalgebra was written by User:Phys, who hasn't been around since November. Unless someone knows what a SuperLeibniz law is supposed to be, I still think AfD is where it's headed. --Trovatore 03:30, 26 January 2006 (UTC)

Oh, I should amend the claim that Poisson superalgebra doesn't give any clue as to a definition; it does in fact give an example. But it's not clear whether it's the only example, nor what would characterize any others. --Trovatore 03:32, 26 January 2006 (UTC)

I see a red link for the article you mention, and searching didn't turn it up either. Did someone speedy delete it already? -lethe ^talk 03:41, 26 January 2006 (UTC)

Ooops, I've found it SuperLeibniz Law here. -lethe ^talk 03:45, 26 January 2006 (UTC)

Ahhh, the thing that is mentioned in Poisson superalgebra is what I know as a graded derivation or an antiderivation. It's defined in derivation (abstract algebra). The stuff in SuperLeibniz Law is, as you suggest, patent nonsense. The question is whether we want to redirect or just delete. Is that name attested anywhere? -lethe ^talk 03:47, 26 January 2006 (UTC)

The notion of a super Leibniz law is a valid one, although what was SuperLeibniz Law was patent nonsense. The concept usually goes by the name of superderivation or graded derivation. If V is a superalgebra and D is a (graded) linear operator on V, then D satisfies the "super Leibniz law" if

$D(ab)=(Da)b+(-1)^{|a||D|}a(Db).\,$

I'll will amend these articles shortly. -- Fropuff 04:50, 26 January 2006 (UTC)

Yep, that's it. The Lie derivative, exterior derivative, and inner derivative satisfy that equation with degrees 0, 1, and –1 respectively. I've not heard it called a superderivation before, but it sounds like a reasonable enough name. -lethe ^talk 05:01, 26 January 2006 (UTC)

I added a section to derivation (abstract algebra). -lethe ^talk 05:16, 26 January 2006 (UTC)

I think the name graded derivation is a more general term applying to Z-graded algebras, whereas the name superderivation means a graded derivation of superalgebras. Maybe a separate article at graded derivation would be best, but I'm fine with a redirect to derivation for now. -- Fropuff 05:48, 26 January 2006 (UTC)

Isn't a superalgebra just a Z₂ graded algebra? -lethe ^talk 05:54, 26 January 2006 (UTC)

Yes it is, but one can have graded derivations on algebras with a more refined grading than just Z₂; e.g. the exterior algebra. It is not common to refer to the exterior algebra as a superalgebra (although it is one). More importantly, it is important to keep track of the more refined grading for linear maps. As you say, the exterior derivative and the interior product have grades +1 and −1 respectively, but as maps of superalgebras I would say they both have grade 1 (i.e. they are both odd). -- Fropuff 06:05, 26 January 2006 (UTC)

Right, right. I think I thought you made a complaint that you didn't actually make, now that I reread your complaint. I added graded derivation to that article, when really what we wanted was superderivation, which is a special case. And I didn't mention it the term at all.. Antiderivation is already there, which is pretty close, but not it. As for whether it should get its own article, I'm not opposed to the idea, but I'm not going to do it. I've got to think about dual spaces some more. -lethe ^talk 06:25, 26 January 2006 (UTC)

I think I thought you made a complaint that you didn't actually make. That's got to be the quote of the day ;) -- Fropuff 06:29, 26 January 2006 (UTC)

Appeal to clean up the page on "list of paradoxes"

There are so many items in the list of paradoxes that are not paradoxes. I commented on just a few examples on that page's discussion page. Could we please collaborate to clean up that page and remove what does not belong? MathStatWoman 09:05, 27 January 2006 (UTC)

No genuine paradoxes in mathematics. So we should just cut the maths? Actually it is OK by me for list of paradoxes to list things called a paradox, and then annotate/comment in individual articles as to the aptness of the name. Lists are mostly a navigational tool; 'added value' in terms of comment is good, but judge them mainly by the help they can give in fiding what you were looking for. In that sense, Category:Paradoxes might need to be more rigorous. Charles Matthews 10:30, 27 January 2006 (UTC)

So there are two ways of understanding the word paradox and people often talk past each other until they notice that they're using the word differently. Both of you seem to be using it to mean simply "contradiction". In my usage a paradox is an apparent contradiction. Paradoxes are much more interesting than contradictions. A contradiction just tells you that one of your assumptions is wrong, which is commonplace. A paradox tells you that something about your intuition is wrong, and that your intuitions need to be reconstructed to fit the facts. --Trovatore 15:21, 27 January 2006 (UTC)

W.V.O. Quine says the same thing in an essay on paradoxes. He identifies "veridical" paradoxes, which are arguments that prove apparently absurd results that are nevertheless correct, such as the Banach-Tarski paradox, and "falsidical" paradoxes, which are apparently-correct arguments that nevertheless prove false results, such as Zeno's paradoxes. -- Dominus 17:06, 27 January 2006 (UTC)

I'm not quite so ignorant. For example Smale's paradox is really Smale's counterintuitive result? But Bertrand's paradox is really a verbal trick about 'uniform'? There is a bit of history on this, monster barring and so on. Charles Matthews 16:43, 27 January 2006 (UTC)

I didn't mean to imply you were ignorant. But what can it mean to say there are no genuine paradoxes in mathematics? (As I said on Talk:List of paradoxes, "genuine paradox" puts me in mind of "genuine faux pearls", a bonus offered on TV ads for those who call now.) --Trovatore 16:50, 27 January 2006 (UTC)

No contradictions in a consistent formal system. But 'paradox' actually connotes only semi-formalised reasoning. Charles Matthews 08:29, 28 January 2006 (UTC)

Article intro text

I'm sure this has come up before, but I'd like to ask - what thought has been given to how "technical" the first paragraph of maths articles should be. I'm of the opinion that the introduction should try only to explain what an interested non-mathematician would understand and find useful - what it is, why it's important, and what it's used for, all in non-technical terms. The detailed technical information can follow later. What do you think? --Khendon 21:10, 28 January 2006 (UTC)

Non-technical is always a great goal. But it may be a challenge. It took an hour of rewrites to get the first line of the dynamical systems article. And I am not sure how useful it is. It is very tempting to say: a dynamical systems is a tuple [M, f, T] where M is ... There are many technical reviews available on the WWW, but I feel there is a lack of non-technical reviews. The reader I try to keep in mind (but often loose) is the college freshman.  XaosBits 23:52, 28 January 2006 (UTC)

Right. It is good for the intro to be motivational. See also the math style manual. Oleg Alexandrov (talk) 23:55, 28 January 2006 (UTC)

One should not try and "dumb down" articles too much. It is important to make sure the article explains everything following from the article (such as any further definitions, concepts, etc that need to be made), but the article should not spend time trying to teach concepts that a reader should already be familiar with. Motivational explanations and examples are a Big Plus. Dysprosia 08:26, 29 January 2006 (UTC)

I agree that the article as a whole should not be "dumbed down". However, I think there are two readers of maths articles - the casual reader who's heard the word "topology" and wants to know what it means, and the mathematician. I think we should cater to both --Khendon 09:41, 29 January 2006 (UTC)

It's important to cater for both sure, but we shouldn't sacrifice "encyclopediality" (to coin a phrase) to do so. Dysprosia 13:01, 29 January 2006 (UTC)

Does the Wikipedia model really work for mathematics?

I am developing a fundamental doubt after spending time watching relation (mathematics) and function (mathematics). I don't see how we can possibly have sensible articles on core concepts on whose definition everything else depends unless someone competent writes them and they are then frozen and edited (by a manager or by a limited class) after consultation only. This doesn't apply to all topics, but these two articles (for example) are about ideas about which many people have ill-informed, strongly held ideas and about which other people, perhaps not so ill-informed, have ideas based on philosophical or pedagogical ideas which deviate too far from the norm for easy accommodation. It was interesting to be able to write an article on New Foundations for people to read -- this is unlikely to attract the attention of too many people of the categories mentioned; articles about obviously technical subjects are not usually subject to this kind of problem, and seem to look pretty good. But central ideas of mathematics (especially ones about which silly statements are prevalent in low-level textbooks or in the popular literature) must require a constant painstaking watch which in the end may not be a sensible use of the time of competent people. (Jon Awbrey should not necessarily assume that I am referring to him). Maybe this does work out in the long run, but I'm certainly finding a watch on these articles to be much less productive and much more frustrating than watching technical articles in set theory... Randall Holmes 02:33, 29 January 2006 (UTC)

Welcome to the real world. :) Randall, both you and Jon are rather new, and I believe that's part of the problem (I remeber my bitter fights with Linas a year ago :) Yeah, the Wikipedia model has its advantages and disadvantages, takes a while to get used to it, and yes indeed, constant watch and occasional frustrations are part of the game. Sorry I can't say something more meaningful, hopefully others will have better insights. Oleg Alexandrov (talk) 06:57, 29 January 2006 (UTC)

Yes, well, Randall none-the-less does bring up a valid point. My response has been to ignore articles on pop topics, but this is not really a "good" answer. I don't know the answer, but direct interested parties to Wikipedia:Stable versions linas 17:06, 29 January 2006 (UTC)

Mirabile dictu, both articles which are bothering me are looking mostly correct today, though the text is becoming increasingly dense and qualified... Randall Holmes 21:57, 29 January 2006 (UTC)

GSL GFDL Copvio problem.

Please see discrete Hankel transform. The article incorporates text taken from GSL, which is GFDL'ed. However, the GSL license has "invariant front and back-cover texts" which the copy did not preserve, resulting in a copyvio dispute. Surely WP has a GFDL sources policy? I don't understand that policy, but links to where it is explained would be handy. linas 17:11, 29 January 2006 (UTC)

Another small step towards MathML support in MediaWiki

Jitse and I have been making progress with MathML support in MediaWiki.

Try out the test wiki.

See also the announcement at the village pump, and our page on Meta.

Please direct all discussion to the talk page on Meta.

Dmharvey 01:50, 30 January 2006 (UTC)

You da' man, David! Major kudos for working on this. I really hope blahtex makes it into MediaWiki someday soon. I'm happy to help out testing. -- Fropuff 02:17, 30 January 2006 (UTC)

I am looking forward to the day when math on Wikipedia will look good, when we won't worry about \, vs \! to PNGfy things, when html and TeX live in peace and harmony, blah, blah, blah... Oleg Alexandrov (talk) 03:41, 30 January 2006 (UTC)

Oleg, given your comments on MathML in the past, I'll take that to be your way of trying to sound encouraging :-) Dmharvey 04:14, 30 January 2006 (UTC)

I never had anything gainst BlahTeX or MathML. It is just I was (and still am) very skeptical about the pace of introduction of MathML and the timing of when we won't need to worry about PNG and HTML and all that. My skepticism is based on my past experiences with other (cool!) things. But you are doing great work, and I hope things will work better/sooner than I think. :) Oleg Alexandrov (talk) 21:16, 30 January 2006 (UTC)

Scepticism is good, action is better. -- Jitse Niesen (talk) 22:10, 30 January 2006 (UTC)

You've got to admit that at least we look a bit better than PlanetMath... Dysprosia 10:48, 30 January 2006 (UTC)

I'm still holding my breath for Safari to implement MathML before I get excited. -lethe ^talk 11:20, 30 January 2006 (UTC)

Me too. Paul August ☎ 19:38, 30 January 2006 (UTC)

That's true. At least HTML/PNG is compatible on nearly *all* browsers. Dysprosia 11:53, 30 January 2006 (UTC)

Don't get me wrong. I'm looking forward to being excited about it. I was even toying with the idea of trying to pitch in to MathML implementation in Safari. I think one day a lot of browsers will have it. -lethe ^talk 12:26, 30 January 2006 (UTC)

I didn't really mean it like that; the fact that MathML isn't supported in Safari highlights the problems a lot of people may have if we eventually switch to MathML. I tend to use Lynx or w3m a lot sometimes in browsing things, and MathML would be unreadable in those circumstances. Dysprosia 00:35, 31 January 2006 (UTC)

I'm of the opinion that we should push for MathML implementation in MediaWiki as soon as possible, regardless of whether or not major browsers such as IE or Safari have native MathML implementations (the PNG/HTML option will still be available to those users). In fact, I think having a high profile site like Wikipedia making heavy use of MathML will be a major motivation for browser developers to implement MathML in their browsers (lest everyone switch to Firefox/Mozilla). -- Fropuff 19:55, 30 January 2006 (UTC)

I like this argument a lot. -lethe ^talk 23:51, 30 January 2006 (UTC)

In fact, the process that Fropuff is alluding to has already started happening (sort of). At the time I released the previous version of blahtex (August 2005), MathML development in gecko (i.e. mozilla/firefox) had been close to moribund for a few years. But as soon as they heard that wikipedia was planning MathML support, a few developers there started fixing all kinds of bugs, and indeed fixed the majority of the really nasty ones that I specifically pointed out to them. I haven't yet seen any evidence of other browsers getting their act together, but maybe with a working demo wiki now available, they'll take more notice. Dmharvey 21:14, 30 January 2006 (UTC)

Thats encouraging. Maybe wikipedia will be the killer app which makes maths on the web finally happen. Its been do-able for at least 10 years now (since the geometry center folks were developing WebEQ) but its never been a priority and never got that critical mass. I'm all for a push for MathML in MediaWiki, might be able to help with coding. There is a MathML (if possible) option in 'my preferences', don't know if it has any functionality. --Salix alba (talk) 22:09, 30 January 2006 (UTC)

The "MathML (experimental)" option presently only produces MathML for the very simplest things like "x + y = 2". Give it a superscript and it stares back blankly at you. But that's besides the point: it is also necessary to deliver the entire document as XHTML, get the browser recognising the MIME types, and a few other things, without breaking browsers that don't understand any of that. Currently MediaWiki doesn't do these things. Dmharvey 22:39, 30 January 2006 (UTC)

BlahTex now work in Internet Explorer (Win) with the MathPlayer plugin. I've also created a page meta:Blahtex/Compatibility to list how well it works with different browsers. Testing of the blahtex wiki welcome. --Salix alba (talk) 15:22, 5 February 2006 (UTC)

Definition of "computational mathematics"

The term "computational mathematics" turns up over half a million Google hits; most seem to come from names of institutions or courses. I've thought of starting a stub, but I'm not sure how to define the term and relate the field (if there is one) to others. My intuitive understanding is that, roughly speaking, computational mathematics is to mathematics what computational science is to science; i.e. it comprises the study and/or use of algorithms for the purposes of mathematics (including discrete and symbolic mathematics, in addition to numerical analysis). Is this correct? Fredrik Johansson - talk - contribs 19:09, 30 January 2006 (UTC)

Good luck with coming up with a definition. I'd say that it's the study of algorithms for mathematical problems, regardless whether the ultimate application is in mathematics or without. My list of fields which can be considered part of computational mathematics: obviously numerical analysis (including optimization and approximation theory), symbolic mathematics, computational number theory, learning theory, computational geometry, image processing, and some complexity theory. But generally it is very hard to define a research discipline, especially one of these fashionable multidisciplinary ones. -- Jitse Niesen (talk) 20:13, 30 January 2006 (UTC)

Springers journal has a nice def [2]

Foundations of Computational Mathematics (FoCM) publishes research and survey papers of the highest quality, which further the understanding of the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis and computer science.

a non copyvio rewrite of that could be a good place to start. --Salix alba (talk) 20:40, 30 January 2006 (UTC)

Don't bother rewriting it - just quote it in the intro. I think this will make a great high-level topic for linking lots of more specialised areas - it might even be a good idea to link it directly from Mathematics. Deco 00:39, 31 January 2006 (UTC)

Yes please; cf Talk:Mathematics#Request for link to mathematical computing. Hv 16:53, 31 January 2006 (UTC)

I'am a bit confused by this discussion. Fredrik, you said above, that you understand it similarly to computational science, so, by this analogy, do you mean application of computational methods to mathematics itself (like experimental mathematics and automated theorem proving)? But then, what other people said, it seems that they mean study of computational methods mathematically, regardless of the application field. So which one of these two possibilities is "computational mathematics"? Samohyl Jan 19:21, 1 February 2006 (UTC)

I mean the former. I don't think "study of computational methods mathematically" would be correct; nor does this phrase, as far as I can tell, agree with what others here have suggested. Fredrik Johansson - talk - contribs 23:14, 1 February 2006 (UTC)

Actually, I meant the second of the possibilities that Samohyl mentioned. On rereading my comment, I still agree with myself ;) -- Jitse Niesen (talk) 23:20, 1 February 2006 (UTC)

And now I'm confused ;-) I'm reading "study of computational methods mathematically" as "mathematical study of algorithms", which seems to be the opposite of "algorithms for mathematical problems" as you said first. Fredrik Johansson - talk - contribs 23:29, 1 February 2006 (UTC)

Sorry, let me try to explain using an example. For weather forecasting, you need to make a mathematical model of the atmosphere (basically a PDE), gather the initial data, solve the PDE, and interpret the result — apologies to the people involved for the huge simplifications. The step of solving the PDE is part of computational mathematics, in my interpretation of the term. The problem you are solving is mathematical on one level (a differential equation), but physical on another level (forecasting the weather). On the other hand, I'm not so sure that automated theorem proving is computational mathematics, because there is no computation involved.

I think the definition from JFoCM is a good start, especially since it is verifiable and does not involve the comments of random Wikipedians. -- Jitse Niesen (talk) 16:15, 2 February 2006 (UTC)

I think the best way to view it is in the context of computational modeling:

Step One- Model Setup/Knowledge of the Problem: Engineer/Scientist. Requires thorough knowledge of the physics etc (i.e. can fluid flow be treated as potential flow or not = engineer not mathematician). Sets up the basic equations to be solved.

Step Two- Formulation of the numerical scheme and method of solution (espicially method of solving large matrix equations): Mathematician. This is, in my mind, the biggest aspect of Computational Mathematics. Usually, mathematicians design this part and Engineers/Scientists scan the literature and use those methods developed (ex GMRES, SOR, etc).

Step Three- Implementation of the numerical scheme: Computer Scientist. Here is the science of actually writing the code on the computer, implementing massively parallel computations, etc. Best done in the hands of a computer scientist.

Step Four- Data Analysis/Insight: Engineer/Scientist. Running the simulations, coming up with conclusions, verification of data.

Of course sometimes, one person does everything, but in the "ideal world" that would be how the process works and explains the specific role/ability each type of scientist can bring to the table.

Differentiation of functions of matrices with respect to matrix

Moved to talk:Matrix calculus'. 09:34, 2 February 2006 (UTC)

Functions of matrices

Do we have an article on functions of matrices? I can see some specific cases like Matrix exponential but not a general discussion. Also (and this question overlaps) what about convergence of series of matrices (such as the theorem that a pwoer series of matrices converges if it converges for all of the eigenvalues of the matrix)? Thanks. --Zero 03:58, 2 February 2006 (UTC)

I'm glad to see that you volunteer to write an article on functions of matrices ;) The closest we have is holomorphic functional calculus, but that's probably too abstract. Look at matrix logarithm, somewhere near the bottom, for how it applies in concrete situations. -- Jitse Niesen (talk) 13:21, 2 February 2006 (UTC)

The power series thing is holomorphic functional calculus, but is also clear enough from Jordan normal form, I guess. Charles Matthews 14:08, 2 February 2006 (UTC)

History of manifold

Hey, if there are any experts reading this talk page, it would be great to see the Manifold#History section fleshed out. Thanks. –Joke 04:24, 2 February 2006 (UTC)

It's not so bad now. Query what Weyl actually did in his book on Riemann surfaces, though. Charles Matthews 14:15, 2 February 2006 (UTC)

Surely it is possible to say more about it than that Riemann and Weyl contributed? What about its influence on other branches of mathematics, and vice versa? What about the relationship to physics? What about the development of modern differential geometry, the contributions of Sophus Lie, etc...? –Joke 15:22, 2 February 2006 (UTC)

Yes, always more to say. However the story about the basic, underlying manifold idea is not the same as that of the history of differential geometry, or of Lie groups. (In a strange way, the technical development of manifolds lagged behind.) Charles Matthews 15:32, 2 February 2006 (UTC)

I agree, but the manifold did not develop in a vacuum. Well, maybe if you believe in the Hartle-Hawking state it did. The page differential geometry and topology has no reference to any history either. My point is that saying Riemann did this, then Poincaré conjectured, then Weyl made it abstract seems a little haphazard. Maybe I should try and do some research. –Joke 16:03, 2 February 2006 (UTC)

Template for deletion

Yes indeed. Oleg Alexandrov (talk) 19:51, 4 February 2006 (UTC)

Seems pretty useless to me. - Gauge 23:41, 4 February 2006 (UTC)

I would think it would be a nice template if it weren't so goddamn ugly. All math books have demarcation for theorems, axioms, definitions, etc. Unfortunately, I don't see how this can be accomplished with current wiki markup. Maybe someday, but not today; this one's gotta go. -lethe ^{talk +} 00:35, 5 February 2006 (UTC)

What appearance would you like? Wiki markup is not the only option; CSS is more powerful. --KSmrq^T 01:24, 5 February 2006 (UTC)

CSS or not, adopting those boxes in any way will make Wikipedia look like American calculus books; with each theorem, lemma, definition, and important formula, in its own shiny box, with different colors for each and so on. Gosh, I hope we don't get there. Oleg Alexandrov (talk) 02:03, 5 February 2006 (UTC)

Agree with Oleg; American calc textbooks are very ugly in their presentation. I don't think we want to be emulating that. If you have lots of axioms, having boxes around each would get out of hand really quickly. I don't see any compelling need to have such a template. - Gauge 06:34, 6 February 2006 (UTC)

If we had something, it would have to be at most an indentation with a boldfaced Theorem inline heading, as is common in textbooks. Putting things in boxes is just ugly (and this particular box is uglier than most). -lethe ^{talk +} 02:42, 5 February 2006 (UTC)

I think it's quite a pretty box. All those purple dots. Look:

Axiom I. Every box contains a unique axiom.

Dmharvey 02:52, 5 February 2006 (UTC)

The template takes only one argument at present, which would have to change if the axiom name is to be bolded automatically. But indentation (left and right), bold, and italics should be possible otherwise.

Axiom 3 (Composition): Given f:a→b and g:b→c, the composition g○f:a→c exists.

This is merely an example. Styling details can be tweaked per taste. --KSmrq^T 04:30, 5 February 2006 (UTC)

I don't think colored text is a good idea. Simply indenting an axiom and making italic should be enough I would guess. Oleg Alexandrov (talk) 04:55, 5 February 2006 (UTC)

I'm not recommending color, only presenting it as an option for people who like purple dots. ;-)

Also, the style can do more than indent. Observe a longer "axiom":

Axiom 9 (Greek): Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Notice the "indentation" of the right margin as well as the left; again, an option. --KSmrq^T 07:52, 5 February 2006 (UTC)

I think all axioms in boxes should be stated in Latin as above ;-) - Gauge 06:34, 6 February 2006 (UTC)

This is my little typographers' joke. The text of the "axiom" is explained at lorem ipsum. And "greeking" means either "to display text as abstract dots and lines in order to give a preview of layout without actually being legible", or to fill with meaningless text like "lorem ipsum". Of course, I would never actually use the florid style in the example, with its ugly and distracting background color and small caps. --KSmrq^T 16:34, 6 February 2006 (UTC)

What, pray tell, is wrong with a simple bullet point? Dysprosia 08:16, 5 February 2006 (UTC)

For one thing, you can't put math tagged equations in a bulleted item without resorting to HTML. -lethe ^{talk +} 10:00, 5 February 2006 (UTC)

• $\cos {x}+3\,$

Looks like you can? Dysprosia 10:25, 5 February 2006 (UTC)

That's fine for a list of formulas, but doesn't work for a theorem or axiom. See this:

• Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}$ where c is the hypotenuse and a and b are the legs.

or with the usual indentation for math tags:

• Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}$

where c is the hypotenuse and a and b are the legs.

It sucks. When I want to make things like this, I resort to HTML tags. And as Jitse will tell you, I often forget to close them. But you get this:

• Theorem 1: A right triangle with sides a, b and c obeys

  $a^{2}+b^{2}=c^{2}$

  where c is the hypotenuse and a and b are the legs.

If there were a template that would give some indentation like that, but without the bullet point, and put theorem, definition, axiom according to an argument, I would consider using it. -lethe ^{talk +} 11:17, 5 February 2006 (UTC)

• Theorem 1: A right triangle with sides a, b and c obeys $a^{2}+b^{2}=c^{2}$ where c is the hypotenuse and a and b are the legs.

This looks like it works fine. One doesn't have to always indent with math tags unless it's supposed to be displayed. And if there is content that needs to be displayed, it shouldn't be in the one line.

• Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}\,$

where c is the hypotenuse and a and b are the legs.

In the second case, observe that using another colon to indent appears to solve the indenting problem. However, there appears to be a minor spacing issue there...

The template option sounds like a good idea, by the way. Dysprosia 11:25, 5 February 2006 (UTC)

your first case is not so great because it has the math png inline. The second one is a bit awkward, but it would serve if nothing else were available. But the html tags are available and do better in my opinion. Anyway, a nice template might be nice. -lethe ^{talk +} 12:13, 5 February 2006 (UTC)

That's if you use the PNG always option. I don't. Dysprosia 12:19, 5 February 2006 (UTC)

To play with the concept I created a template Template:Pfafrich/Axiom which has a configurable style option so the look can be changed.

• no style same as a blockquote

Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}\,$

where c is the hypotenuse and a and b are the legs.

• user defined style

Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}\,$

where c is the hypotenuse and a and b are the legs.

• default style

Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}\,$

where c is the hypotenuse and a and b are the legs.

It turns out the axiom box fails when used with * its just that TfD notice hides this. So in a wiki * bullet point we have

• Theorem 1: A right triangle with sides a, b and c obeys

$a^{2}+b^{2}=c^{2}\,$

where c is the hypotenuse and a and b are the legs.

The green box should surrond the whole theorem. It fails because MediaWiki does template substitution before interpreting the * bullet syntax. MediaWikis does the simplest thing when it finds a * - it just puts li tags at beginning and end of line, closing whats necessary. The upshot is that its imposible for a template to box multiline theorems in a * bullet point. Using html <li> will work.

• Theorem 1: A right triangle with sides a, b and c obeys

  $a^{2}+b^{2}=c^{2}\,$

  where c is the hypotenuse and a and b are the legs.

--Salix alba (talk) 23:28, 6 February 2006 (UTC)

I find all the frameboxes, regardless of how they look, to be not so pleasing. In my opinion, they give an unprofessional/naive appearance to the Wikipedia pages, while not helping in understanding the concepts. Neither mathworld nor planetmath use them, nor any books or math publications (as far as I am aware), save again for American calculus and college algebra books. If one really wants an axiom to stand out, I would think indenting it would do a better job. Oleg Alexandrov (talk) 03:49, 7 February 2006 (UTC)

I agree with Oleg that outlined boxes are terrible. Why are you making us look at them? Oleg is right, indentation should be enough. But of course a template might be a nice way to accomplish an indentation (because of the math tags issue). Your first one, the one with no outline, I might consider using that. Maybe I should change the axiom template and then change my vote. -lethe ^{talk +} 04:12, 7 February 2006 (UTC)

Lethe is right, why are you making us look at them? Oleg Alexandrov (talk) 04:21, 7 February 2006 (UTC)

I agree with the both of you. A bullet point suffices. Dysprosia 11:17, 10 February 2006 (UTC)

Copula (statistics)

Can someone take a look at this article, specifically the value of theta at the end of the Archimedean copula subsection? A couple of months back, it said theta=+1. I looked there, and though I don't know the topic, it seemed to me it had to be -1. I changed it and marked it as uncertain. Today I noticed that an anon with no other edits has changed it to theta=0. Once again, I think that's likely wrong, but I don't have the knowledge or time to fully think it through. Can someone check? I want to be sure we don't have some sneaky vandalism happening. Martinp 19:06, 7 February 2006 (UTC) (a lapsed mathematician)

0 it is.

$\lim _{\theta \to 0}(a^{\theta }+b^{\theta }-1)^{1/\theta }=a\cdot b$

Arthur Rubin | (talk) 19:57, 7 February 2006 (UTC)

Good. Thanks. That's an interesting limit, btw. Would make a good exam question... Martinp 15:40, 8 February 2006 (UTC)

New stub cat (topology)

Following prescribed discussion, I've created a new stub category, {{topology-stub}}. Assistance in populating it would be appreciated (a lot of articles marked with {{geometry-stub}} are really topology, and there are many articles marked with just {{math-stub}} that are topology). --Trovatore 19:29, 7 February 2006 (UTC)

Proofs and derivations

In many of the pages on wikipedia, articles go over proofs and derivations of forumlae and other such things. Most of the time I don't need a proof, and in some cases the proof obscures the end formula. I think a very clean and elegant way to include proofs would be to link to a separate page that goes through a proof or derivation. This way, an article can be kept uncluttered and clean, while being complete and non-mysterious. (btw, is this the wrong place for this suggestion?). I'd like to know if anyone feels the same way I do. Fresheneesz 22:01, 7 February 2006 (UTC)

We've had previous discussion on this. Basically proofs should only be here if they have some merit or interest. Charles Matthews 22:07, 7 February 2006 (UTC)

See Wikipedia:WikiProject Mathematics/Proofs for discussion, and the Math_style_manual#Proofs for the policy. Oleg Alexandrov (talk) 22:51, 7 February 2006 (UTC)

Here are a few examples like what you suggested: Proofs of Fermat's little theorem, Proofs of Fermat's theorem on sums of two squares, Proofs of quadratic reciprocity. I'm sure there are plenty of others. Dmharvey 03:54, 8 February 2006 (UTC)

Dmharvey references the very finest proofs, those that are well-enough written to be deserving of real articles. By contrast, the dirty, ugly ones that got ripped out of articles can be found in Category:Article proofs. This is, I believe, what you are talking about. linas 04:26, 8 February 2006 (UTC)

So would it be ok if I randomly snatch proofs from articles, and put them in their own page, if I think the page they're on would be more readable with just a link to the proof? Fresheneesz 21:29, 8 February 2006 (UTC)

If you think it improves readability, be bold! Dmharvey 22:27, 8 February 2006 (UTC)

I think I have nothing to do here

I was hoping to help in the areas that I like (not abstract algebra), but all of these are full. Only abstract algebra articles are available to give a respectable edit, the problem is: I'm really not interested in abstract algebra but I want to contribute here, what should I do. juan andrés 03:32, 8 February 2006 (UTC)

I hardly think any area is "full"! However you would be a pretty unusual sixteen-year-old if you could just pick mathematical topics at random that you know well, and easily find important subjects that don't already have articles. Why don't you start by looking at some stub articles, and seeing if you can expand them? You don't necessarily need to already know the material you'll be adding; looking it up is considered better procedure anyway, and as a byproduct you'll learn some interesting things.

Look at Wikipedia:WikiProject Stub sorting/Stub_types#Mathematics to see the various stub categories listed, pick something that looks interesting, and have fun! --Trovatore 03:41, 8 February 2006 (UTC)

There are 300+ articles in Category:Elementary mathematics and its subcategories, and almost all are in poor condition, are poorly explained, are missing details, etc. Do not be mislead by the word "elementary": while all of these topics can be first taught/introduced at an elementary level, many also can lead to very sophisticated mathematics. My favorite example is the torus, which appears in many many places, including leading edge research. If you can take some elementary topic, and fill it out so that it connects with higher math, that would be excellent. linas 04:20, 8 February 2006 (UTC)

Per linas's comment, also don't forget that "elementary mathematics" doesn't mean the same thing as "mathematics that is easy to explain". I should spend some more time around there some day. Dmharvey 05:09, 8 February 2006 (UTC)

Thank you. That's what I was talking about. Sorry if I could not answer but I was very busy with school homework. I know is very difficult to explain because you have to go back to the basics. juan andrés 20:21, 18 February 2006 (UTC)

blahtex 0.4.1 released

No bug fixes today, but one very nice new feature: correct vertical alignment of PNGs. This is something that PlanetMath has that I think is very cool (actually it's their underlying converter LaTeX2html that does it), but I'm using a different, somewhat experimental strategy. :-)

Try it out on the interactive demo, and also have a look at what it does with the equations from Wikipedia (which I've just updated from some more recent database dumps).

It's not enabled yet on Jitse's test wiki. It might be some time before it gets enabled, not because it's technically difficult, but for other semi-technical reasons that might be discussed another day...

Also, the blahtex manual is now online in HTML format, should make it easier to read.

Enjoy, Dmharvey 04:06, 9 February 2006 (UTC)

This is totally awesome. Deco 04:16, 9 February 2006 (UTC)

Blahtex Compatibility Project — seeking volunteers

Hi math(s) people,

As you all know, Jitse and I are working on developing some MathML support for Wikipedia/Mediawiki. For this to actually happen, a lot of things have to go right simultaneously.

One of the issues we need to deal with eventually is that blahtex's input syntax is ever-so-slightly different from texvc (i.e. the current input syntax on wikipedia). In fact, blahtex's input parsing is much closer to TeX's parsing than texvc is. Here are some examples of where they differ:

• The characters $ (enter/leave math mode) and % (denoting comments) are illegal in blahtex, but texvc treats them as literally the $ sign and the % sign. The correct TeX for these is \$ and \%.
• You can leave out curly braces in texvc sometimes, where TeX wouldn't allow it. For example: "\hat\overrightarrow x" is OK on wikipedia now, but not cool in TeX or blahtex; it should be "\hat{\overrightarrow x}". Similarly "x^\left( y \right)" is legal in texvc but not in blahtex or TeX.
• Because of the way TeX handles macros, certain constructs like "x^\cong" are illegal in TeX (needs to be "x^{\cong}), even though other ones like "x^=" are ok.

These differences between blahtex and texvc are entirely deliberate. The idea is that we should make it as easy as possible to translate wikitext into other formats, using standard tools. The closer we are to TeX, the easier it is to do this.

So the question is: if and when we ever switch over to using blahtex for MathML support, what will happen to all the existing equations on Wikipedia that break under blahtex?

The good news is that only about 1,000 out of 180,000 equations on Wikipedia (this data includes the ten largest language versions) have problems, and of those, most of them fall into easily defined categories, like the $ and % sign issues described above. A complete list can be found on the blahtex website (http://blahtex.org) under the "Wikipedia samples" section.

I propose that we fix these equations, one by one, over the next few months, or however long it takes, and I would like to ask people here to volunteer to help out with the effort. Probably some of it can be automated (it's easy to change $ into \$) but some of it probably requires some human attentiveness.

This is not an entirely trivial task, and I think it would be best if someone volunteers to organise the effort. I don't have time myself to organise it right now; besides real life, I have code to write! This "Director of Blahtex Compatibility" might consider doing the following: setting up a page where people can volunteer to fix up "blocks", based on (say) the md5 of the equation. If you need the list of equations in a different format, I can provide that; I have code that can extract it from the Wikipedia database dumps fairly easily. Also they might want to write a page explaining what this is about, so that people can use a link to the explanation page in their edit summary. And they might want to find someone willing to write a bot to handle the automate-able parts of the project.

Please put up your hand if you're willing to organise this. And of course please speak out if you think this is a really stupid idea. Dmharvey 18:05, 9 February 2006 (UTC)

I'm willing to take responsibility for dewiki.--gwaihir 00:11, 10 February 2006 (UTC)

The other major problem is malformed html tags written directly in (i.e. not using MediaWiki code). For example

<ul>
<li>line one
<li>line two
</ul>

this is legal html but not legal xhtml, and it breaks the BlahTex wiki. It might be possible to integrate HTML-Tidy into the code so that we get pure xhtml out, but its going to be a major problem. Malformed html abounds for example Help:Formula had an extra </table> tag (now fixed on meta).

I might be up for helping with compatibility (director sounds too grand).

Testing on various platforms also appreciated. --Salix alba (talk) 00:31, 10 February 2006 (UTC)

Thanks Gwaihir.

The issue raised by Pfafrich (Salix Alba) concerning malformed HTML is an important one (a *very* important one), but not on topic :-). Here I'm only talking about the stuff inside <math> tags. Dmharvey 00:51, 10 February 2006 (UTC)

I suppose I can answer Pfafrich's point a little better here. HTML tidy is already integrated into mediawiki. But it's switched off on blahtexwiki at the moment, because HTML tidy doesn't like math tags. Jitse is working on a clean solution to this. So it's not as big a problem as it sounds. Not easy, but not insurmountable. Dmharvey 01:10, 10 February 2006 (UTC)

Fixed occureces of $ in main article namespace (a few left in Talk and old ref desk) see User:Pfafrich/BlaxTex $ bugs for all occurences . A possible earier way round the problem is to search for malformed latex from the database dumps, a relatively simple grep and sed found all the $'s. --Salix alba (talk) 03:50, 10 February 2006 (UTC)

Pfarich, nice work. We need that done on the other languages too :-) I'm concentrating on the ten largest ones: en, de, ja, fr, it, es, pt, pl, sv, nl. Maybe this will help: I've put up a list of all the problem equations (i.e. all the ones I have listed at blahtex.org) in a simple text format at http://blahtex.org/errors-20060203.txt. Be careful: if you feed the data to a machine, keep in mind that some entries have more than one web address listed; use the "-----" line to work out where. Let me know if a different format would be more convenient. Dmharvey 14:01, 10 February 2006 (UTC)

Is this the right place to ask specific questions (like: what's wrong with $x\not \subset y$? Error message given here reads: "No negative version of the symbol(s) following "\not" is available"; but TeX doesn't complain).--gwaihir 10:55, 10 February 2006 (UTC)

Yes it is the right place to ask. The answer is: that's a bug in blahtex, and it's on my list to fix. Don't worry about those ones for now. Thanks. Dmharvey 14:01, 10 February 2006 (UTC)

Update: I've corrected this behaviour for blahtex 0.4.2. This particular one (\not\subset) will be translated correctly now, and I've also added all the others that have specific MathML characters associated to them. If you try one that blahtex doesn't know (like "\not\partial" which occurs in fr:Matrice de Dirac), it will now only give up on the MathML output, and will still succeed for PNG output. A similar issue is errors like "The symbol "1" is not available in the font "bb"", which should give you $\mathbb {1}$. The updated behaviour is that it gives up on the MathML output but still does the PNG output. This is not ideal, but it's something I will revisit later. Dmharvey 22:44, 10 February 2006 (UTC)

Well, \mathbb1 is nothing more than a dirty hack for some missing macro/mathchardef. It should not work. If this symbol is needed, a corresponding command should be made available.--gwaihir 23:34, 10 February 2006 (UTC)

Well said. This is why it's not a priority. Soon I will expand coverage of symbols to get as much as possible of LaTeX and AMS-LaTeX. Dmharvey 23:39, 10 February 2006 (UTC)

My own view would be to have BlahTex be as compatible with texvc as possible, and introducing the feature which allows it to be more compatible with TeX (and less wtih texvc) later. That because having MathML be accepted and working on Wikipedia would already be hard enough, thus, worrying about slight incompatibilities with the existing system would be an unnecessary distraction. Oleg Alexandrov (talk) 20:08, 10 February 2006 (UTC)

I agree, but it's a fine line to be walking. The earlier versions of blahtex (0.2.1... or perhaps even earlier ones that I never released) were in fact more compatible with texvc, because they used a yacc-based parser, as texvc does. But I discovered that to be able to do more interesting things, this approach had to be abandoned. On the other hand, blahtex has a command line option "--texvc-compatible-commands" which enables use of all of the texvc commands which are not standard TeX/LaTeX/AMS-LaTeX. This is enabled on Jitse's wiki, and I expect it to be enabled if blahtex ever gets deployed on the real thing. Here's the list of commands, i.e. commands that work on wikipedia but in no latex installation that I know of: \R \Reals \reals \Z \N \natnums \Complex \cnums \alefsym \alef \larr \rarr \Larr \lArr \Rarr \rArr \uarr \uArr \Uarr \darr \dArr \Darr \lrarr \harr \Lrarr \Harr \lrArr \hAar \sub \supe \sube \infin \lang \rang \real \image \bull \weierp \isin \plusmn \Dagger \exist \sect \clubs \spades \hearts \diamonds \sdot \ang \thetasym \Alpha \Beta \Epsilon \Zeta \Eta \Iota \Kappa \Mu \Nu \Rho \Tau \Chi \arcsec \arccsc \arccot \sgn. These ones could of course be easily simulated by means of macro definitions (and that's in fact how I implement them in blahtex :-)). In contrast, the real problems (the ones I mentioned above) are the ones that *cannot* be solved by adding a few macros. For a while I even tried writing *two* parsers that could live side-by-side.... but it was too much trouble. I spent quite a while analysing how much of a burden this would be, and the net result is that 1000 equations --- across ten different languages --- is actually not so bad. I decided it was worth making a clean break. I can assure you that compatibility has been uppermost in my mind, but compromises had to be made. I think this is the least bad solution. Anyway, it was a good chance to fix tons of other things in texvc which are partly a consequence of its parsing strategy. For example, it's annoying that \mathop{\rightarrow}^f doesn't put the "f" above the rightarrow, like it should: $A\mathop {\rightarrow } ^{f}B$. (And the spacing's wrong there too.) Actually, given what pfafrich has been up to, I wouldn't be surprised if we were already down to 900, and with a few more helping hands, the issue will pretty much disappear before we get around to considering deployment... Dmharvey 20:35, 10 February 2006 (UTC)

A short comment, hope it's not too much of a nonsequitur as I don't know much about how you're implementing blahtex: why don't you resort to standard TeX to get certain "difficult" things done instead of falling back on LaTeX and nothing deeper? For example, won't the AMS \buildrel do what you need instead of \mathop (which I gather is a LaTeXism)? Dysprosia 05:24, 13 February 2006 (UTC)

I don't completely understand your question, but I can make two comments: (1) I don't know AMS-LaTeX nearly as well as I should, so for example, I've never used \buildrel, and (2) \mathop is buried even deeper than LaTeX, it's a TeX thing. Any advice you have is appreciated. (Hmmm... wikipedia is very broken today... can't seem to log in.... so this is Dmharvey, 15:35, 13 February 2006 (UTC))

LaTeX is built on TeX. TeX is not the evil twin of LaTeX ;) I don't know what you're doing in the backend of blahtex, but if you're interfacing with LaTeX, presumably you can include plain TeX commands. So, if you figure out how to do something in plain TeX, why not give the plain TeX code to LaTeX and get it to do what you like? If you don't want to use the entire complement of AMSTeX or AMSLaTeX, you can always just snip out the bits you want from the AMS code. Sorry I'm not more precise on this. If you'd like me to attempt something specific, let me know and I can give it a shot. Dysprosia 06:15, 22 February 2006 (UTC)

Carathéodory theorem

I found out that there is no real entry on Carathéodory theorem in wikipedia. The article Carathéodory's theorem (measure theory) links back to outer measures, and you cannot find the definition of Carathéodory theorem for extension of measures on algebra. I don't know what you think, but the article is really not clear about what the theorem is, and I would consider this theorem fundamental in measure theory. Ashigabou 11:29, 10 February 2006 (UTC)

Are you talking about Carathéodory's theorem (convex hull)? Probably renaming the article is in order. (Igny 13:51, 10 February 2006 (UTC))

Oh, you meant absence of the Caratheodory extension theorem as defined in [3].(Igny 14:01, 10 February 2006 (UTC))

exactly. I know the theorem myself, but I am not that familiar with other "abstract theories", as I studied it recently in the theoritical fundations of probability; I wouldn't be able to link it to other fields. I created a stub, but I am not sure that semi-ring is the standard naming convention (subset S of the power set of X, closed under finite union, and difference can be written as a finite union of elements of S). Ashigabou 15:32, 10 February 2006 (UTC)

#REDIRECT Carathéodory's theorem -- linas 23:52, 10 February 2006 (UTC)

Why is it Carathéodory's theorem but Cauchy theorem (as opposed to Cauchy's), which is also a dab page? Should we standardise? —Blotwell 01:57, 11 February 2006 (UTC)

Kramers-Kronig relation

Hello, up until a few minutes ago there were two different articles Kramers-Kronig relations and Kramers-Krönig relation. Having determined that Ralph Kronig spelled his name with o, not ö, I merged both articles to one named Kramers-Kronig relation. However, since I know nothing at all about math and physics, it would be very good if someone who actually understands the text could look at the new article and make any necessary changes. Thanks! Angr/talk 18:16, 12 February 2006 (UTC)

blahtex 0.4.2

Now can do every symbol from LaTeX/AMS-LaTeX. (Well, almost all of them.) Results may vary depending on the fonts you have installed. At the very least you should be able to see them as PNGs. Dmharvey 02:37, 13 February 2006 (UTC)

Cool! But won't this break texvc when blahtex is incorporated? That is, texvc will choke on a symbol that blahtex accepts. (Of course, the correct thing to do is fix texvc not handicap blahtex.) -- Fropuff 04:59, 13 February 2006 (UTC)

Um, yes texvc will of course choke on symbols that blahtex accepts, but I don't really that this is a problem. Right now on blahtexwiki, Jitse has set it up (hope I've got this right) so that both texvc and blahtex are attempted, texvc's output is used wherever it succeeds, and blahtex is used for anything else. This means that (1) all MathML output is generated by blahtex, (2) PNG output is generated by texvc whenever texvc can manage it, otherwise blahtex does the PNG output, (3) all HTML output is handled by texvc, because blahtex doesn't do any HTML at all. By the way, I started this whole project trying to "fix texvc", but I soon gave up on that, and started again from scratch. Hence, blahtex. (-- Dmharvey, who can't log in now, some time on Feb 13.)

What, every? Almost every. --Trovatore 05:02, 13 February 2006 (UTC)

That's what I said. Almost every. Soon, with everyone's eagle eyes, we'll hopefully be able to substitute "every". (-- Dmharvey, who can't log in now, some time on Feb 13.)

AfD: Foundational status of arithmetic

Up for deletion: Foundational status of arithmetic - an interesting if slightly unusual article on the history of arithmetic. Contains some non-standard views, but maybe it can be cleaned up? 17:42, 13 February 2006 (UTC)

Maybe. Looks like a chore, though. Could be tagged with NPOV in the meantime. It points to arithmetization of analysis, which seems equally problematic; it seems to take the astonishing view that analysis has been mapped into the arithmetic of the natural numbers. (It's just possible that it means this has been done in higher-order logic, which is arguably true.) --Trovatore 17:48, 13 February 2006 (UTC)

By inspection

I am rather unhappy with this article, both the name and the content. I would think that the best thing to do would be to have it deleted, but maybe there are ways of renaming it and rewording it to make it an acceptable mathematics encyclopedia article. Comments? Oleg Alexandrov (talk) 02:52, 14 February 2006 (UTC)

I wrote this little thing after using the phrase in another article, Evaluating sums, which I thought had potentially a naive enough audience that they would appreciate seeing an explanation of this piece of mathematical jargon. I was uncomfortable writing about jargon, but it's not strictly a dictionary definition so I thought it would be excusable. There's more to say than I felt comfortable shoehorning into mathematical jargon, though, so I gave it its own article; however, it is by far the least substantial of the jargons linked to from that page. I don't know if there's much more to say than what I and Charles Matthews have already written; perhaps it can just be put into mathematical jargon anyway.

However, that only addresses one aspect of it being a bad article. What is unacceptable about it to you? For example, aliter and one and only one are analogously brief; what do you think of them? Ryan Reich 03:07, 14 February 2006 (UTC)

OK then, what I don't like is the name. Maybe something like method of inspection or something, or indeed part of the mathematical jargon. Don't know. :) Oleg Alexandrov (talk) 04:09, 14 February 2006 (UTC)

The name is one thing I don't really dislike. However, some other jargons, like arbitrary and canonical, have solved the naming problem by merging into a much larger article on the word taken in all its contexts. There is an article inspection; should I perhaps insert the contents of by inspection there? Ryan Reich 04:21, 14 February 2006 (UTC)

Trigonometric and hyperbolic functions: create separate articles?

Our article trigonometric function lacks much information, but is huge and difficult to expand as is. I think it would make sense to create a separate page for each function (cosine, inverse cosine ...). MathWorld has very rich pages on the individual functions, which are much more useful than Wikipedia's overview for someone with a good basic understanding of the topic. Of course, the main article should be kept as an overview. Same thoughts go for the hyperbolic functions. - Fredrik Johansson - talk - contribs 03:33, 14 February 2006 (UTC)

I am not convinced. Sine and cosine overlap too much as it is. Septentrionalis 05:53, 15 February 2006 (UTC)

I have long thought that the inverse trigonometric functions, at least, needed their own page. I started a draft at User:Fropuff/Draft 5 but I didn't get very far. I'm ambivalent as to whether we should have separate article for each function. -- Fropuff 07:50, 15 February 2006 (UTC)

A separate page for the inverses would help. Fredrik Johansson - talk - contribs 16:10, 15 February 2006 (UTC)

Rather than a split by type of fnction, I's suggest a split by topic (which mirrors the current topics covered in the article): so, for example, there could be Trigonometric function history, and Trigonometric function series and Trigonometric function identities, and so on. linas 22:39, 15 February 2006 (UTC)

Well, we already have the long article on trigonometric identities. I don't think we really need a separate article on the history; it fits in quite nicely in the main article. -- Fropuff 01:40, 16 February 2006 (UTC)

Multi-variable articles

I am still not satisfied with multi variable calculus articles (some of them only). Jacobian and gradient are not developped enough in my opinion. My main point, I guess, is we should have an article which generalizes derivative in one dimension for many practical cases (domain, codomain being vector spaces , with a special treatment for matrix spaces); we have an article on Frechet derivative, but it emphasize the genral case (infinite dimension). I think that in finite dimension, having a good article on derivative with several variables in the context of Frechet is necessary: it has all the good properties we expect from the scalar case (composition rule, inverse rule, differentiability imply continuity, etc...) that partial derivative do not have, and could explain the gradient and Jacobian definition, and some really common rules (for example the multi variable change in integrals). Some people disagree with me on this view, but I started to really understand gradient, jacobian and matrix calculus only once I studied Frechet derivative, and this view is adopted in at least two different documents, one being a reference, I think (I am not a mathematician, so I may be wrong though; the book I am talking about being Analysis on manifolds, from Munkres). As I studied this point recently quite heavily, I am willing to write the article, but I am not sure about the title, and how to link it to other article in multi-variable calculus. Ashigabou 01:54, 15 February 2006 (UTC)

I am not sure what exactly you want, but I think it would be more useful to expand the articles we currently have. So, develop the article on Jacobi matrix and mention that it satisfies

$f(x+h)=f(x)+J_{f}(x)\,h+o(|h|)\qquad (*)$

and thus it is a Frechet derivative. If the "some people" refers to me, then I'm afraid I didn't express myself clearly. The property (*) is essential for understanding multivariate calculus. What I meant to say is that most people will encounter the Jacobi matrix before they have heard of Frechet derivatives, and therefore you cannot motivate the Jacobi matrix by saying that it's simply a Frechet derivative, but you can (and probably should) refer to property (*) in the motivation.

The article on chain rule (what you called "composition rule") mentions the rule with Jacobi matrices and Frechet derivatives, inverse function theorem has the rule for inverse function, etc. If you want to write a high-level overview, you can add some paragraphs to multivariate calculus (if it gets too long, you can always split of a part to, say, multivariate differential calculus). All these articles can be improved, and I suggest you concentrate on that rather than writing a new article. Don't be afraid of changing existing articles. This goes in particular for matrix calculus (I'll comment on your remarks there).

I don't know Munkres' book, but from what I've heard it's pretty good, but more of a text book than a reference work. However, Munkres has a more general setting in mind: calculus on manifolds, rather than calculus in Rⁿ. -- Jitse Niesen (talk) 12:03, 15 February 2006 (UTC)

Agree with Jitse. Do not confuse the Jacobean with the Frechet derivative: although similar, most calculus books are built on the Jacobean, not Frechet. Personally, I'd already had plenty of classes in "calculus on manifolds"; I'd known a half-dozen different concepts of derivatives, long before I'd ever seen the words "Frechet derivative". Focus on Jacobean, which does what you want for finite-dimensional spaces, and leave Frechet for the infinite-dimensional stuff, for which it was invented. linas 22:52, 15 February 2006 (UTC)

I agree that most calculus books are built on the Jacobian; whether it is a good thing or not is a different matter; I personnally think it is a mistake, because you cannot really understand matrix calculus. I agree that talking about Jacobian with an emphasize on the linear map it represents would be in the right direction (from my POV :) ), but how do you explains derivative of matrix with respect to matrix ? You both seem to think that Frechet is really useful for infinite dimension only, and I don't understand that (I am open to explanations, though, of course). I think taking a maybe somewhat original approach to multi variable calculus would be interesting. At least, I was never satisfied with the standard approach (using partial derivative only) during my undergraduate courses. Ashigabou 00:14, 16 February 2006 (UTC)

I will rephrase my point differently: when I wanted to understand multi variable differentiability, I was interested in a concept which generalized all the 'good' properties of the derivative in 1 dimension, that is differentiability implies continuity, etc... Wether calling it Frechet or not, I don't care, that's not really the point. I feel like an article about how to extend derivability in several dimensions while keeping most good properties would be good; something more than partial derivative. If you think this can be done without Frechet, then I would be glad to hear how. Ashigabou 00:26, 16 February 2006 (UTC)

I'm having great difficulties understanding what you mean, and why you think that you need the Frechet derivative. Si tu veux, tu peux écrire français. Is your point that a function may have partial differentials and thus a Jacobi matrix, without being Frechet differentiable? -- Jitse Niesen (talk) 14:00, 16 February 2006 (UTC)

I don't feel like the difficulty is coming from my English, but anyway: en scalaire, on apprends la definition de la derivée, et pas mal de théorèmes fondamentaux qui sont liés; derivabilité implique continuité, valeur intermédiaire, théorème de Taylor, dérivée de la fonction inverse, etc... Je trouve que ce serait intéressant d'avoir un article qui généralise ces concepts en plusieurs dimensions. In English: in undergraduate, we learn that if f has a derivative at the point a, f is continuous at the point a, that if f has derivative on [a, b], there is c in [a, b] such as f(b)-f(a) = f^'(c)(b-a), that if f is Cⁿ, f has a Taylor expansion of degree n, etc... When I had some courses about multi-variable calculus, we were told the concept of partial derivative, and that was about it, and on wiki, this is the same: gradient, jacobi, defined as vector of partial derivative; partial derivative are a bit strange, because even when they exist, f may not be continuous. I wondered for a long time how can you have a generalization of the derivative for multi variable functions with all the nice properties of the scalar, and the approximation of f(x+h)-f(x) by a linear map with respect to h is the natural extension. This is again related to my remarks in matrix calculus: for now, all the formula are said to be notations, and I think this is plain wrong, that all those matrices and tensor represent linear map which correspond to Frechet derivative (at least in the C¹ case). . When Linas says that Frechet is one of the derivative generalization, I don't agree; I think this is *the* natural generalization for 'nice enough' spaces (Banach spaces). I have some nice examples how to use the definition in Frechet context to find most formula in matrix calculus, but I am told this is different, this is just a notation, and I really don't agree, at least not with some more explanations (you know, those stubborn Frenchs :)... ). Thank you for your interest ! Ashigabou 00:55, 17 February 2006 (UTC)

Hi Ashigabou—I agree with your point that approaching the derivative through the concepts of linear maps and best local linear approximations is the way to go. As usual many undergraduate-level courses and texts are lacking here. There is no reason why this approach must be more difficult than focusing on matrix computations and partial derivatives; quite the contrary. I wonder if you'd like to take a look at a very remarkable book on these topics called (very modestly) Advanced Calculus by Shlomo Sternberg and Lynn Loomis. This is without question the finest treatment of this area of mathematics I've ever encountered. Is the approach to the derivative used in this book the sort of thing you had in mind?  — merge 10:28, 18 February 2006 (UTC)

I'm not actually sure what this discussion is about. We can and should have multiple approaches to an area like multi-variable calculus, for which there are superficially-different approaches well documented in the literature. If Fréchet derivative is somewhat too abstract, we can take a more 'gradualist' approach there, or in some other article. Charles Matthews 10:50, 18 February 2006 (UTC)

Ashigabou, I still don't quite know what you want, but I think I mostly agree with you, except for some details. The only advice I can give you now is just to do what you think is best. Once we see what you've written, it will be clear where you want to go. Based on what I've read, I expect that it will be generally okay and it will fill a gap in our coverage of multivariate calculus. I agree that Frechet is the most natural generalization of derivatives in R^n. -- Jitse Niesen (talk) 15:13, 18 February 2006 (UTC)

PROD (Proposed deletion): Empty Summation Equations

I proposed Empty Summation Equations for deletion, using the new Wikipedia:Proposed deletion process. Since this process is only being tested, I thought it would be fair to let you know. I didn't follow the debate, but my interpretation is that Proposed Deletion is for those articles that fail the criteria for speedy deletion, but for which it is still obvious that they should be deleted. -- Jitse Niesen (talk) 14:05, 16 February 2006 (UTC)

Can the /Current activity bot be modified to include this new type of activity? Arthur Rubin | (talk) 14:53, 16 February 2006 (UTC)

Yes. With a bit of luck, the article will appear on Current activity tonight. -- Jitse Niesen (talk) 19:15, 16 February 2006 (UTC)

Revert war at Real number

See for yourself [4]. Comments? Oleg Alexandrov (talk) 19:39, 16 February 2006 (UTC)

It is clear that what DYLAN LENNON has been repeatedly adding is not appropriate for this article. I can understand this happening once due to a lack of knowledge about what is noteworthy, but the repetition makes this unwelcome, and knowingly disruptive. Elroch 20:40, 16 February 2006 (UTC)

Possibly not notable articles

I nominated Colloquium (College of Engineering, Guindy) and Ramanujan Rolling Shield for deletion, as as they appear nonnotable. Comments and votes welcome. Oleg Alexandrov (talk) 04:07, 17 February 2006 (UTC)

I nominated (yesterday) Hiroshi Haruki, and I nominated a couple of DYLAN LENNON's creations for speedies. Comments and votes welcome. (I also removed a number of his lines

"The easiest proof" of (this theory) is due to Name that I never heard of.

Arthur Rubin | (talk) 20:22, 17 February 2006 (UTC)

DYLAN is surely a problem user. Some anon wrote on his talk page a while ago that he was banned from the Japanese wikipedia for trolling. Wouldn't surprise me. Oleg Alexandrov (talk) 21:08, 17 February 2006 (UTC)

Although DYLAN is a problem, it now appears (from the comments made in the AfD) that Haruki is adequately notable, although the article surely doesn't reflect it. Is there a {{sub-stub}} tag? Arthur Rubin | (talk) 00:13, 18 February 2006 (UTC)

Believe it or not, but {{substub}} has been deleted. Six times. I'm sure it has been discussed extensively, and I don't want to know how many edit wars had been going on about whether some article was a stub or a substub. -- Jitse Niesen (talk) 02:22, 18 February 2006 (UTC)

Some of MR LENNON'S links to ja appear to be incorrect or misleading. Then again, some of them seem to be right. We need someone who knows a bit of japanese to review them. Dmharvey 17:45, 18 February 2006 (UTC)

Good articles list

If you look at Wikipedia:Good articles, you'll see that only four articles are listed. I am pretty sure that there are far more than four good mathematics aricles on Wikipedia. So, I would like t orequest that if anyone knows of any other articles that fulfill the required criteria, could they please list them. Tompw 13:22, 18 February 2006 (UTC)

You can usually get a hollow laugh out of mathematicians with lines like should not omit any major facets of the topic. We really don't do completeness, except in some classifications. What would it take, to say that of an article like homology theory or Lie group or partial differential equation? So those guidelines are not written for us. Charles Matthews 14:00, 18 February 2006 (UTC)

Where does it say that? The requiremnts given for a good article are that it:

1. Be well written
2. Be factually accurate (which means error-free for a maths articles)
3. Use a neutral point of view (generally get this one for free :-) )
4. Be stable
5. Be reference (which isn't always needed for maths articles)
6. Wherever possible, contain images to illustrate it. The images should all be appropriately tagged.

Anyway, actions speak louder than words... so will try and seek some out. Tompw 19:50, 18 February 2006 (UTC)

Right after your point 6, it says:

Good articles may not be as thorough and detailed as our featured articles, but should not omit any major facets of the topic.

Now I don't think that necessarily excludes math articles, even ones like homology theory. I would interpret it as meaning something like "any subfield of homology theory accounting for (say) ten percent of the total research effort in that field should get at least a mention". It's not reasonable to read it as meaning that we have to track down the content of every PhD thesis written in the area. --Trovatore 20:01, 18 February 2006 (UTC)

OK, I saw and was editing my reply, but you got in first. However, I agree with you that we have to interpret "major facet" in our own way. Tompw 20:08, 18 February 2006 (UTC)

ALthough the Wikipedia:Good articles process is "sub-optimal" (if not broken) in a variety of ways, it is "well intentioned". From what I can tell, "someday", there will be a print version of WP, and thus, the articles suitable for inclusion in a print version must be identified. There are now many wikiprojects trying to categorize all of thier articles into "good bad and ugly". Seperately, there is a debate at Wikipedia:Stable versions about mechanisms by which the correctness and authority of an article can be atested to. A "good bad ugly" classification will probably feed into that process. I'm not convinced that now is the time to launch into the busywork of classifying math articles, but now is the time to get famliar with the issues. linas 00:53, 22 February 2006 (UTC)

Wikipedia:Articles for deletion/Safe sex makespan

Despite the name, this is a combinatorics / operations research article. It could probably need some sources and a new name, but it's a somewhat interesting problem. If somebody here knows this problem (known as "Glove problem" on Mathworld), please comment at the AfD. Kusma (討論) 00:01, 19 February 2006 (UTC)

Archives

I've reorganized this page's archive files a bit. I've refactored for readability the older archive pages, adding sections, ordering chronologically, merging two smaller ones, renaming some for consistency, signing, indenting etc. These changes are reflected in the changes I made to the archive-box at the beginning of the page.

I've also created a new file Wikipedia talk:WikiProject Mathematics/Archive Index (don't click on it unless you have the time to wait for it to load, It's rather large) which I've added to the top of the archive-box, which includes each of the individual archive files, in effect creating a single searchable file containing the complete history of this page. I urge each one of you to read it through carefully and in its entirety, if you have trouble falling to sleep at night. Anyway I thought such a file might be useful if you are looking for that excellent argument you made for or against some issue, that you'd like to refer to, but can't seem to find. It happens to me all the time.

Paul August ☎ 22:27, 19 February 2006 (UTC)

Many thanks! Each and every one of us will go carefully reading the archives to make sure you did a good job, as per your request. :) Thanks indeed, archives turn out to be more useful than one thinks at the moment of archiving. :) Oleg Alexandrov (talk) 02:00, 20 February 2006 (UTC)

can't remember the name of something

I'm not sure, but I think we might be missing an article on something. Unfortunately I can't remember its name, but I can describe it. It should be related to articles like bifurcation diagram, Feigenbaum's constant, chaos theory, dynamical system etc. If you look at the bifurcation diagram, and list the periods of the stable orbits from left to right (including the "islands of stability"), you get some ordering on the positive integers, which starts out 1, 2, 4, 8, ... but then does funny things in a non-well-ordered way. The picture is confusing me a bit (especially since it looks like 6 shows up twice, which is not suppoed to happen !!!), but I'm sure this has a name, it's called "so-and-so's ordering", but I can't remember who. And I seem to remember that the same sequence crops up no matter which dynamical system you choose, kind of like feigenbaum's constant, well at least for some reasonable class of systems. Anyone know about this? Dmharvey 15:30, 20 February 2006 (UTC)

ok, got it now: Sarkovskii's_theorem Dmharvey 15:34, 20 February 2006 (UTC)

blahtex compatibility update

Thanks to the efforts of Pfafrich on en, and of gwaihir and LutzL on de, and possibly others too, the blahtex compatibility project has been making substantial progress. Here's a table showing the number of problem equations on each wiki. The first column is the numbers before they got started, and the second column shows the counts for today's dumps. ("Today's dumps" means "today" for en, de and ja, but is still lagging by about two or three weeks for the other languages.)

      BEFORE   AFTER
en      342     287
de      372      68
fr      103      92
it       81      69
pl       57      49
es       37      32
pt       35      35
nl       34      16
ja       28      32
sv       10       9

TOTAL  1099     689

So already almost 40% of problems have been dealt with.

(Note: some proportion of the decrease -- not sure exactly how much -- is attributable to changes in blahtex. In particular it is now more permissive about using font commands in strange ways like ${\mathcal {a}}$, so these aren't reported in the second column.)

An updated list of errors is available at http://blahtex.org/errors-20060220.html.

I encourage anyone who feels like helping us to jump in! Dmharvey 23:00, 20 February 2006 (UTC)

I should add that the samples on http://blahtex.org/ have not been updated with the new dumps, and they won't be updated for a little while yet. Dmharvey 23:08, 20 February 2006 (UTC)

If people are interested in helping on en-wiki I've created a set of pages detailing some of the imcompatabilities User:Pfafrich/Blahtex en.wikipedia fixup, and listing their status. So far all the errors are very minor using % rather than \%. People are welcome to fix bugs listed there, about 100 articles. --Salix alba (talk) 16:42, 21 February 2006 (UTC)

Real, again

OK, it seems we indeed have a problem user, the same DYLAN LENNON, recently reincarnated as WAREL. See the last 100 entries in the history of real number. [5] He was also inserting things at Proof that 0.999... equals 1 and other places. Seems to know math, but has unreliable edits, and is very perseverent. I would like to ask some of you to put real number on your watchlist. So far, it was mostly Jitse and me (with Zundark and an anon) who tried to keep this user at bay. Don't quite know what to do about this. Oleg Alexandrov (talk) 17:02, 21 February 2006 (UTC)

Applying WP:3RR should at least alleviate the problem; I see it's been tried. Septentrionalis 05:57, 22 February 2006 (UTC)

Frivolous articles on little-used geometric terms

See ana (mathematics), kata (mathematics), and spissitude. I don't mind these being merged and redirected to some sensible place, but giving them individual articles tends to give the false impression that the terminology has some currency.

The articles fourth dimension and fifth dimension have related problems. From fourth dimension:

The cardinal directions in the three known dimensions are called up/down (altitude), north/south (longitude), and east/west (latitude).

Well, come on, no they're not, not in general. These articles all seem to take for granted that there's some sort of preferred coordinate system with respect to which we can name directions. I think fourth dimension and fifth dimension should be moved to four-dimensional space and five-dimensional space, respectively, and substantially rewritten to address this problem. --Trovatore 20:12, 21 February 2006 (UTC)

Those articles on ana and kata and spissitude are unlikely to get any bigger than the stubs they are now so they should be indeed combined in a single article describing the terminology.

About moving fourth dimension to four-dimensional space, that may be more complicated. That article is rather big, and is partially about the four dimensional space, but it has sections devoted exclusively to the fourth dimension. Food for thought. Oleg Alexandrov (talk)

I remember debating "the fourth dimension" with grade-school playmates; this is a valid topic for anyone who has no math education beyond addition and multiplication. It should be dealt with at that level. (I also remember hearing about "the fifth dimension" in some movie, or an Outer Limits episode maybe, and thinking "that script-writer got it all wrong, there ain't no such thing") linas 01:34, 22 February 2006 (UTC)

So what exactly can we sensibly and accurately say to such a person about "the" fourth dimension? Which fourth dimension? I think the article as it stands is just wrong; there is no sensible ordering of dimensions (though of course in GR spacetime there's a timelike dimension that can be distinguished from the other three spacelike ones). --Trovatore 03:33, 22 February 2006 (UTC)

Presumably, the fourth dimension would be one orthogonal to the 3-dimensional space we live in (whether it be a timelike dimension or a spacelike one). Whether or not such a dimension exists is debatable, but we can at least ascribe some meaning to the term. -- Fropuff 05:20, 22 February 2006 (UTC)

There isn't any unique 3-dimensional space we live in; there are various spacelike slices. Which one do you pick? --Trovatore 05:32, 22 February 2006 (UTC)

All of them, if you wish. Look, I'm not trying to say the term has a precise definition, but rather loosely binds some related ideas that people like to think about. The article doesn't fall completely within the scope of mathematics (or even physics) and shouldn't be treated as such. -- Fropuff 05:37, 22 February 2006 (UTC)

I'm not sure what's stated in the article has any clear meaning at all, mathematical or otherwise. That's my objection to it. --Trovatore 05:41, 22 February 2006 (UTC)

Well, I agree with you there. I'd say it could do with a complete rewrite (although I'm not volunteering). -- Fropuff 05:43, 22 February 2006 (UTC)

These are references to fairly notable speculations about a physical/psychological fourth (space-like) dimension; see Charles Howard Hinton or John William Dunne, I forget which. (I presume the reference to Henry More the Platonist is at least half true, however.) Cat as history of mathematics and forget about them. Septentrionalis 06:02, 22 February 2006 (UTC)

I had 4D in fairly good shape last time I had a stab at it. Pity it seems to have gone south from there... Dysprosia 06:09, 22 February 2006 (UTC)

Alas, its probably one of those articles which takes constant vigilence to keep the nonsense at bay. Sometimes I think the whole stable versions idea isn't half bad. -- Fropuff 06:21, 22 February 2006 (UTC)

Lists of PRNGs

I see that list of pseudorandom number generators ran into copyright trouble, and was deleted about a week ago . This really needs recreation, with more care to avoid whatever caused the trouble (something about the GNU manual, some eejit copying in too much). I can get back the old text, if someone wants to work on this. Charles Matthews 12:11, 22 February 2006 (UTC)

Just wrote a new stub. Dysprosia 12:21, 22 February 2006 (UTC)

Found the old text from the database dump, see talk page. Is it fair use to have copyvio material on talk page for discussion? --Salix alba (talk) 13:46, 22 February 2006 (UTC)

Better really not to have it back on the site, in the history. It is very likely still on some mirror sites, but perhaps with corrupt formulae and so on. I'll email the text to anyone who needs it. Charles Matthews 15:49, 22 February 2006 (UTC)

If this is GSL-related, then I want someone to explain to me why copying GFDL'ed material from a Gnu/FSF GPL'ed software is considered to be a copyvio. (I ask because there are a few other WP articles that have gotten take-down notices from the GSL authors, which were mostly ignored). linas 17:21, 22 February 2006 (UTC)

From what I can tell Wikipedia:Cleanup Taskforce/List of pseudorandom number generators it was not copyvio which led to its deletion, more just a case of list cruft, not meeting wikipedia standards for an article. Looking at the licence it is OK to include GFDL material, as long as its source is acknowledged. It might be better to take your Q to Wikipedia talk:Copyrights where they will know more on such issues. --Salix alba (talk) 20:15, 22 February 2006 (UTC)

According to the deletion log

• 22:30, 14 February 2006 Splash deleted "List of pseudorandom number generators" (GFDL article, but with front- and back-cover texts which WP does not permit per Wikipedia:Copyrights)

so I don't think the cruftiness is why it was deleted. It is a good argument against recreating it as it was, though; the stuff on the talk page does not look like a good article. I don't actually know what is meant by "front- and back-cover texts".) --Trovatore 00:58, 24 February 2006 (UTC)

"front- and back-cover texts" is a reference to an optional part of the GFDL, see http://www.gnu.org/licenses/fdl.txt. Dmharvey 01:08, 24 February 2006 (UTC)

A question about differential equations

Hi everyone. This is probably not the best place for this request, but seeing that no-one has replied to a question I have posted in the reference desk, I was wondering if anyone here would be so kind as to help me with a problem that has been troubling me for eons, thus earning my undying gratitude. -- Meni Rosenfeld (talk) 20:20, 23 February 2006 (UTC)

combined set theory

This, according to the author of the page Avrill, is a bit of original research, and Arthur Rubin and Trovatore agree, see here and here. So I prodded the article. After which Avril blanked the page (thereby removing the "prod" tag), meaning it is technically no longer a valid candidate for an uncontested deletion. However, I'm inclined to interpret Avril's blanking of the page as a request for deletion, but since I was the one who added the "prod" tag, I don't think I should be the one to delete it. Would some other admin please take a look and delete it if you think it is appropriate? Thanks. Paul August ☎ 23:56, 24 February 2006 (UTC)

You're being overly process minded. Blanking a page is a nonadmin way of marking a page for deletion, as is recognised in the speedy deletion policy. It's obviously the right thing to do, so just go ahead and do it. --- Charles Stewart(talk) 16:11, 25 February 2006 (UTC)

blahtex 0.4.3

is now available at http://blahtex.org/. The main changes are: now supports \color, support for \not is cleaned up a lot, and a few other bugfixes. The new version hasn't been installed on the test wiki yet (http://wiki.blahtex.org/) because Jitse is out of town for a while.

Also, the sample pages have been updated with the more recent dumps. I'm throwing in russian, chinese and hebrew now (ru, zh, he) as well.

Compatibility project update

More progress has been made with blahtex compatibility on Wikipedia. We are now down to 463 errors across 13 wikipedias. I know there's a few people working on this in the background; I'm starting to tackle some of the smaller wikis myself. It's a bit frustrating that the wikipedia dumps are updated so infrequently (most of them are almost a month old now), making it hard to locate equations that haven't already been dealt with. Therefore, for the convenience of people working on this project, I've written a script that pulls down (via CURL and Special:Export) a live copy of all equations which were broken in the most recent dump, runs blahtex on them, and produces an up-to-date list of errors. So this list will miss any brand new errors that showed up since the last wikipedia dumps, but I expect the number of these to be miniscule. I will try to run this script every few days, and the results will be kept at http://blahtex.org/errors.html, so we can monitor progress. Many thanks to those who have been helping with this. Dmharvey 22:05, 25 February 2006 (UTC)

341 and counting.... and it looks like both de.wikipedia and fr.wikipedia are finished. Good stuff folks! Dmharvey 13:46, 26 February 2006 (UTC)

Ruud for admin

Luck has it that we mathematicians are a close-knit bunch who do good work. :) I nominated another one of us (Lethe was promoted serveral weeks ago), for admin, namely Ruud. If you are familiar with Ruud's work, you can vote at Wikipedia:Requests for adminship/R.Koot. Oleg Alexandrov (talk) 04:00, 26 February 2006 (UTC)

what's happened to planetmath?

When I go to planetmath.org, I see a weird "coming soon" message and a link to a mysterious wiki. Does anyone know what's going on with that? -lethe ^{talk +} 08:01, 28 February 2006 (UTC)

Worksforme. Dysprosia 08:05, 28 February 2006 (UTC)

Weird. It's still not working for me this morning. -lethe ^{talk +} 14:47, 28 February 2006 (UTC)

Works fine now. Oleg Alexandrov (talk) 16:12, 28 February 2006 (UTC)

Mar 2006

recategorizing recreational mathematics

I've been being WP:BOLD with the subcategories of Category:Recreational mathematics. In particular I've emptied its rather ill-defined subcategory Category:Mathematical recreations and puzzles; a lot of its articles have found much better homes, but those that really did want to be somewhere under both Category:Recreational mathematics and Category:Puzzles I've put in one of a few joint subcategories such as Category:Mechanical puzzles. (Putting "puzzles" as a subcat of "recreational mathematics", as suggested on one talk page, isn't really an option: there are a lot of puzzles there that really aren't mathematical.)

While I was at it I also emptied Category:Puzzle games, which had an identity crisis as some people thought it was Category:Puzzle computer and video games while others couldn't tell it from Category:Puzzles.

Anyway, I expect I've offended innumerable people one way or another. If I've put your favourite article somewhere you don't think it belongs, please don't hesitate to move it (hopefully not into the categories I've carefully emptied). If you dislike the entire new categorization, please don't hesitate to argue with me about it. Though I can't imagine I've made things worse, since everything was categorized more or less at random to begin with. —Blotwell 14:35, 1 March 2006 (UTC)

Category:Mathematicians by religion

Category:Mathematicians by religion has a single subcategory, Category:Jewish mathematicians. I would think that being Jewish does not necessarily mean being religious. And do we actually need to categorize mathematicians on whether they were relegious, and if yes, what relegion they were practicing? Oleg Alexandrov (talk) 23:48, 1 March 2006 (UTC)

Being a jew does not, of course, make one religious, any more than being a christian makes one religious. So the categories' names do not imply that the mathematicians in question are religious - They just state to which religion they belong. And I think such categories are useful, in the same way that categories of mathematicians by nationality are useful. But obviously, additional categories for other religions, not just judaism, are in order for it to be meaningful. -- Meni Rosenfeld (talk) 07:19, 2 March 2006 (UTC)

I note that Category:Christians in science is applied both to Blaise Pascal, a Christian writer, and Bernhard Riemann, where as far as I can see it does little. I didn't much like like classifying mathematicians by nationality, when it came in; but it was inevitable with the growth, and the issue of several nationalities has the solution of including all of them. There are problems with all such classifications, and I'm not keen on them. Charles Matthews 09:05, 2 March 2006 (UTC)

Hmm, I wonder if Voltaire belongs in the Category:Christians in science, as, like me, his parents were Christian? I don't like this kind of categorization either; I think its basically some subtle political POV-pushing. May I suggest one possible cure: IF the person preached a religion (other than math) at one point in thier life, or published articles on faith (in newspapers, as letters to the editor, etc), THEN they may be classified by faith. However, if they had the bad luck of having Christian, or Jewish parents, that alone is not a reason to classify. I would insist on proof of religious activity before allowing classification. linas 14:49, 6 March 2006 (UTC)

french spelling

Um, I don't actually know french, but I thought only the first "e" in "etale" had an acute accent. So is this edit incorrect? Dmharvey 03:11, 2 March 2006 (UTC)

I think in this context, it's correct: the term in Hartshorne is "éspace étalé". Ryan Reich 03:30, 2 March 2006 (UTC)

So how do you know when it's étale and when it's étalé? Dmharvey 03:36, 2 March 2006 (UTC)

As far as I can tell, it's étalé here, and étale for morphisms. "éspace étalé" means roughly "slackened space", or "stretched-out space", which is reasonable given what it is, while an "étale morphism" is simply a "slack morphism". The metaphor is roughly the same, in that the slackness refers to a space constructed from layers laid out flat, and the grammatical difference distinguishes the "slackened space" constructed from something which was not, of itself, slack, from the "slack morphism", which is inherently so. Of course, "éspace étalé" is not used much anyway. Ryan Reich 03:56, 2 March 2006 (UTC)

It is certainly espace (not *éspace) étalé in French, but this leaves open the question of what the English translation of this expression is. I had been under the impression that it was called the étale space nevertheless, but Google seems to support both usages. —Blotwell 05:12, 2 March 2006 (UTC)

Étaler being a verb, étalé is the past participle (has been spread out, roughly). My MicroRobert says étale, adjective, can be applied to the sea as 'calm', when the tide is about to turn. We have been using sheaf space for espace étalé, which is not so common in English. HTH. Charles Matthews 09:13, 2 March 2006 (UTC)

• Please continue with sheaf space. Septentrionalis 21:08, 6 March 2006 (UTC)

After a check in the "Annales de l'Ecole Normale Supérieure", the good term is "espace étalé". --pom 11:18, 2 March 2006 (UTC)

Location of "elementary function" article

I think Elementary function (differential algebra) should be moved to Elementary function, currently a disambiguation page with little value. Despite the title, said article covers the concept of elementary functions in the general sense. Fredrik Johansson 23:50, 2 March 2006 (UTC)

I think it would simplify a few links and a line could be added to the article pointing to the list of common functions. When Elementary function (differential algebra) was created what is currently List of mathematical functions was in an article called Elementary functions, so I had to create something else. XaosBits 02:10, 3 March 2006 (UTC)

Could someone execute the move? Fredrik Johansson 04:56, 6 March 2006 (UTC)

Definition of General Linear Group

Charles Matthews and I are having a discussion about the correct definition of general linear group. It might be useful to have more input. The question is whether it should be defined initially in terms of rings or fields. Talk:General_linear_group A5 22:19, 4 March 2006 (UTC)

LaTeX

I have created a template to tag articles in need of LaTeX formatting. My concern is that it uses the LaTeX logo, which may or may not be a problem. The image was created using LaTeX, and using LaTeX to create images like ${\frac {q}{2}}$ doesn't seem to be a problem; yet, the image is still a logo with questionable copyright status. I was wondering what everyone else thought? Isopropyl 00:04, 5 March 2006 (UTC)

I would like to note that per the math style manual html formulas are perfectly acceptable (unless they look awful, like Σ_i=1ⁿ). It is also advised that one not modify somebody else's formulas by converting them from HTML to LaTeX or viceversa.

In fact, formulas which become PNG images may actually be preferrable in HTML, as then they show up as text, and look better on the page, also per the math style manual.

All in all, I don't see any pressing need for putting the {{LaTeX}} template on articles which are properly formatted, but only in HTML. Of course, one may use this template for articles which have no formatting whatsoever, like people writiting x_2 or x2 without bothering to use proper markup or math tags. That's what I would think.Oleg Alexandrov (talk) 23:37, 5 March 2006 (UTC)

Thanks for your input! I'll keep it in mind in the future. What is your opinion on the logo used in the tag? Isopropyl 23:42, 5 March 2006 (UTC)

Should a page use a combination of LaTeX and HTML formatting, or should its use be consistent throughout an entire article? I have tagged sections with {{LaTeX}} when the section in question deviated from the precendent set by the rest of the article. Isopropyl 23:45, 5 March 2006 (UTC)

I don't quite know, and for myself I would be fine with a mix. But if you find it stylistically ugly to have html mixed with LaTeX, then a better solution would be maybe to just convert the html to LaTeX right away, rather than put a "work needed" template on it and hoping that a kind soul would do it some time. There is a huge amount of articles needing serious work, as listed at Wikipedia:Pages needing attention/Mathematics, and I think that labeling an article as needing work because of TeX/HTML inconsistency would be probably not good. Cheers, Oleg Alexandrov (talk) 23:57, 5 March 2006 (UTC)

I agree with Oleg. Paul August ☎ 01:48, 6 March 2006 (UTC)

Most linked to and least linked to maths articles

I've been playing around with the database dumps and extracted the most links and least linked mathematics articles.

• top linked maths articles
• orphaned maths articles
• maths redirect frequency

The top linked articles might be useful for directing our efforts as these are probably most visited pages. The orphaned articles and redirects could help with some housekeeping. For example there is Squircle which seems quite dubious, and there are several highly linked redirects which indicate a need for some topics to be expanded. --Salix alba (talk) 13:54, 6 March 2006 (UTC)

Heh. Pi has 314 links... Ryan Reich 14:15, 6 March 2006 (UTC)

No way.... Dmharvey 14:33, 6 March 2006 (UTC)

And it holds slot 77 which is almost pi/4. linas 15:31, 6 March 2006 (UTC)

I wonder about the correctness of these lists. I was browsing the "orphaned" list and I was very surprised to see Stone–Weierstrass theorem, which of course is linked to from many articles. Paul August ☎ 17:15, 6 March 2006 (UTC)

It is quite a tricky job, especially where redirects are concerned. For Stone–Weierstrass theorem the only pages which link directly to it are 6 redirect pages [6]. For some technical reason, I've not included redirects in the count of articles. So these lists are the bests my little scripts can produce at the moment. If people feel the need, I'll try to update them to get closer to a real number. In the case of Stone–Weierstrass, I'd actually say the appearence in the list is a good thing. Looking closely, the hyphen in the article name is an odd unicode character (0xE28093) rather than a regular ascii hyphen (0x2D). I'd say this would be a good case for the article to be moved to the name with the ascii hyphen. --Salix alba (talk) 18:31, 6 March 2006 (UTC)

Ok I see. Yes I noticed the odd name. I think I will move the article. Paul August ☎ 19:51, 6 March 2006 (UTC)

• JA: I thought we were standardizing the use of ndashes, not hyphens, for conjoining names of distinct people, as distinguished from hyphenated names of one person. Jon Awbrey 20:04, 6 March 2006 (UTC)

Were we? I missed that. Why would we want to do that? Paul August ☎ 20:12, 6 March 2006 (UTC)

• JA: I'm sure I was directed to do that by some WikiPundit or other -- I just assumed it was to mark an obvious logical distinction for the sake of better hyper-indexing or sumting. Jon Awbrey 20:25, 6 March 2006 (UTC)
  • Somebody likes m-dashes and n-dashes, hardcoded by use of &mdash; and &ndash; and goes through substituting them. I'm not sure why; portability, maybe? Septentrionalis 21:13, 6 March 2006 (UTC)
    • I think I would strongly oppose that policy, on ground of human nature. Most editors will use the ascii hyphen, never get to see the policy on ndashes, leading to the same redirecting problems we have seen on Stone–Weierstrass. --Salix alba (talk) 21:31, 6 March 2006 (UTC)
      • Well, I haven't seen these improvements in article names; only in text. But there does seem to be a tendency to avoid hyphenated article titles: loan word not loan-word. Septentrionalis 23:26, 6 March 2006 (UTC)

• JA: YARTIW (yet another reason to ignore wikipundits). Jon Awbrey 21:40, 6 March 2006 (UTC)
• dear reader, for a more complete view of the status of the discussion, please do have a look at User_talk:Jon_Awbrey#En-Dash_Protocol_Reigning_Over_Polynominal_Titles_.28EDPROPT.29

Endashes

I knew we'd have to discuss this one eventually. The arguments for the A-endash-B theorem if A and B are two people are (a) it parses uniquely if you don't happen to be able to recognise double-barrelled names, and (b) it is a more professional piece of format. I would, however, always recommend creating [[A-hyphen-B]]'' first, as a precaution, so as to pick up any hungry red links; and only then move to the endash version. Charles Matthews 21:58, 6 March 2006 (UTC)

Yeah, I didn't like it at first, but after thinking about it (and looking at typeset documents) I have to agree. Not so much for the unique parsing, which is a good argument in principle but not so much in practice (you can't reliably conclude that Burali-Forti is a single person just because the article is at Burali-Forti paradox, even assuming you do notice the difference in the length of the dash/hyphen, which I wouldn't have if it hadn't been pointed out). But the endashes really do make the title look more like typeset documents and less like Usenet.

Maybe someone could send a bot around to look for article names that are duplicates except for the hyphen-endash distinction (these should always redirect to the same place), and for articles with endashes with no corresponding hyphen redirects (redirects should be provided). --Trovatore 22:24, 6 March 2006 (UTC)

Agreed. Some folks care as much about typographical niceties as mathematicians care about proof validity, or musicians care about pitch correctness. Lack of personal interest or awareness of these subtleties is no good excuse for hostility toward the interests of those who do care. Accents and quotation marks are another common battleground. With redirection, there is no need to fight. The hypen-redirects-to-dash idea seems like a reasonable compromise. --KSmrq^T 22:26, 6 March 2006 (UTC)

• dear reader, for a more complete view of the status of the discussion, please do have a look at User_talk:Jon_Awbrey#En-Dash_Protocol_Reigning_Over_Polynominal_Titles_.28EDPROPT.29

Three forms of mathematical induction

This article was intended to be comprehensible to all mathematicians.

It was not intended to teach mathematical induction. It was not intended to explain what mathematical induction is, nor how to use it.

It was nominated for deletion by those who did not understand it. To some extent, they did not understand it because it was a stub and failed to explain what audience it was intended for and what its purpose was.

A bunch of (mostly) non-mathematicians looking at the stub form in which the article appeared when it was nominated from deletion saw that

• It was not comprehensible to ordinary non-mathematicians who know what mathematical induction is, and

• The article titled mathematical induction is comprehensible to ordinary non-mathematicians, even those who know --- say --- secondary-school algebra, but have never heard of mathematical induction,

...and voted to delete.

And so I have now expanded the article far beyond the stub stage, including

• Substantial expansion and organization of the introductory section.

• Two examples of part of the article that is probably hardest to understand to those who haven't seen these ideas.

• An prefatory statement right at the top, saying that this article is NOT the appropriate place to try to learn what mathematical induction is or how to use it, with a link to the appropriate article for that. It explains that you need to know mathematical induction before you can read this article.

Therefore, I have invited those who voted to delete before I did these recent de-stubbing edits, to reconsider their votes in light of the current form of the article.

I also ask others here to vote on it by clicking here.

(Nothing like nomination for deletion to get you to work on a long-neglected stub article!) Michael Hardy 23:42, 6 March 2006 (UTC)

WAREL

My assumption of good faith in User:WAREL (formerly User:DYLAN LENNON) is being sorely tested. I know I'm not the only one who has wasted a lot of time over the past few weeks dealing with him/her. I'm wondering whether anyone else here has any thoughts about how to deal with WAREL, short of deploying an automatic WAREL-edit-reverting-bot. Dmharvey 18:00, 7 March 2006 (UTC)

For context, see the following article histories Decimal representation, Real number, Twin prime conjecture, as well as User talk:WAREL (Link to today's version, as WAREL likes to delete things he does not like. See especially the bottom section.) Oleg Alexandrov (talk) 19:47, 7 March 2006 (UTC)

I left a comment at Wikipedia:Administrators' noticeboard/Incidents#Disruptive_contributor to_mathematics articles. Oleg Alexandrov (talk) 05:47, 9 March 2006 (UTC)

al-Khwarizmi

This isn't about mathematics, but it is about a mathematician. Anybody who has spare time and is willing to read a long talk page is kindly request to comment on the dispute regarding al-Khwarizmi's etnicity at Talk:al-Khwarizmi. Cheers, —Ruud 14:49, 9 March 2006 (UTC)

How about showing the whole lot of them the way to Wikinfo, which wants editors like that? ;-> Septentrionalis 19:24, 9 March 2006 (UTC)

Somehow I doubt that most persons involved are interested in updating his biography beyond the first two sentences. —Ruud 19:30, 9 March 2006 (UTC)

Articles for the Wikipedia 1.0 project

Discussion moved to Wikipedia:WikiProject_Mathematics/Wikipedia_1.0 Tompw 16:40, 13 April 2006 (UTC)

Wikipedia talk:Scientific peer review

Notice: interested contributors may wish to participate in the Wikipedia talk:Scientific peer reviews by working scientists.

--Ancheta Wis 17:10, 11 March 2006 (UTC)

Can you guys have a look

Gallagher Index is a Political Science article and subject. But currently it could probably do with a mathematicans eye (alongside a few more things as well). Essentially, is there a neater or nicer way of doing the table at the bottom as an example of how the index is generated? Cheers, --Midnighttonight 08:47, 13 March 2006 (UTC)

Categorizing articles

On my suggestion, Salix alba made a list of Wikipedia articles which are not categorized, but which are linked from a math article. That list has a bunch of false positives, but also articles which are math and are not categorized. I suggest we start a cat wiki-pet (short for a Categorizing Wikiproject), going through those articles and categorizing them.

I split the list into 47 sections of 50 articles each. One may choose a section to work on, and sign at the bottom when done. I did the first three, and found roughly 3-5 articles out of 50 which may need categorizing. See the list at User:Salix alba/maths/uncategorised maths. Oleg Alexandrov (talk) 20:14, 14 March 2006 (UTC)

I don't know much about the category system, but if I just tag relevant articles with Category:Mathematics, is that enough to get them on the radar? (i.e. should I mark a section as "done" if I do this?) Dmharvey 03:03, 15 March 2006 (UTC)

I'd shoot for at least one level more specific than Category:Mathematics. The names of the big categories are pretty intuitive: Category:Algebra, Category:Mathematical analysis, Category:Mathematical logic, Category:Geometry, Category:Topology, Category:Number theory. Just make sure to remember the "mathematical" before "analysis" or "logic". --Trovatore 03:16, 15 March 2006 (UTC)

Sometimes one can pick the right category by looking at the articles going from the current one. But yes, putting them in Category:Mathematics is a good first option. Then my bot will list them to the list of mathematics articles, so more people will see them and may refine the categorization further. So yes, marking a section as done if the articles there are listed in some category is good, thanks. Oleg Alexandrov (talk) 03:18, 15 March 2006 (UTC)

ok guys thanks Dmharvey 03:27, 15 March 2006 (UTC)

I made the sections be 20 items rather than 50, as those were too big I think. To continue with the note at the top of this section, the person who does most work will get a cat as a wiki-pet (the Wikipet which anybody can touch (and edit)). Oleg Alexandrov (talk) 05:08, 15 March 2006 (UTC)

Oleg, you are SO going to award it to yourself. That is, like, so totally not fair. Dmharvey 19:48, 15 March 2006 (UTC)

Not all is lost, the race is still fully open! By the way, if you look at my bot's changes page, you will see a good harvest of math articles for March 15. Awesome work! Oleg Alexandrov (talk) 03:37, 16 March 2006 (UTC)

Now, I eager to get the wiki-pet, reviewed a section, categorized around 10 of the 20 there, felt good of myself, and when I got to editing the section to say "done", I see the section was done already! Dmharvey, now that's unfair. :) Oleg Alexandrov (talk) 04:55, 16 March 2006 (UTC)

Perhaps people should mark their territory -- in a nice way -- at the top of the score of items when they start work on it? Jon Awbrey 05:00, 16 March 2006 (UTC)

I doubt it is worth it; I meant it to be a silly joke rather than a complaint. Oleg Alexandrov (talk) 05:01, 16 March 2006 (UTC)

$''\!$ Jon Awbrey 05:32, 16 March 2006 (UTC)

Cheaters!!!! Hey, I noticed that some of the "finished" sections are still contain uncategorized articles. Even if the article is not about math, please do make an effort to put it into some category, somewhere!!! linas 01:08, 18 March 2006 (UTC)

Be my guest, my friend. :) Oleg Alexandrov (talk) 02:10, 24 March 2006 (UTC)

History of human knowledge about pi

This is the new title of History of pi. Even I think this is pædantry, so it may be over the top. Can we discuss this here, away from the Pi day crowds? Septentrionalis 00:48, 15 March 2006 (UTC)

"History of pi" deserves an article. To think that a table of the history of numerical computation of pi is the same thing as a history of pi is very silly. I've moved the table to another article, and labeled this article a stub. Michael Hardy 01:40, 16 March 2006 (UTC)

Agree w/Michael. I remember reading, as a young student, of plenty of interesting snippets about Egyptians knotting strings, silly legislation in kansas about pi=3, and what not. It deserves an article. linas 22:26, 17 March 2006 (UTC)

LOL... I remember adding that to (what is now called) Chronology of computation of pi (see under 1897), except the reference I have is for Indiana not Kansas. Dmharvey 22:34, 17 March 2006 (UTC)

MathWorld

Hi guys,

I was wondering why I can find so many maths-related articles here that do not reference relevant pages from MathWorld. I'm not sure what their license model is, but I can only assume that this is the reason why it's not popular around here? Please let me know if you think including their articles as references is a desirable thing. I'm watching this page, so do reply here. - Samsara (talk • contribs) 13:18, 15 March 2006 (UTC)

Obviously, we can't include relevant sections of MathWorld articles, as that would be a copyright violation. The reason for not referencing MathWorld articles is probably the uneven quality (yes, even by our standards) and the presence of clear errors (possible copyright traps) and probable neologisms. (I don't think the neologism being published as part of Mathematica makes it any less a neologism.) — Arthur Rubin | (talk) 13:56, 15 March 2006 (UTC)

I agree with Arthur and the reasons he provides. A policy of providing links to mathworld just doesn't make sense for us. However, if you come across a particular article where they have a much stronger version, then certainly linking to theirs would be useful (even better: bring ours up to snuff). -lethe ^{talk +} 15:30, 15 March 2006 (UTC)

Yeah, making it a policy to link to mathworld does not make sense, but I would think we should be encouraged in making external links to mathwolrd on case-by-case basis when those links are relevant (not necessarily much stronger than ours :) Oleg Alexandrov (talk) 16:11, 15 March 2006 (UTC)

Just to clear up a possible misunderstanding: I was referring to the license model because Planet Math is more frequently linked to. Is quality really so divergent between the two? I'm not trained as a mathematician, so I admit my judgement is poor. - Samsara (talk • contribs) 16:17, 15 March 2006 (UTC)

We actually copy planetmath articles, see WP:PMEX, that's why we must refer to the original versions, per their site license. Oleg Alexandrov (talk) 16:21, 15 March 2006 (UTC)

I second Arthur's comments. Just in the past month or so, I've had to remove several external links to MathWorld because when I checked them out, I found out they contained major errors. Sometimes these MathWorld articles can be good, but other times, it looks like a real hack job. So it's definitely not good to just unilaterally add the MathWorld links. I think it best for editors working on particular articles in their area of knowledge to add the links they actually found the most useful. --C S (Talk) 10:20, 10 April 2006 (UTC)

Please vote on this proposed deletion

at Wikipedia:Articles_for_deletion/Proof_that_22_over_7_exceeds_π#.5B.5BProof_that_22_over_7_exceeds_.CF.80.5D.5D.

The delete votes seem to be from non-mathematicians who erroneously think they understand the article. The main idea is this:

$0<\int _{0}^{1}{\frac {x^{4}(1-x)^{4}}{1+x^{2}}}\,dx={\frac {22}{7}}-\pi .$

Therefore 22/7 > π.

But the article also includes exposition, discussion, and mention of the appearance of this problem in the Putnam Competition.

One "delete"-voter says this is no more significant than, for example, a proof that π > 3.14159 or the like. The fact that 22/7 is a convergent in the continued fraction expansion of π seems to mean nothing to that person or to escape his notice altogether. The fact that this particular integral is so simple and has a neat pattern also seems to escape them. Another shows signs of thinking that all articles on π-related topics should get merged into one article (see list of topics related to pi). Michael Hardy 02:22, 16 March 2006 (UTC)

arXiv

So what's the deal with linking to the arxiv? This has come up quite a number of times in the last little while. Someone has gone trigger-happy recently on some papers there by Diego Saá, and it took a lot of convincing to get User:WAREL to stop linking there. (Or maybe he/she is still at it.) I would think generally such papers do not qualify for linking from Wikipedia, unless there are very good reasons to the contrary. Somehow a link to the arXiv has an air of respectability that you don't get from your home page on geocities etc, but it's not deserved, and we shouldn't be misleading people into thinking that the arXiv is a reliable resource. Dmharvey 02:16, 17 March 2006 (UTC)

I agree. One should only use references to books and peer-reviewed journals. Oleg Alexandrov (talk) 02:54, 17 March 2006 (UTC)

That's not how it works in mathematics research, and I see no reason why Wikipedia should adopt stricter rules for citations in its mathematics articles than most of the mathematics community itself. Wikipedia would only be shooting itself in the foot. --C S (Talk) 05:08, 25 March 2006 (UTC)

Well, we should prefer refereed references. Of course for journal references that are also on the arxiv, we should provide an arxiv link (not everyone has access to an academic library). Furthermore, there are worthwhile things on the arxiv which don't get published in journals. A lot of times, Witten, for example, publishes a lot of his papers only through the arxiv, he doesn't feel that journal referees are qualified to vet his papers. And there are précis on the arxiv which are very good resources but not original work, and therefore not appropriate for journals. But of course, there is also crackpottism on the arxiv, so care is certainly required. -lethe ^{talk +} 04:07, 17 March 2006 (UTC)

You definitely need a lot of care when citing papers by a guy who "doesn't feel that journal referees are qualified to vet his papers". :) Oleg Alexandrov (talk) 15:49, 17 March 2006 (UTC)

That is a dangerous attitude; but in the case of Witten I suspect many of the referees would agree, and are probably relieved that they do not have to try to keep up! --KSmrq^T 16:17, 17 March 2006 (UTC)

Off-topic: but Alexander Grothendieck stopped publishing in journals as well. linas 23:32, 17 March 2006 (UTC)

The arXiv is mostly reliable, except for the general mathematics (GM) section which is where the crank articles seem to get listed. I removed all the links to Diego Saá's papers that I could find; they were added by User:Diegueins, who claims to be his son. R.e.b. 05:57, 17 March 2006 (UTC)

In the last six months, I have found there a paper proving P=NP and another proving P$\neq$NP. No comments... pom 16:18, 18 March 2006 (UTC)

Please sign up on the participants list!

If you have this talk page on your watchlist, then you should add your name, field(s) of expertise and interests to the Wikipedia:WikiProject Mathematics/Participants page! I know there are some newcomers who haven't yet signed up, and I suspect there are some old-timers as well. linas 22:15, 17 March 2006 (UTC)

I meant to sign up at some point, but I glanced over the list and, frankly, many of you guys seem to be so good that it's kind of scary (I'm only an undergrad student) :-) - only half joking. But now, if you say so... AdamSmithee 00:20, 18 March 2006 (UTC) And after signing up, I see that my nick and the alphabetical ordering puts me on top of the list :-D AdamSmithee 00:28, 18 March 2006 (UTC)

I would join but you see, I'm on vacation. Good luck to you all. -- 127.*.*.1 01:17, 18 March 2006 (UTC)

Let me also add, feel free not to add yourself to that list or any others, for any reason. I myself don't see what purpose the list serves, and don't like adding myself to lists like that, though I did so eventually. -lethe ^{talk +} 03:41, 18 March 2006 (UTC)

Obviously the list doesn't have any kind of official status, but it does create a kind of community, as well as crystallizing one's own role in the Mathematics project in one's own mind. Mostly it seems sort of like the ritual of everyone gathering in a circle and placing hands one above another to seal a pact. And I'd encourage AdamSmithee to put his name on the list simply because he feels out of place; doing so will put him correctly in place :) Ryan Reich 06:18, 18 March 2006 (UTC)

Actually, I got into a discussion recently about how many particle physicists there are working in WP; looking at the participants list help put a lower bound on the number. This is a lot like any department directory or phonebook or census: rarely looked at, but terribly useful when its really needed. That, and indeed, the community feeling of the historical "I was here" thing. In 20 years, the list may be interesting to review: "I remember old so-n-so." linas 02:58, 19 March 2006 (UTC)

Statistics on User:WAREL

I submit the following statistics as an argument to block WAREL for, I suppose, a few days.

User:WAREL was born 17th Feb 2006. He/she has a total of 242 edits since then. The following survey includes 99 of those edits (41%), plus a few of User:DYLAN LENNON's edits (WAREL is a reincarnation of DYLAN LENNON).

• Perfect number: 23 edits. At least 13 immediately reverted. Many prior edits by DYLAN LENNON going back to July 2005 -- generally not reverted
• Twin prime conjecture: 17 edits, all reverted
• Real number: 12 edits, 11 reverted (As DYLAN LENNON: 14 edits, 10 reverted)
• Decimal representation: 11 edits. 10 reverted.
• Zeta constants: 6 edits, 3 reverted
• Finite field: 6 edits, 3 reverted, the other 3 self-reverted
• Proof that 0.999... equals 1: 5 edits, all reverted
• Decidability (logic): 5 edits, all reverted
• Riemann hypothesis: 5 edits, 1 reverted
• Chen prime: 4 edits, 2 reverted
• Decimal: 3 edits, all reverted
• Halting problem: 2 edits, both reverted.
• Fermat's last theorem: 1 edit, reverted
• Soliton: 2 edits, both reverted
• Wiener's tauberian theorem: 1 edit, reverted
• Cousin prime: 1 edit, reverted
• List of real analysis topics: 1 edit, reverted

Of these 113 edits, there are at least 88 reversions, which is 78% of the edits listed above, or 36% of all edits logged.

He/she was even reverted twice on his/her own talk page.

WAREL has been reverted by at least 17 distinct editors: User:Jitse Niesen, User:JoshuaZ, User:Dmharvey, User:EJ, User:Schildt.a, User:Arthur Rubin, User:ANTI-WAREL, User:Oleg Alexandrov, User:Elroch, User:Mfc, User:Trovatore, User:Zundark, User:Fropuff, User:Fredrik, User:Paul August, User:KSmrq, User:Melchoir, many of whom you will recognise as being respected contributors to mathematics articles.

On the other hand, I note that WAREL has also made several nontrivial, non-reverted contributions to several mathematics articles: Riemann hypothesis, Perfect number, Hilbert's fifth problem, Perfect power, Proof that the sum of the reciprocals of the primes diverges. He/she also makes plenty of edits to articles in which I am not competent, especially relating to Japanese mathematicians and musicians. Therefore, in my opinion, a permanent block is not (yet) warranted, even given the fact that he/she was permanently blocked on the Japanese wikipedia.

Dmharvey 01:23, 20 March 2006 (UTC)

I wrote a note on his talk page a few days ago about his revertions at decimal representation, and Jitse wrote one today about perfect number (see User talk:WAREL).

I have a silly suggestion. How about writing a petition on his user talk page, telling him that if he engages in any disruptive activity again, at any article, he will be blocked for 12 hours? Then we could all sign it, and then, should he disrupt again, any of us administrators would be able to block him with a clear heart. Wonder what you think. Oleg Alexandrov (talk) 06:53, 20 March 2006 (UTC)

Your suggestion is not silly. I think it would be important to emphasise in this petition that although some of his/her contributions have been appreciated, his/her almost complete disregard for other editors' opinions is not. I've spent enough time on this now; if someone else writes it, I will sign it. Dmharvey 13:11, 20 March 2006 (UTC)

<math> rendering bug

Just noticed at perfect number (at the bottom of the section on odd perfect numbers), this math tag:

 <math>2^{4^{n}}</math>

is getting rendered as this html:

 <span class="texhtml">2<sup>4</sup><i>n</i></span>

to appear as:

 24n

.. which is clearly wrong.

I wasted some time tracking down the paper to check the clearly wrong result before realising that it was the rendering rather than the text that was at fault. I don't know if this is a well known bug, but a brief search on Mediazilla didn't throw up any candidates. I have reported it to the Wikitech-l mailing list mailing list. Hv 16:12, 20 March 2006 (UTC)

I've noticed this before. It's actually not a bug in the LaTeX => HTML converter. It has to do with HTML tidy, which is a program that processes the HTML after the converter is done with it. The correct translation would be something like 2^4ⁿ. I think what happens is that HTML tidy sees the second ^{and assumes that the author forgot the slash. So it inserts an extra slash producing 2⁴n}</sup>. Then it sees the next </sup> and can't find a matching ^{so it kills that one too. Finally the last} dies. This is just a theory, but I'm pretty sure that texvc gets the conversion right in the first place. Dmharvey 18:30, 20 March 2006 (UTC)

See for example http://bugzilla.wikimedia.org/show_bug.cgi?id=108. Dmharvey 18:35, 20 March 2006 (UTC)

Thanks for the pointer. Is this HTML Tidy we're talking about? Because if so I'm surprised there's no mention there that it is being used on WP. (I also had a quick browse of the HTML Tidy bugs database, and saw no related item there.) If not, can you point me at some details of the HTML tidy you mean? I'd like to track this problem further ... Hv 19:52, 20 March 2006 (UTC)

Yes, that's the Tidy I mean. There is a flag $wgUseTidy in the mediawiki source which enables use of HTML Tidy. I'm pretty sure they use it on WP itself. You could try asking User:Jitse Niesen, I know he's at least one person who's been thinking about Tidy recently :-) Dmharvey 20:16, 20 March 2006 (UTC)

Indeed, I do know about it. This is fixed in the current version of HTML Tidy, but that is not yet installed on the MediaWiki servers. Details are in mediazilla:599. I haven't yet seen your post to the mailing list (perhaps it's help up in a queue), but the solution is to upgrade HTML Tidy. -- Jitse Niesen (talk) 23:16, 20 March 2006 (UTC)

Cool, I even managed to find the changelog that fixed it ([7]) but I guess that's redundant now. (I also followed up with a "never mind" to my wikitech mail, so it may never get through to the list.) I look forward to the new version. Hv 23:23, 20 March 2006 (UTC)

Decimal representation or decimal expansion?

There is a discussion on which name is more appropriate at talk:decimal representation. Comments welcome. Oleg Alexandrov (talk) 03:39, 21 March 2006 (UTC)

Problem at transfinite number

There is an editor, User:Jagged 85, whom you may recognize as being interested in the contribution of Indian mathematicians. At transfinite number he has been making edits that attribute the concept to certain ancient Jaina mathematicians/philosophers. The evidence presented is, in my estimation, of the sort that would be accepted only by someone who either has an agenda, or who does not really understand the contemporary concept. I'd appreciate it if some interested folks would drop by and take a look. --Trovatore 21:46, 22 March 2006 (UTC)

I fully agree with your assessment. In fact, I'll go further: this is obvious crackpotism. Various ancient philosophers have made dubious or meaningless claims about infinity (I had found a quote by Aristotle stating that the number of grains of sands on a beach was "infinite"), but none of them corresponds to what we now view as transfinite numbers; and Indian mathematicians were so proud of their invention of the decimal system that they had fun writing very large numbers as cosmic cycles, and sometimes they confused them with infinity, but obviously this has nothing to do with the modern concept. I support any move toward removing the incriminated section. --Gro-Tsen 22:04, 22 March 2006 (UTC)

It is no more (and no less) nonsense than Galileo's work on infinite numbers, in which he found that the natural numbers were equinumerous with a subset (the set of squares) and recoiled in horror. It is not the transfinites. Septentrionalis 22:41, 22 March 2006 (UTC)

Well, if it could be documented that the Jaina had the notion of equinumerosity (as witnessed by one-one matching), that would already be a step in the right direction, though I still don't think it would be enough to use the word "transfinite". As I understand it the historical context is that Cantor didn't want to use the word "infinite" because he was talking about things that were not absolutely infinite. They were trans-finite, beyond a limit, but not in-finite, without limit. That last sentence may be a bit of retrospective etymology on my part, but I think it really is the basic idea, whether or not Cantor had that specific etymological reasoning in mind. --Trovatore 22:46, 22 March 2006 (UTC)

A section reviewing the general history of eastern and western ideas about infinity, including Aristotle's ideas, as well as Gaileo's shock, would not be out of place somwhere on WP. We do, after all, have Category:History of mathematics and the topic of infinity, just like the question "what is four dimensions", was a legit intellectual excercise over the millenia. No doubt Immanuel Kant had some pronouncemnts as well. linas 00:54, 25 March 2006 (UTC)

Never mind. That article exists, its called infinity, and the Indian stuff should be moved there. linas 01:02, 25 March 2006 (UTC)

Another tedious orthography question

Vladimir Arnold or Arnol'd? Vladimir Drinfel'd or Drinfeld? We should be consistent: and preferably across all references to them in WP. (In both cases we currently use the apostrophe sometimes, but far from consistently.) —Blotwell 06:46, 24 March 2006 (UTC)

For Арнольд, we may as well defer to the way it appears on his books and web page, "Arnold". --KSmrq^T 02:02, 25 March 2006 (UTC)

Transliteration of the soft sign ("ь")—which does not so much represent a sound as a modification—is problematic, and conventions vary. But for names, it appears that in a context like this, appearing before a consonant, it would typically be omitted. Wikipedia allows us to choose that one as primary, for the article name, and use redirects for the variants. --KSmrq^T 18:35, 25 March 2006 (UTC)

Springer Encyclopaedia of Mathematics

I just stumbled across the Springer Online Encyclopaedia of Mathematics it claims to be

the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. This online edition comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics

and seems to live up to its description. It seems like this could be a useful resouces for many articles. --Salix alba (talk) 00:14, 25 March 2006 (UTC)

Yes, and its pretty good too, at least for the 3-4 articles I looked at. I created a template fr this, which may be usd as the following (for example:) {{springer|id=f/f041440|title=Fredholm kernel|author=B.V. Khvedelidze, G.L. Litvinov}} which results in

B.V. Khvedelidze, G.L. Litvinov (2001) [1994], "Fredholm kernel", Encyclopedia of Mathematics, EMS Press

linas 00:47, 25 March 2006 (UTC)

Would be a good idea to add those entries to Wikipedia:Missing science topics. I will try to look into that these days. Oleg Alexandrov (talk) 06:45, 25 March 2006 (UTC)

First article I hit was the normal distribution [8] I was quite disappointed in that it doesn't have a single graph of it. That said, it'd be worth copying the index into a new article or added to the missing science topics. Cburnett 06:56, 25 March 2006 (UTC)

No, you can't do that; this came up before with MathWorld. It's a copyright violation.

The Springer encyclopedia seems pretty weak in set theory. --Trovatore 07:29, 25 March 2006 (UTC)

Also compare the article on Self-adjoint operator in WP to the one in Springer. Tell me which one is better.--CSTAR 14:45, 25 March 2006 (UTC)

Ours is definitely more self-adjoint:

C^*=C.

Oleg Alexandrov (talk) 19:30, 25 March 2006 (UTC)

Is it worth an article SpringerLink Online Encyclopaedia of Mathematics? --Salix alba (talk) 20:21, 25 March 2006 (UTC)

I would think it's probably worth an article (I never heard of it before this discussion, but we're not talking about something put up by some random hobbyist; this is Springer). The issue is how to write a neutral review that's not original research. That's a problem to which I have not thought of any good answer (it's why I slapped my own article on Kunen's book, Set Theory: An Introduction to Independence Proofs, with an OR tag). --Trovatore 20:53, 25 March 2006 (UTC)

See what reviews it has in the scholarly press. Scholar.google.com should have something (this should solve the Set Theory problem, anyway.) If that fails, it can be put in WP space, as a resource. Septentrionalis 21:26, 25 March 2006 (UTC)

They have a lot of great articles. They're beating us in a lot of areas, and already kick the crap out of mathworld (soon it'll be time to put mathworld out of its misery). However, have you seen their diagrams? Complete garbage! -lethe ^{talk +} 17:23, 26 March 2006 (UTC)

I have merged their lists of entries into the Wikipedia:Missing science topics. I highly doubt that this is a copyright violation in any way, as while their lists may be copyrighted (the order of entries I guess :), individual items in the list are not, and after merging together the mathworld links and the springer links and removing the bluelinks, little if any resemblance is left to their orginal lists.

By the way, I brought some order in that Wikipedia:Missing science topics by completing incomplete entries (mathworld had those), putting things in lowercase, regularly removing the bluelinks, and providing links to google search and google books for each entry. Those lists can be rather good at suggesting new redirects, new articles, or judging where we are lacking. Oleg Alexandrov (talk) 21:28, 26 March 2006 (UTC)

Actually, I will send Springer an email asking if they mind using their list as a resource for our redlinks list. Just to be safe. :) Oleg Alexandrov (talk) 00:19, 27 March 2006 (UTC)

I've looked things up in the library's copy one or two times; good to see I don't have to go all the way there now... :-) Anyone know if the online edition differs significantly from the one in print? Fredrik Johansson 00:32, 27 March 2006 (UTC)

none of the springer links seems to work. how does one get to it from the springer website? thanks. Mct mht 07:15, 5 April 2006 (UTC)

The Springer server is down every now and then. Will come back eventually. Oleg Alexandrov (talk) 02:36, 6 April 2006 (UTC)

blahtex 0.4.4 released

Major changes since 0.4.3 are:

• support for Japanese and Cyrillic in PNGs
• much faster PNG output, because we're using dvipng rather than dvips/imagemagick

Useful links:

• test wiki at http://wiki.blahtex.org (recently got attacked by spammers :-))
• page illustrating blahtex's features
• blahtex home page
• updated error list (currently 337 errors)

Dmharvey 14:10, 26 March 2006 (UTC)

The dx in \int f(x) dx doesn't look right in the MathML output (it's rendered "d x"). Fredrik Johansson 14:45, 26 March 2006 (UTC)

Which browser+version are you using? This was a known problem with earlier versions of Firefox. Dmharvey 14:48, 26 March 2006 (UTC)

Firefox 1.5.0.1. Fredrik Johansson 14:58, 26 March 2006 (UTC)

Hmmm... does the same thing happen at all font sizes? Dmharvey 20:54, 28 March 2006 (UTC)

Normal, no style, enlarged.

Essentially. Increasing the text size a few times doesn't change the absolute width (it stays at 3 pixels); it looks normal if I use an obscenely large font. By the way, the space gets one pixel narrower if I disable the page CSS style (but still looks too wide, though this could be in my imagination). See image. Fredrik Johansson 21:28, 28 March 2006 (UTC)

That's a bummer. Thanks for pointing this out. I looks like Firefox is interpreting the "d" and "x" as belonging in separate "frames" and doesn't want to overlap them; therefore because the "d" is italicised and tall, it pushes the "x" to the right. I'm not totally sure about this, especially since there's a one pixel overlap in your second example, but that could just be some rendering thing that happens after the frames have been positioned. I will put it on my list of bugs to pursue; it's probably something that the Firefox folks will need to deal with. Dmharvey 03:39, 2 April 2006 (UTC)

gradient issues

There is some disagreement on what to include in the gradient article. It is argued by some parties that it should be a disambig. Comments welcome at talk:gradient#Should gradient be a disambigutation page? Oleg Alexandrov (talk) 17:20, 26 March 2006 (UTC)

Programs for linear algebra illustrations

What programs would people around here recommend for making images to illustrate geometry and linear algebra concepts (and the like)? I'd like to manually input coordinates for vector arrows, line segments, points, etc., choose colors and line styles, and output the result to SVG. Eukleides looks good, but it doesn't do 3D and I need that. Fredrik Johansson 23:45, 26 March 2006 (UTC)

Matlab gives you complete control, 3D, and output to color EPS. Here is a (free) program which it seems outputs to svg [9]. May be more. Of course, Matlab costs money, but should be available at any university, if you are in academia. Here are some pictures I made with it. Oleg Alexandrov (talk) 00:16, 27 March 2006 (UTC)

Yeah, I have access to Matlab, but not at home (not conveniently, anyway). Fredrik Johansson 00:22, 27 March 2006 (UTC)

You could learn a scripting language and roll your own tool. It shouldn't be that difficult. Dysprosia 02:41, 27 March 2006 (UTC)

Next thing you build your own rocket in your backyard, and could as well write your own encyclopedia. :) Oleg Alexandrov (talk) 04:03, 27 March 2006 (UTC)

Been there done that SingSurf, good for algebraic surfaces. It relies on JavaView which is quite good for 3D maths and is free as in beer but not speach. Also see Interactive geometry software for others. --Salix alba (talk) 12:04, 28 March 2006 (UTC)

IE compatibility

I wonder what people think of a policy of changing unicode html tokens to tex tags in order to ensure compatibility with Internet explorer browsers which apparently have problems with some unicode symbols. I guess compatibility with IE takes precedence over our own MoS guidelines, right? What do you folks say? -lethe ^{talk +} 11:53, 28 March 2006 (UTC)

We shouldn't use Unicode gratuitously in articles anyway. Unicode is far from being a ubiquitous standard, and when someone tries to edit in something that isn't Unicode capable, it screws up the entire article. That's not good behaviour. Dysprosia 11:57, 28 March 2006 (UTC)

When I work on my Windows laptop I don't see some Unicode characters on Wikipedia, even though I use Firefox and not IE. I guess it is a problem of missing fonts more than browser.

Changing unicode to LaTeX may be a huge amount of work, and may yield expressions which are a mix of both html and TeX. It would be fine I think if people do it on a case by case basis, but I would not be sure about making that a policy.

To comment on Dysprosia's comment, Unicode is a fact of life on Wikipedia given interlanguage links and foreign names/words. Luckily not that many browsers screw Unicode anymore, maybe just Lynx or really old browsers. Oleg Alexandrov (talk) 18:52, 28 March 2006 (UTC)

Well, I happen to use Lynx some times when I don't have access to a graphical browser, or (less often for me), when I use other operating systems I may use a browser that may not support Unicode. I'm not saying that Unicode should be completely removed from articles, it just shouldn't be used when there are other more portable equivalents out there that won't be mangled if someone edits with something that's not Unicode compatible. For example, one shouldn't just use a Unicode alpha when an α will be just as suitable. Dysprosia 22:55, 28 March 2006 (UTC)

I don't understand your example. Isn't that a unicode alpha that you've displayed? We shouldn't use unicode when unicode will suffice? -lethe ^{talk +} 23:04, 28 March 2006 (UTC)

No, it's a HTML entity, edit the section and have a look: &alpha; renders as α. Dysprosia 23:08, 28 March 2006 (UTC)

Oh, I see. But uh, don't the web browsers render the HTML tokens with unicode? I thought they did, and so therefore HTML tokens and UTF-8 text are equivalent (for viewing purposes). Or am I mistaken? -lethe ^{talk +} 23:11, 28 March 2006 (UTC)

The difference is that the Unicode alpha is just another character in the text, like "t", or "q". The HTML entity is the string "&alpha;". All good computer systems should support ASCII, and the HTML entity consists of only ASCII characters, so no matter if you use a computer that supports Unicode or if you don't, the string will be unchanged. However, some browsers that don't support Unicode simply ignore the Unicode characters, so if someone edits with one of those browsers, it will look like all the Unicode characters in the article have suddenly disappeared. If the browser chooses to render "&alpha;" with a Unicode character, that's fine, but it doesn't mean that that Unicode character is somehow equivalent to the HTML entity -- they aren't. Hope that explains things a bit better... Dysprosia 23:16, 28 March 2006 (UTC)

Yes, I understand now. UTF-8 text will get lost in the edit box by some browsers, even though it renders the same. Thank you for explaining. -lethe ^{talk +} 06:58, 29 March 2006 (UTC)

Replacing Unicode would be bad policy. This question was already decided when the wiki software switched over to UTF-8 as a standard. The world has gone Unicode, and that includes even standards-flouting Microsoft. To the best of my knowledge, all contemporary browsers can display Unicode characters if configured with adequate fonts. Usually Code 2000 will suffice. --KSmrq^T 21:29, 28 March 2006 (UTC)

I brought this up because some user went on a crusade to replace all instances of ℵ with $\aleph$ inline and display mode alike. I didn't like it, but apparently IE doesn't display ℵ correctly even if you have a font for it (which we learned because it displays if he changes web browser). -lethe ^{talk +} 23:08, 28 March 2006 (UTC)

PNG shouldn't be used inline. Dysprosia 23:10, 28 March 2006 (UTC)

That is also my opinion, but do we not have an obligation to lower our standards to support IE? Some might say we do. -lethe ^{talk +} 23:16, 28 March 2006 (UTC)

The HTML entity ℵ looks like it works... Dysprosia 23:25, 28 March 2006 (UTC)

Are you saying that ℵ displays differently from ℵ in IE? Septentrionalis told me once that he couldn't see ℵ correctly (I don't know for sure what setup he was using). --Trovatore 23:33, 28 March 2006 (UTC)

Doesn't work for me, either. I certainly prefer ℵ, regardless, as it's difficult to distinguish ℵ from the Hebrew letter by inspection if they were in Unicode, and those may display differently on different browsers. — Arthur Rubin | (talk) 23:36, 28 March 2006 (UTC)

I'm saying that ℵ should work on IE, that is, it should actually display. It shouldn't matter that much that it "looks different". I don't have IE so I can't check this. Dysprosia 23:56, 28 March 2006 (UTC)

I do not see the point of distinguishing ℵ from the Hebrew letter. Next we will be wanting an α different from alpha. I'm using a computer in the same cluster; both ℵ and ℵ now display well (and almost identically) in this IE set-up, but the second is a little square box in the edit window. Septentrionalis 00:08, 29 March 2006 (UTC)

alefsym definitely looks better alongside roman text than a Hewbrew aleph. The Hebrew aleph is too big. Do you not also find it so? -lethe ^{talk +} 07:05, 29 March 2006 (UTC)

I don't understand what you're talking about. If you want an aleph, you have ℵ, which actually does work. Dysprosia 00:10, 29 March 2006 (UTC)

OK, when I reboot into Windows to look at this in IE, I just see a square for the ℵ character. This is in IE 6.0.2900.someothernumbers, SP2, WinXP Home Edition, Version 2002, SP2. I suppose to really figure out what's going on I should say what fonts I have installed, but there are too many to conveniently list. --Trovatore 00:43, 29 March 2006 (UTC)

It's probably not a font issue, since if you try another browser on the same system, it will display. It's an IE issue. Now the question is, do we want to replace inline HTML token/UTF-8 with tex to support IE? -lethe ^{talk +} 07:05, 29 March 2006 (UTC)

I am the "user [who] went on a crusade to replace all instances of ℵ with $\aleph$". I was just replacing characters which I could not read with IE in those articles which I was trying to clean up for other reasons. alefsym causes the same problem as "ℵ" in IE. Also there is an element symbol which does not display correctly; and a proves symbol. Although these are rare. Oddly, I think that the actual Hebrew letter aleph works (at least I see the Hebrew letters OK in Google when I switch languages). JRSpriggs 05:24, 29 March 2006 (UTC)

Why do novices constantly "fix" things that obviously are not broken for most people? If the Unicode characters are in the article, there is nothing wrong with the characters for the author, and presumably for most readers. Adjust your own browser, your fonts, your configuration. Common sense and common courtesy suggest you at least ask before launching an ill-conceived massive alteration campaign—especially if you haven't been editing long enough to create a User page!

Suggestion: Look at this page and adjust the things under your control so you see as few missing characters as possible. (Note: For me, none are missing. Again, I highly recommend Code 2000.) This is a page in my personal user space; do not edit it! --KSmrq^T 07:07, 29 March 2006 (UTC)

I have been editing here for about two months. I did not create a user page because I have no interest in talking about myself for the public. I have a User-talk page to communicate about our shared work here. You are wrong to say that these characters are "obviously are not broken for most people". Most people use Internet Explorer 6.02 or earlier. So most of our readers will not be able to read the characters in question. And remember, this is an encyclopedia for the general public, not a private domain for you and the other authors to glory in their own words. Do not worry, I will not edit your user pages. JRSpriggs 07:33, 29 March 2006 (UTC)

Don't get defensive. KSmrq has a good point. We have a community here with established conventions. You can do whatever you like, make whatever decisions you want, decide what's the best format to use in articles, but we have the same rights, and in order to keep from devolving into continual revert wars, we try to respect consensus and community guidelines. When you've been here a while, you get a stronger feeling for that. Now, obviously you feel that wikipedia has to conform to IE's capabilities. Maybe you should try to win people over to your view instead of fighting with them. At the moment, I'm on the fence, but about to fall on the other side. -lethe ^{talk +} 07:43, 29 March 2006 (UTC)

Several distinct issues are at play. One is the recurring integration of novices into the community, with the usual exuberant misstep and jaded correction. A second is the display of the rich panoply of Unicode characters, whether mathematical or otherwise, in articles as viewed with a diversity of browers and fonts. Almost always the problem is with the fonts and browser settings. The Unicode characters are here to stay, especially when BlahTeX generates MathML for Wikipedia. A third issue is what appears in edit windows. The wiki software could be conservative and convert non-ASCII characters to named or numeric entities, but a browser that can display a page with Unicode characters can probably edit them as well.

But my point is none of these. I'm genuinely puzzled by the hubris of editors who assume that the article is broken because their view of it shows missing characters, especially when the same character appears in many articles. Do they think everyone else is stupid or blind? I don't know the statistics for Wikipedia readers, but one browser watch site shows slightly over 50% IE6 users, so it would seem reasonable to assume that many people had viewed any given Wikipedia article in IE6 without complaint. Yet these editors inexplicably fail to draw that conclusion.

Which leads to a design question: Is there anything we can do to head off these edits before they occur? The insert menu already shows a large assortment of non-ASCII characters, but obviously that's not enough of a hint to some editors. Should every article page have a prominent link to help with missing characters? --KSmrq^T 09:10, 29 March 2006 (UTC)

I know what we need. Here pages that use indic fonts include a template which indicates that they're being used and that if you want to view the page, you have to make sure your system is ready. If we want to use stuff in a math article which doesn't have widespread support, we could have a template like that one. That would probably keep new editors from changing font stuff, right? -lethe ^{talk +} 12:26, 29 March 2006 (UTC)

This page contains Indic text. Without rendering support, you may see irregular vowel positioning and a lack of conjuncts. More...

What about the difference between ''x''&sup2; x² and ''x''² x²? I'd say the latter looks better on my screen. --Salix alba (talk) 23:39, 29 March 2006 (UTC)

Only a few superscript characters have Unicode points, so consistency weighs in favor of the <sup> tags. For example, look at x²x³ = x⁵ versus x²x³ = x⁵. Similarly, a few special fractions have Unicode points, while most do not. For example, compare ¾ (entity frac34) to ³⁄₇ (using entity frasl, and tags <sup> and <sub>). --KSmrq^T 01:21, 30 March 2006 (UTC)

Move of "Ruler-and-compass constructions" to "compass and straightedge"

John Reid moved the article "Ruler-and-compass constructions" to "Compass and straightedge". As the article currently stands, I think there are problems with the new name. I intended to move the article back to its original name, until we can reach a consensus, but I inadvertently left out the hyphens and moved it instead to Ruler and compass constructions. Please share your views on any of this at Talk:Ruler and compass constructions. I will volunteer to make any necessary changes after we arrive at a consensus about what to do. Thanks — Paul August ☎ 17:58, 28 March 2006 (UTC)

Poll on "ruler" vs "straightedge"

Some of us can't agree on how to properly call the article Ruler and compass constructions, with the other option being Compass and straightedge. "Votes" at Talk:Ruler and compass constructions are solicited. :) Oleg Alexandrov (talk) 21:49, 29 March 2006 (UTC)

Neusis

Please see Jim Loy's angle trisection page. He shows a few methods using forbidden tools; I call your attention to the so-called tomahawk and to the movable, marked carpenter's square. Is the use of these tools not equivalent to neusis? John Reid 18:33, 31 March 2006 (UTC)

Please! Neusis? Yes? No? John Reid 19:59, 7 April 2006 (UTC)

Apr 2006

Parametric coords

Hi all. I saw there wasn't any article on parametric coords. I am willing to create one, if needed. However, since it might be the same thing as curvilinear coordinates, I've just put in a redirect for now. I've asked the question on Talk:Curvilinear coordinates, but so far nobody can tell me if they are identical, or just related, topics. Please take a look and post your conclusions at that talk page. StuRat 21:24, 1 April 2006 (UTC)

If someone does write the article, please don't use that name, but spell "coordinates" out in full. Ryan Reich 22:14, 1 April 2006 (UTC)

Absolutely. I do like to add redirects from short names to full names, though. This allows users to enter shorter words like "coords", "lab", "gym", etc., which are both more convenient and less likely to contain spelling errors. StuRat 02:31, 2 April 2006 (UTC)

Parametric coordinates really require a parameterisation, for example a parameterised curve or surface. For that reason I've now made parametric coords redirect to parametric equation. --Salix alba (talk) 09:40, 2 April 2006 (UTC)

Yes, but not all parametric equations describe a parametric curve or surface. Therefore I feel that an article specific to this application of parametric equations is justified. StuRat 02:29, 3 April 2006 (UTC)

Direct logic

Could someone take a look at Direct logic? I see some potential problems with this, given who the author is. —Ruud 16:01, 2 April 2006 (UTC)

IMHO, it looks like this is original research and doesn't belong. How does one tag an article to indicate as much?Lunch 18:42, 3 April 2006 (UTC)

Petition on WAREL's talk page

For background, see Wikipedia talk:WikiProject Mathematics#Statistics on User:WAREL several sections above.

Fresh out of his most recent 48 hours block, WAREL/DYLAN has been engaging in edit wars at field (mathematics) and division ring, moving, incorrectly, interwiki links from the former to the latter, see WAREL's contribs and DYLAN's contribs.

I wrote a petition on the top of his talk page asking him to stop revert wars, as this has been going for too long. If you are familiar with WAREL's edit warrior activity, and think that it's a bad thing, you may help by signing the petition. I doubt WAREL/DYLAN will learn anything from it, but it may give more legitimacy to future attempts at blocking him for disruption. Oleg Alexandrov (talk) 17:46, 3 April 2006 (UTC)

I've tried to figure out what this editor's motivation could possibly be, and my current working hypothesis is that he's engaged in a "destructive testing" experiment to figure out exactly how much it's possible to get away with before drawing blocks/RfC/permanent ban. Otherwise it's hard to understand why he keeps pushing just inside the edge of written rules, trying to get trivial changes kept, ones it's hard to believe he thinks would make any real difference.

Is it time to think about bringing the experiment to a successful conclusion? --Trovatore 21:06, 3 April 2006 (UTC)

Guys, make it an RfC. It's what that is for. Charles Matthews 21:35, 3 April 2006 (UTC)

I am currently editing Wikipedia:Requests for comment/WAREL -lethe ^{talk +} 22:30, 3 April 2006 (UTC)

I guess the RfC has to be certified by other people, so anyone who cares to, certify it. -lethe ^{talk +} 22:55, 3 April 2006 (UTC)

Great, thanks! I guess the RfC has been certified, I see a lot of names there. I now unblocked WAREL so that he can comment in the RfC. Oleg Alexandrov (talk) 00:04, 4 April 2006 (UTC)

DYLAN and finite fields

While I am not sure on what to do about the current dispute at field (mathematics), which is centered on the use of "field" at the Japanese Wikipedia, DYLAN LENNON now claims that a finite division ring is not the same as a finite field, and removed the interwiki link from our "finite field" to the Japanese "finite division ring". Comments welcome at talk:finite field. Oleg Alexandrov (talk) 18:57, 6 April 2006 (UTC)

My Muddle

I have frequently had an unpleasant experience when looking up mathematical terms in Wpedia. I go to the article I want and, reading the definition of the term, I encounter another term I don't understand. If there is a link connected to the term I open a new tab to find the definition of the second term. In reading the second definition I find the need to look up a third, then a forth, fifth, sixth. I am soon swamped by "hanging" definitions. But, not infrequently, a term is used without any attempt to define it. Do mathematicians write these articles only to communicate with other mathematicians? Surely an encyclopedia is meant to educate people about things they don't already know. Too Old 00:19, 7 April 2006 (UTC)

This is more or less of a problem depending on the topic in question and how much effort has been spent on writing it. If you mention it here, or on the discussion page of the relevant article, it's more likely to get fixed. Dmharvey 00:25, 7 April 2006 (UTC)

Hmm...I sometimes find that some calculus-related articles make more sense on Wikipedia than Wikibooks — Ilyanep (Talk) 00:38, 7 April 2006 (UTC)

Wikipedia is not meant to teach you the background knowledge you need. Wikipedia is an encyclopedia, not a collection of tutorials. If you want that, try Wikibooks. Dysprosia 00:40, 7 April 2006 (UTC)

Yes, it is good to keep things accessible, that means having relevant links to all concepts encountered. That of course does not mean it is Wikipedia's fault if you start reading an article about a term you don't know only to run into links to other terms you don't know. Wikipedia is (and should be) after all a loose collection of essays, not a course (and even for a course, you have prerequisites :) Oleg Alexandrov (talk) 01:08, 7 April 2006 (UTC)

An encyclopedia should not be of use only to a specialist, like a physician's medical database. An encyclopedia is, IMHO, meant to be a resource for the generally well-educated layperson, who might need the occasional definition, but definitely should not need a tutorial to understand an article. The background you speak of should not have to be extensive prior knowledge of the subject. When I consult, for example, the article on steel, I find an extensive treatment of the subject, occasionally having to find a definition, but not having to undertake a course in metallurgy in order to understand the article. When I go to look up a definition in that article, I need not go further and further afield in order to understand the definition. Too Old 01:37, 7 April 2006 (UTC)

An encyclopedia is a reference work, a collection of facts that are explained well and do not attempt to excessively mollycoddle the reader. You are comparing apples and oranges with your example of steel there -- mathematics, as well as certain other fields, are necessarily reliant on your accumulation of prior knowledge. A more apt analogy is expecting to understand an article on quantum spin. That article does not and should not teach you the basics of physics before launching into the actual article content, but it can give some motivation and make some simple insightful analogies. Dysprosia 01:52, 7 April 2006 (UTC)

I would like to dispute you on one point without arguing with the intent. The argument that "math is special" because it is more structured (or more rigorous, or constantly evolving, or any other argument I've seen used at various times) is very silly and I don't think it's good here. There are a lot of topics that can be covered with only elementary background. What do I mean by elementary? Well, read steel carefully and see what it assumes: right off the bat it talks about alloys, various chemical elements, technical ideas like "ductility" and "tensile strength", and the notion of atoms. All fundamental ideas in chemistry and physics. Too Old seems to have had no problem with these, yet I don't feel that this corpus of prerequisites is any larger than asking people to know calculus or Euclidean geometry. But I don't know that this was his problem, since he never said which articles he's found too technical.

I guess my point is that I feel like "math is hard" pulls too much weight around here even (especially!) when spoken by mathematicians. A reasonable article should assume the reader's knowledge of terms which form a language of discourse for the subject, so that each sentence need not be interrupted with definitions and qualifications, but anything that (in the context of the discursive standard) could be taken as technical should be explained. Rather than telling Too Old to go off and get an education, we should at least extract some productive information from his complaints and see what sort of stylistic changes might be needed around here. Ryan Reich 03:03, 7 April 2006 (UTC)

The companion matrix article, for instance, assumes you know what a polynomial is (and knowing what a polynomial is requires its prerequisites), knowing what a matrix is and the necessary basic matrix algebra necessary, plus a little more advanced matrix theory such as the characteristic polynomial is, diagonalizability, plus if you'd like to get through the rest of the article, assumes you know some basic field theory and linear algebra. There are articles and areas of mathematics with much worse prerequisites than that -- there are a lot of extremely deep areas, just pick something that is right near the bottom of that "depth". Mathematics does build on prior knowledge and decreeing this fact as "silly" doesn't quite make much sense.

No one is telling Too Old to "go off and get an education", though one should not blame the article for one's gaps in knowledge. Of course, a bad article can and does exist where it explains the concepts in an illucid way, and that of course should be fixed, but an article should not aim to teach the reader prior knowledge -- that responsibility is up to the reader, not the reference work. Dysprosia 03:43, 7 April 2006 (UTC)

My complaint was that the claim that math has special depths of prerequisites is silly. Go look at any science; they're just as bad. In particular, the use of this claim in this context, namely in response to someone who was almost certainly referring to articles that an amateur might be interested in reading, is silly, since such articles can without doubt be disposed of without using advanced concepts (of course, later in the article advanced ideas may arise. That has never been part of this discussion, though). In particular, I was not claiming that all math can be done at an elementary level (actually, I think I made allowances for the opposite). The example you give simply supports my contention that a common language be established at the start of the article. What might not be a good idea, in this particular case, would be for the article to introduce the theory of companion matrices in the context of modules over a PID, since it can be done more simply. This is the sort of distinction I'm making, yet I'll bet some people (I might be one of them, depending on my mood) will argue that the article should talk about companion matrices this way, since it's "more correct". That argument only works if it doesn't sacrifice clarity. Ryan Reich 04:12, 7 April 2006 (UTC)

I don't understand why you make the claim because I never did claim myself that math has "special depths of prerequisites" -- I said "mathematics, as well as certain other fields", and made special note that physics is just as bad. Otherwise I think we may be in violent agreement. Dysprosia 04:37, 7 April 2006 (UTC)

Oleg, you've absolutely hit the nail on the head. Dysprosia 01:52, 7 April 2006 (UTC)

Two sources of difficulty are obvious: (1) the structure of the subject, and (2) how it's presented. It is a fact of life that knowledge is a web, not linearly structured in dependency. Knowledge of A supports understanding of B, but also knowledge of B supports understanding of A. A writer of a text must work hard to order the presentation linearly, and at best achieve only partial success. Often a text read a second time will make more sense, because the additional context is available. A writer of a web article has no control over order of access. The only option is to include definitions, not just link to them; but taken too far, these intrusions become an obstacle themselves. Instead, some people use popups to get a quick look at a linked definition without opening a tab (or a window, in an antiquated browser). --KSmrq^T 01:24, 7 April 2006 (UTC)

Pop-ups are life savers (well okay time-savers) — Ilyanep (Talk) 01:31, 7 April 2006 (UTC)

We don't write our articles solely for mathematicians; we endeavor to make them as readable as possible. Accessibility is definitely a consideration for us. But only one of many, so sometimes an article is not as accessible as we might like. If you think the articles need help, then you know what to do. This is a wiki, be bold, edit. Complaining about the quality of some difficult work done for free by volunteers in their spare time is not going to win you any friends. -lethe ^{talk +} 01:57, 7 April 2006 (UTC)

For the record Talk:Hilbert_space#The_Layperson, Talk:Calabi-Yau manifold, Talk:Lie_group#is_this_useful.3F, some more examples of people with the exact same complaint. Happens a lot, I guess. If there were some magical way to easily write mathematics articles that were easy to learn, I would employ it in my writing. -lethe ^{talk +} 04:00, 7 April 2006 (UTC)

Per Ryan Reich, please make the complains specific. There are reasonable complaints, and there are unreasonable ones. :) Oleg Alexandrov (talk) 03:13, 7 April 2006 (UTC)

Well, it seems that I am not alone. But, people, I did not mean to attack your virtue. There was a suggestion that I should "be bold, edit". Were I 30 or 40 years younger, and had the resources, I might take up the serious study of mathematics. I then might find a way to rewrite some of these articles to make them more accessible. But, life is too short... I have had my say. I leave you now to play The Glass Bead Game among yourselves. If you have any thing to say to me I shall be happy to read it on my talk page, or you may email me. Too Old 07:11, 7 April 2006 (UTC)

Sorry, but sciences just aren't for everyone; you have to have a certain basic knowledge to be able to understand more complicated concepts in mathematics, physics, and so on. There's only so much we can do about that. —Nightstallion (?) ^{Seen this already?} 14:51, 7 April 2006 (UTC)

I think Too Old has a valid criticism, frequently repeated. The coverage of mathematics is often at too high a level, organisation of articles is confusing, core topics like Algebra are woefully inadaquate. Yes we have done good work todate, our coverage is extensive, but there is still a long way to go.

I propose creating Wikipedia:WikiProject Mathematics/Essential articles where we can identify which are the most important mathematics articles, assess then for quality and also mathematical level required. An example we could follow is Wikipedia:WikiProject Computer and video games/Essential articles which nicely organises that fields core material. This would also fit in with the Articles for the Wikipedia 1.0 project discussed above.

Is anyone interested in helping on this? --Salix alba (talk) 23:09, 8 April 2006 (UTC)

WAREL/DYLAN indef blocked

Well, the RfC and all our pleas seem to have no effect on his behavior. I blocked both accounts indefinitely, and wrote a note at Wikipedia:Administrators' noticeboard/Incidents#Indef block of WAREL/DYLAN LENNON.

This will generate serious questioning, as we are talking about an indefinite block, no less, so your comments there are appreciated, to make the case that this is a community-backed decision. Oleg Alexandrov (talk) 17:49, 7 April 2006 (UTC)

formal laurent series

Should formal Laurent series redirect to Laurent series (as it currently does) or to formal power series (my preference)? Dmharvey 18:20, 7 April 2006 (UTC)

I think formal power series is better, especially since the doubly infinite Laurent series cannot be treated formally (with rare exceptions). — Arthur Rubin | (talk) 18:52, 7 April 2006 (UTC)

Maybe the section on formal laurent series in the article Laurent series should be merged into the corresponding section of formal power series. -lethe ^{talk +} 18:54, 7 April 2006 (UTC)

Done. Dmharvey 17:03, 9 April 2006 (UTC)

references: multiple page numbers for same book

I've been trying out the new cite.php tool, i.e. with the <ref> and </references> tags. See for example quasi-finite field. But it looks a bit silly there, because I have two different page numbers for the same book. Does anyone know a slicker way to handle this? Dmharvey 18:22, 7 April 2006 (UTC)

David, I've made an edit at quasi-finite field, to suggest another way of handling your situation. However, I don't really like the look of the cite tool, I prefer the rf/ent templates, so I've also made a second edit using the rf/ent templates, to see if you like the way they look better. Paul August ☎ 21:49, 7 April 2006 (UTC)

I gotta admit I don't like any of the options very much. What I really want is something like LaTeX's \cite command, i.e. each reference gets e.g. a number or sequence of letters, and then you can specify the page number inline. So for example it would read like "according to [Se, p.198] you can do ..., or you can see later on [Se, p.204] suggests blah blah blah", and then in the references it just has one item, "[Se] Serre, Jean-Pierre, Local fields, etc". But it doesn't look like any of the automated mechanisms allow one to do this. Dmharvey 02:27, 8 April 2006 (UTC)

Solicit help organizing topics relating to approximation theory

I have recently created some material in the approximation theory page, relating to polynomial approximations to special functions. This is related to function approximation, Chebyshev polynomials, and polynomial interpolation, but in ways that I'm not clear about. I'm not an expert in the taxonomy of this area of mathematics, only in the specific things about which I wrote. In particular, I know that there is a field of interpolating polynomials through given data points, and that Chebyshev polynomials (and their roots) are involved in this. I can't believe that "approximation theory" is just about Remes' algorithm or use of Fourier/Chebyshev analysis to make optimal polynomials. So this whole area may be somewhat messed up, and my material might be in the wrong place. Would someone who knows his/her way around in this area be willing to take a look and move things around?

William Ackerman 00:40, 8 April 2006 (UTC)

Copies of long essay on multiple talk pages

User:BenCawaling has added apparently identical copies of a 2,500 word essay titled "About the incomplete totality of the infinite set of prime numbers" to the following talk pages:

Talk:Riemann hypothesis

Talk:Gödel's incompleteness theorems

Talk:Cantor's theorem

Talk:Cantor's diagonal argument

Talk:Bijection

Talk:Prime number

Talk:Fermat's last theorem

I don't think that Wikipedia is the right place for this diatribe, and we certainly don't need multiple copies of it - but as it's all on talk pages, I don't know what policy or guideline could be quoted in support of removing it. Does anyone have an opinion on what should be done about this (if anything) ? —Preceding unsigned comment added by Gandalf61 (talk • contribs) 11:41, April 8, 2006

I think we should remove it as a kind of spam. Paul August ☎ 15:36, 8 April 2006 (UTC)

Replace all but one of them with a link to the remaining one? Or replace all with a link to his userspace? -lethe ^{talk +} 15:37, 8 April 2006 (UTC)

I suppose any of these things would be OK, but there's a risk that it would constitute paying him too much attention. At least he's been good enough to confine his ramblings to a single section on each talk page, and as far as I've seen no one's bothered to respond. If it stays that way, maybe he'll get bored and go away, and the screeds will eventually pass harmlessly into archives. Of course if he were to start editing article pages, or injecting irrelevancies into other discussions on talk pages, then action might have to be taken. --Trovatore 18:32, 8 April 2006 (UTC)

You are right about the unnecessary multiple copies of some of my discussion text. I have just downloaded Wikipedia's "How to edit a page" and would make the deletions and links to one in "Prime number" article talk page. For now, you may do as you please with my "contributions".

You are wrong about no one's responding --- countless with positive reactions do in my Yahoo e-Mail address (I intentionally include it because, just like David Petry's last comments "As I see the situation now" in his "Controversy over Cantor's theory" article, the majority of Wikipedian administrators and editors are Cantiorian fanatics who (loking at their user pages (where there are any) are not at all mathematically qualified to discuss these stuff and whose best response is bad-name-calling (just read the next 3 messages) or appeal to their or their idolized "authoritative knowledge" but not actually refuting the arguments proferred even though they cite only elementary mathematics understandable by even honor high school students. The Yahoo e-Mail messages that I received confirms to me that Wikipedia articles are widely read by mostly amateur mathematicians or stidents. I was hoping to give them alternative understanding of the most controversial issues in modern mathematics to discuss with their professors.—Preceding unsigned comment added by BenCawaling (talk • contribs)

A better idea would have been to actually contribute to the creation or update of an article, instead of spamming multiple pages. By the way, thanks for insinuating that we are nothing but name-callers, then accusing us of being "Cantorian fanatics". Isopropyl 03:21, 14 April 2006 (UTC)

Crank spam. Delete. Charles Matthews 18:39, 8 April 2006 (UTC)

Agreed; delete. Talk pages are explicitly devoted to discussions about the article itself. --KSmrq^T 22:05, 8 April 2006 (UTC)

Agreed; crank spam. There is lots of that in talk pages in violation of the stated purpose of talk pages, unfortunately. However, in most cases enforcing this policy is probably a pain. In this case there's so much of it that it should all be deleted. So I guess the message to crank spammers is this: if you have something cranky to say, keep it short.--CSTAR 22:34, 8 April 2006 (UTC)

I have moved this essay to User:BenCawaling/Essay and replaced each copy on an article talk page with a link to its new location. Gandalf61 08:46, 14 April 2006 (UTC)

WAREL is back

This is getting interesting: two socks at the same time: [10] [11]. And an anonymous edit: [12]. Oleg Alexandrov (talk) 19:57, 8 April 2006 (UTC)

How sure do we have to be that these are him before we permban the socks? That's my inclination. -lethe ^{talk +} 20:32, 8 April 2006 (UTC)

I was under the impression that on-sight permabanning of socks was reserved to Willy on Wheels-level offenders. Isopropyl 20:40, 8 April 2006 (UTC)

Oleg, just do it. We'll pick up the pieces later. We can always apologize to anyone blocked by mistake; it's not like any huge permanent damage is done. --Trovatore 20:50, 8 April 2006 (UTC)

Oh, and by the way, this last incident should more than justify restoring the permanent ban on WAREL. --Trovatore 20:52, 8 April 2006 (UTC)

Someone made the comment that WAREL isn't learning anything from these repeated blocks. I think that if we keep unblocking him and he continues along the same path, we're the ones who aren't learning anything. Those who are about to block, we salute you. Isopropyl 21:25, 8 April 2006 (UTC)

I banned 64.213.188.94 (talk · contribs) indefinitely. -lethe ^{talk +} 22:33, 8 April 2006 (UTC)

I asked Lethe to shorten the block for a day, as IP addresses can be shared, unlike user names. On the more general problem, I start thinking that WAREL may actually not only be a highly arrogant user but also have some kind of compulsive disorder. In the worst case scenario he will play a cat and mouse game making new accounts just as we block them. No easy solution in sight. Oleg Alexandrov (talk) 00:25, 9 April 2006 (UTC)

Interesting common line of thought there. I almost posted a comment that when the permanent ban is put into place, a suggestion to seek psychiatric help should be posted on his user page. That would make it clear we have WAREL's interest at heart. On a practical matter, what IP addresses have the named accounts used by WAREL had? Elroch 00:56, 9 April 2006 (UTC)

Looking through the "contributions" of 64.213.188.94, from day one I see lots of silly vandalism and trolling of the worst sort, interspersed by occasional relatively lucid postings on the very mathematics subjects WAREL and DYLAN LENNON like to post, such as Perfect number and Masahiko Fujiwara. I also see some fascination[13][14][15][16] with one Doyle Farr, apparently a black student at Franklin Pierce College. Whether shared IP or not, I can't say that a permanent ban would be a big loss to Wikipedia. Lambiam^Talk 04:04, 9 April 2006 (UTC)

I don't think this anecdotal evidence makes a very strong case that the next person who tries to edit from that IP won't be a legitimate, good-faith contributor. Let's keep our responses targeted. OTOH I think immediate permanent blocks should be imposed on User:DEWEY and User:KOJIN and future recognizable sockpuppets as they appear. If we make a mistake it can always be corrected. --Trovatore 16:28, 9 April 2006 (UTC)

Length of an "arc" or of a "curve"?

At Talk: Length of an arc I added a comment arguing that the title ought to be Length of a curve (presently a redirect to Length of an arc). Please discuss there if you care (one way or another). Lambiam^Talk 03:18, 9 April 2006 (UTC)

{numbers}

Number systems in mathematics.
Basic
$\mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C}$ Natural numbers $\mathbb {N}$ Negative numbers Integers $\mathbb {Z}$ Rational numbers $\mathbb {Q}$ Irrational numbers Real numbers $\mathbb {R}$ Imaginary numbers Complex numbers $\mathbb {C}$ Algebraic numbers Transcendental numbers Transfinite numbers Split-complex numbers $\mathbb {R} ^{1,1}$
Complex extensions
Bicomplex numbers Hypercomplex numbers Quaternions $\mathbb {H}$ Octonions Sedenions Superreal numbers Hyperreal numbers Surreal numbers
Others
Nominal numbers Serial numbers Ordinal numbers Cardinal numbers Prime numbers p-adic numbers Constructible numbers Computable numbers Integer sequences Mathematical constants Large numbers Pi π = 3.141592654... e = 2.718281828... Imaginary unit $i^{2}=-1$ Infinity ∞

Here is the {{numbers}} template. Today is the second instance when somebody felt templated to insert it in all the articles linked in there (first time was a while ago). I feel this is the case when being in Category:Numbers is enough for these articles, and the gain given by this template in all articles is not offset by the huge size of the template and the distraction it causes on the page. Comments? Oleg Alexandrov (talk) 04:01, 10 April 2006 (UTC)

The template is certainly sort of obtrusive visually. On the other hand these are all articles aimed at a pretty elementary audience. Maybe it is useful for them to have this reminder of how the various sets of numbers fit together. Could we find some of them to ask? --Trovatore 07:39, 10 April 2006 (UTC)

This is an absurd template. How many times and places do we need to know about, say sedenions? Perhaps if the template limited itself to the basics it might be justifiable. --KSmrq^T 08:41, 10 April 2006 (UTC)

I agree. It's absurd. I'm very skeptical as to its utility even for the "elementary audience" Mike mentions. I would think an appropriately placed link to number systems or whatever would be better; I think we all know how to keep a brower window or tab open :-) --C S (Talk) 08:49, 10 April 2006 (UTC)

This is the sort of thing I made {{otherarticles}} for. Septentrionalis 22:31, 10 April 2006 (UTC)

Neusis again

I'm a bit miffed that my original post on this topic seems to have been blown by without comment. I'm not an expert and I really don't know the answer.

Please see Jim Loy's angle trisection page. He shows a few methods using forbidden tools; I call your attention to the so-called tomahawk and to the movable, marked carpenter's square. Is the use of these tools not equivalent to neusis? John Reid 01:57, 11 April 2006 (UTC)

Maybe it's just that no-one here knows the answer. Dmharvey 02:23, 11 April 2006 (UTC)

A curious fact of life in posting to forums like this is the extreme differences in volumes of responses questions can provoke, differences which sometimes seem to be independent of the merit of the questions. The answer to your question requires technical study of the tools in question. The general situation is that we know compass-and-straightedge constructions only allow solutions to linear and quadratic equations; the additional tools allow solutions to broader classes of equations such as cubics. This much every serious mathematician knows. However, it may not be obvious which additional classes any particular tool admits. For example, we know a number of different tools that can be shown sufficient to solve cubics (hence permit trisection); but that does not mean they are equivalent in power. So my short answer to your question is, "I don't know." If everyone who does not know the answer to a question posts a statement to that effect, we are overwhelmed with useless noise; therefore the convention is that only those who know (or, sigh, think they know) post — which in this case may be none of our regular readers. After a respectful amount of time with no response, it is acceptable to ask a followup question. A good followup: "Is there a problem with my question?" :-D --KSmrq^T 03:34, 11 April 2006 (UTC)

I believe the movable square is equivalent to neusis; I think, but am less certain, that the tomahawk is. I have no proof of either right now, which is why I haven't posted. Septentrionalis 03:55, 11 April 2006 (UTC)

(rolling eyes) Oh, that I should have asked mathematicians for opinions! "What color is that tree?" "It might appear to be some shade of green on the side that was visible at the time of obseveration." ;-) It really would be informative to hear a number of expert users say "I don't know."

It's okay. For the immediate, ugly, practical purpose of editing the project, it's enough that I think both are cases of neusis, Pmanderson suspects it, and nobody yet is ready to say they're not. That's enough information for me to proceed with my rounds. If an expert has more information later, well, we'll change it. Thank you. John Reid 18:22, 12 April 2006 (UTC)

Edit war over Jaina "mathematics"

Before I continue the edit war which has developed between "Jagged 85" and myself (with some others), I would like to bring the case to our community. Jagged 85 has been adding (what I consider) irrelevant material to several articles in the "Cardinal numbers" category (and I think elsewhere as well). I removed it once. Now he has put it back. This inspite of the fact that there is an already existing article on Indian mathematics to which he has been adding. See Talk:Cardinal number for more information. In my opinion, he is just cluttering up these articles and making them hard to read. There are no mathematical theorems or hard facts in his writing, just attempts to grab credit for the Jaina. JRSpriggs 03:20, 11 April 2006 (UTC)

Yeah, this is a bit of an ongoing problem, and not just about the Jains, but about ancient Indian mathematics in general. Jag, and maybe a couple of others, repeatedly make "anti-Eurocentric" claims that strike me as having a political axe to grind. See especially Kerala school#Possible transmission of Keralese mathematics to Europe, which consists mostly of speculation that European mathematicians could have learned of these claimed precedents and thus may not really have made their discoveries independently. Now, he does have lots of sources; my guess is that they have a political agenda as well, but that's speculation on my part, given that I haven't seen the sources. --Trovatore 04:03, 11 April 2006 (UTC)

A political agenda won't surprise me. I recall the dispute at Arabic numerals, which was moved to Hindu-Arabic numerals and back in total 12 times hist, and see also Talk:Arabic numerals. That not meaning to say that I have anything against India or its great contributions. Oleg Alexandrov (talk) 04:34, 11 April 2006 (UTC)

Long, long, long, long, LONG "stub" articles!

Please look at:

Template:Algebra-stub

I've deleted the "stub" notice from a few dozen of these. Please help. Click on one. If it's too long to be called a "stub", deleted the {{algebra-stub}} notice. Start at the bottom, since I started from the top, so the ones NOW near the top have been dealt with. Some are AMAZINGLY long articles, and are called "stubs". Others are fairly short and could use more material but are clearly too long to be called stubs.

Then we can go on to "geometry-stub", etc., etc., etc., etc.......... Michael Hardy 03:09, 12 April 2006 (UTC)

I've checked every article in the category [17]. --MarSch 11:59, 12 April 2006 (UTC)

Weisstein reliability (or not)

Debate is getting a bit heated at Wikipedia:Articles for deletion/Radical integer and Wikipedia talk:Articles for deletion/Radical integer, with one contributor arguing that it's not within our purview as editors, even if experts, to judge the reliability of anything written in Weisstein's encyclopedia, unless some other source directly contradicts it.

That idea strikes me as a recipe for disaster. Weisstein's work has so much overlap with our project, and is so full of idiosyncracies, that we have to view with caution any article on which he's the only source. If our hands are tied on this, the quality of WP math articles is at risk. Please come and state your views. --Trovatore 21:34, 13 April 2006 (UTC)

I think you're right, as knowledgable editors, we have to use some discretion about what sources are allowable for original material to be included; otherwise we will have to allow all kinds of crackpot material. However, I don't really see a need to take a hardline stance about Weisstein. We can also use our discretion about what of his meanderings should be allowed, which is why I haven't really entered into that debate. -lethe ^{talk +} 00:12, 14 April 2006 (UTC)

Oh, of course. I'm not saying we should automatically reject material just because it comes from him. I'm just saying it needs extra scrutiny when it comes only from him. More scrutiny than might be required with regard to sole-source material from a recognized specialist in whatever the subject matter is. --Trovatore 01:06, 14 April 2006 (UTC)

Well then we're in complete agreement. -lethe ^{talk +} 01:10, 14 April 2006 (UTC)

Also agree (on both points).--CSTAR 02:23, 14 April 2006 (UTC)

Soni's theorem

Has a trivial subject and I could not find any google hits. Should it stay? Oleg Alexandrov (talk) 04:10, 14 April 2006 (UTC)

I'd say no. --Trovatore 04:14, 14 April 2006 (UTC)

I couldn't find anything about it either --MarSch 11:47, 14 April 2006 (UTC)

I would say this article is a strong keep. It has been refined by another user, and I believe the content is much clearer now. This theorem is not trivial, it is like the Trivial Inequality (I don't know if non-mathematicians will understand that reference, so I will explain). This theorem is useful by itself, and not at all obvious. However, when combined with other things, such as De Moivre's, this can be incredibly useful. It should not be deleted for any reason. perhaps a more experienced mathematician can refine it... Mysmartmouth

I nominated it for deletion using the WP:PROD process. So, if nobody objects in 6 days, it will get speedy deleted. Oleg Alexandrov (talk) 20:42, 14 April 2006 (UTC)

Deprodded by author, listed on AfD by me. --Trovatore 23:01, 14 April 2006 (UTC)

Please add your comments to the AFD page.--C S (Talk) 23:30, 14 April 2006 (UTC)

Help with matrix groups

I've been working on the matrix group page and need some help with the content. In particular I'm trying to summarize the types of classical groups but don't have the necessary background to do so. Some of the changes involve generalizing the definitions on other pages (such as unitary group) to arbitrary fields as well as possibly adding some pages (such as projective special orthogonal group).

I've put a summary of the changes I think would be helpful on Talk:Matrix_group. TooMuchMath 05:00, 14 April 2006 (UTC)

Update: The page is starting to come along, however we now have some redlinks if anyone wants to take a shot at them:

• projective special unitary group
• projective symplectic group
• general symplectic group
• projective orthogonal group
• projective special orthogonal group

TooMuchMath 17:39, 21 April 2006 (UTC)

Well as you can see the links are no longer red and the classical groups portion of the page is looking pretty good. More contributions are welcome, of course! TooMuchMath 22:52, 24 April 2006 (UTC)

The links have become redirects, but have the target articles added the necessary discussions? For example, "projective special orthogonal group" redirects to "orthogonal group", but that article says nothing specific to support the redirect. --KSmrq^T 23:09, 24 April 2006 (UTC)

references for basic topics

Since we seem to be discussing references/sourcing so much recently.... can I ask what is the deal with references for all of our articles on more basic topics? For example, none of the following articles have any book/journal references: irreducible polynomial, normal subgroup, null space, vector space, affine scheme, group (mathematics), symmetric group, function composition. And there are plenty more, they're very easy to find. For such articles, sourcing would have two primary purposes: (1) historical information about where the concept first appeared, possibly in nascent form (this is hard because it involves genuine historical research), and (2) pedagogical, i.e. "where you can learn more about this idea". The second one is obviously problematic because in some cases there are many thousands of textbooks that cover the relevant material. On the other hand, sometimes I feel like there are some double standards going on in the background: for topics which all of us here know are important and standard, we don't require any sourcing, but things like "radical integer" make sparks fly.... Dmharvey 12:20, 14 April 2006 (UTC)

I certainly think that for basic subjects, referencing one or more modern textbooks on the subject would be really useful. For example, something like "An introduction for Undergraduates is given by 'Algebra' Splodgett and Madeup (Cambridge 2003). A textbook more suitable for postgraduates is 'Introduction to Algebra' Spurious and Fictitious (Springer Verlag 1998)." (I pick on Algebra because I was recently looking at [Elementary Algebra] and that has poor references (though I didn't know of a good one to use myself). There's no way that a wikipedia page, no matter how good, can teach a basic mathematical topic and therefore a textbook reference (and some insight into what level of student it would suit) would be very helpful. I realise this could possibly cause issues with people recommending their own books or particular favourite texts. --Richard Clegg 14:10, 14 April 2006 (UTC)

There are double standards and double standards; I think this double standard is absolutely rational and legitimate. I am unembarrassed to say I think we should have that double standard. Just the same, the point is well taken: While not as essential for topics we know about than those we don't, sourcing is still useful and the article isn't really complete until it's provided. --Trovatore 19:34, 14 April 2006 (UTC)

Well, sure, we should source things properly. If they aren't, then we shouldn't include it. On the other hand, we often give editors the benefit of the doubt. If there are no sources for something, then if the creator of the article is a known, respected contributor, not known for randomly inserting crazy crap into Wikipedia, then we give him/her time to find a source. I think it's perfectly fine to rely on the trust built among known contributors. In this case, it was a respected contributor Henrygb who had created the article, even giving a source. However, in this case, another respected contributor questioned the source, as upon investigation the source cited a mailing list which is not available for view and other searches through the usual methods, Google, MathSciNet, etc., were unable to find the term "radical integer". In this case, it's not applying a double standard to ask, "Should we allow this material?" It's natural and perfectly fine to engage in discussion, even amongst contributors who hold a great deal of trust for each other. Such discussion acts as a "reality check", making sure we don't get carried away and making sure we ultimately uphold the standards.

Even when the editor is an anon, we often give the benefit of the doubt, investigating how common the terminology is and whether the results are mentioned in some well-known resources. I'm even amazed at the lengths people sometimes take to investigate rather dubious-sounding claims, in the interest of completeness and fairness.

So I would say there is no double standard here. We often allow anyone to edit and insert material without citing, as if we didn't, we wouldn't gain a lot of content. On the other hand, to make sure we don't allow the crap to build up, we rely on trust of known contributors and also our expertise, e.g. "hey, this guy says some cubics can't be solved by radicals; that's not what I learned in undergrad algebra!" Eventually, though, we should be adding sources, and indeed some people are clearly going through articles and added citations where needed. So it's not accurate to say we don't require sources for some articles. --C S (Talk) 20:18, 14 April 2006 (UTC)

Let's not mix apples and oranges. Sources for mainstream mathematical content act as enrichment, "See also". The content is not in dispute, perhaps with a few lunatic exceptions. Many of the algebra topics, for example, could cite Mac Lane and Birkhoff's Algebra (ISBN 0023743107), or van der Waerden, Moderne Algebra (ISBN 0387974245), or Artin's Algebra (ISBN 0130047635), or numerous other texts; and they should. In other cases, we have questions of proof, or notation, or history, or who-knows-what. It is not practical to referee every article like a journal paper, and even then many assertions are accepted without proof. We concentrate our demand for references on statements that raise suspicion. In principle, we should be able to defend "1+1=2", but in practice that level of citation would be absurd. --KSmrq^T 22:41, 14 April 2006 (UTC)

I would agree with KSmq. The rules for when a reference is not required (as I remember from high school) is if the information is "widely known" (which in high school meant that it was avaliable in three or more sources). "Moscow is the capital of Russia" would not need a citation for this reason. Even when we do run into problems with conflicting definitions ("St. Petersburg is the capital of Russia" was true for a time) citations aren't strictly required if both definitions are or have been widely used. In fact a discussion of the historical (or motivational) reasons for differing definitions is often more useful than a citation in these cases. A citation is required only when a definition is obscure. Aside from the academic integrity motivations for proper citation, this is particularly important on Wikipedia to ensure the "no original research" policy as well as to weed out the junk science. That said, a good reference or two can enrich the content substatially, so even for widely known topics it would be a good idea to add references. TooMuchMath 18:16, 15 April 2006 (UTC)

That's nicely put. This is the "rational double standard" I was advocating above. However I wouldn't formalize the "three sources" standard; I think the appropriate test is more whether an ordinarily prepared worker in the specialty would know the facts asserted. --Trovatore 19:26, 15 April 2006 (UTC)

OK, I agree with the bulk of what everyone's saying here, certainly I agree with the "rational double standard". I intended my comment to focus more on the educational usefulness of Wikipedia, rather than its veracity. In fact, if I had more time available now, I would consider trying to organise a "let's find book/pagenumber references for all those unreferenced basic topics articles" project, for the sole purpose of assisting those who are using Wikipedia as part of their mathematics studies. It's getting to a point now where an undergraduate and even a graduate student (like myself) can profitably use Wikipedia as their first stop when looking stuff up, and it would be incredibly helpful to have more pointers to denser sources of information. Unfortunately I don't have the time now. (nudge nudge wink wink) Dmharvey 19:47, 15 April 2006 (UTC)

This is a problem I have encountered when ever I nominate maths articles for Good Article status - they very often comment on teh lack of sources. The trouble is that many of the common topics (groups, vectors etc.) are written entirely of own knowledge, which means the source is out own knowledge hence the lack of physical references. That said, I think we should always list *some* references, if only to provide a place for readers to verify the info or find out more. Don't forget it says under any edit box that "Content must not violate any copyright and must be verifiable". Any book which know contains infomation for the article in question is suitable. Putting the article name in Amazon's search box often provides something suitable. (Although the references I list tend to come from the reading list for my uni's maths course). Tompw 20:01, 15 April 2006 (UTC)

PDE Surfaces

Copied from Talk:Mathematics --Salix alba (talk) 14:18, 15 April 2006 (UTC)

This seemed like the best place to get people's attention about the article PDE Surfaces, written by Zer0 cache. I suspect that it's promoting research, but I can't be sure. It would be appreciated if other editors can check this out. I've also left a small query at PDE surfaces talk page. MP (talk) 11:28, 11 April 2006 (UTC)

it seems fully referenced... hmm I guess Salix Alba fixed it already. --MarSch 17:43, 15 April 2006 (UTC)

Hm, what about the naming? I've already downcased it, but it didn't occur to me at the time that it would probably be more standard to move it to PDE surface, assuming there is such a thing as a PDE surface that makes sense in isolation from other PDE surfaces. On the other hand, if it's the description of a method rather than a kind of mathematical object, should it perhaps be method of PDE surfaces? --Trovatore 17:48, 15 April 2006 (UTC)

mathematics for AID

mathematics is curerntly going very well on Wikipedia:Article Improvement Drive. Maybe you want to vote for it --MarSch 18:13, 15 April 2006 (UTC)

debate over external link at Talk: Serge Lang

There's an extremely heated debate going on the talk page for Serge Lang between two editors, User: Revolver and User: Pjacobi. The issue is whether an external link to an article on the AIDS wiki (which was written by Revolver) should be allowed. I've just made my thoughts known there, and I also noticed that an RFC had been filed, but no comments had been made here (which is requested on the RFC page). --C S (Talk) 04:18, 17 April 2006 (UTC)

Theorem 1

I nominated Theorem 1 for deletion. I tried using {{prod}} first but its author disagreed. Comments welcome. Oleg Alexandrov (talk) 03:55, 18 April 2006 (UTC)

Delete. The author says "There is a list, and this is #1." I'm not aware of any cosmic list of theorems. Now it does have something of a place of distinction -- postulate #4 of book 1 of Euclid's elements. But it isn't "theorem #1". Will there be a theorem #2? William Ackerman 17:16, 18 April 2006 (UTC)

There is no point in commenting here. To find the discussion, go to the article in question, and follow the link at the top of the page. --Trovatore 17:17, 18 April 2006 (UTC)

NPOV dispute at geostatistics, kriging, and spatial dependence

There is an NPOV dispute at the above articles: we need expert advice from statistician(s), especially those familiar with spatial statistics.

Briefly: User:JanWMerks claims that geostatistics is a scientific fraud, and has repeatedly edited these related articles to reflect that POV. Myself, User:Antandrus, and others were trying to point out Wikipedia rules, such as WP:NPOV, WP:VERIFY, and WP:NOR. Much edit warring ensued.

Now, the dispute (at spatial dependence) is over whether the F-test is a valid statistical test for spatial dependence. Also: several references (at geostatistics and kriging) are being used to support the claim that kriging is invalid, and I don't have easy access to a good library to check these references.

I hope that someone is willing to research the claims of invalidity better than I can, or perhaps simply provide a third opinion about the dispute.

Please feel free to visit Talk:Geostatistics, Talk:Kriging, and Talk:Spatial dependence to help out. Thanks!

-- hike395 17:40, 22 April 2006 (UTC)

cron vs hedron

I wonder if these two Greek suffixes mean the same or almost the same thing. Then, the following redirects may make sense:

• Great dirhombicosidodecacron --------> Great dirhombicosidodecahedron
• Great dodecahemicosacron --------> Great dodecahemicosahedron
• Great dodecahemidodecacron --------> Great dodecahemidodecahedron
• Great icosihemidodecacron --------> Great icosihemidodecahedron
• Small dodecahemicosacron --------> Small dodecahemicosahedron
• Small dodecahemidodecacron --------> Small dodecahemidodecahedron
• Small icosihemidodecacron --------> Small icosihemidodecahedron

I stumbled into them at the Missing science project, and don't know what to do about them. Thanks. Oleg Alexandrov (talk) 18:55, 22 April 2006 (UTC)

I think the ones on the left are duals of the ones on the right or something. They should be given seperate articles. -- 127.*.*.1 20:33, 22 April 2006 (UTC)

Indeed the coverage of dual is week at the moment. I've mentioned this on Talk:Polyhedron. --Salix alba (talk) 22:39, 22 April 2006 (UTC)

Delete "Category:Continuum theory"?

This category called "Category:Continuum theory" is a subcategory of "Set theory" and of "General topology", but it contains no articles. Should it be deleted? How can I propose it for deletion? JRSpriggs 07:20, 26 April 2006 (UTC)

Wikipedia:Categories for deletion explains the deletion process. It might be applicable for speedy deletion. --Salix alba (talk) 07:34, 26 April 2006 (UTC)

Yup, WP:CSD says that empty categories can be speedied. I'm going to do it. This category defines a continuum as a compact connected metric space, which isn't right. The real line is not compact. -lethe ^{talk +} 07:56, 26 April 2006 (UTC)

Continuum has more than one meaning in mathematics. In continuum theory, which is related to dynamical systems, continuum does indeed mean what the category said. Perfectly cromulent articles which would have belonged in this category include pseudo-arc, indecomposable continuum and solenoid (mathematics). —Blotwell 14:49, 26 April 2006 (UTC)

Well, if the category had a correct definition, and also there are articles which could live in it, then the deletion was inappropriate. I will now undelete, and promise to be more careful when speedying things in the future. Thank you. -lethe ^{talk +} 20:34, 26 April 2006 (UTC)

Help requested at hyperbolic 3-manifold

An editor insists on removing red links as "cleanup". I think the participants here realize the importance of red links to this project (and Wikipedia in general). I'm puzzled why anyone would insist on removing them, but this editor has been quite stubborn, insisting that the articles *must* be created before links to them can be included in this article. --C S (Talk) 00:41, 28 April 2006 (UTC)

I've made some comment's at the user's talk page (User talk:PHDrillSergeant); hopefully, this should be enough. --C S (Talk) 01:01, 28 April 2006 (UTC)

Edward R. Dewey

A stock market "analyst" who sold a correspondence course on "cycle analysis".[18] This link includes a table of contents which I think makes clear how trivial Dewey's "system" is; please comment on Wikipedia:Articles for deletion/Edward R. Dewey. Septentrionalis 19:13, 28 April 2006 (UTC)

Should Radical integer be deleted?

A newly created article Radical integer has been listed for deletion. Should it be kept or deleted? Note that the article resolves a long-standing redlink in Algebraic integer listed on Wikipedia:Missing_science_topics/Maths8. Weigh in. Lambiam^Talk 17:50, 9 April 2006 (UTC)

I'm the one who listed it for deletion, because the given source (MathWorld) looked hinky and in a quick search I couldn't find the term clearly and independently attested. I'm not a number theorist, so if it's not something one of Eric Weisstein's buddies just made up one day, by all means say so. --Trovatore 17:59, 9 April 2006 (UTC)

Someone somewhere has got to have a short name for Algrebraic integer expressible by radicals, but this doesn't seem to be it. Septentrionalis 22:33, 10 April 2006 (UTC)

Radical extension, extension by radicals, or (most common, I think) pure extension is standard, and radical number I think I've seen. Radical integer is logical and has a MathWorld article to go with it, which speaks in its favor. It seems to me that all of this should be discussed somewhere in an article on solvable extensions, but I can't find any such article. Should I write one? I don't want people deleting it if I do. Gene Ward Smith 21:25, 13 May 2006 (UTC)

Let me summarize the history as I see it:

1. The article radical integer was sourced only to MathWorld and all the Google hits seemed to trace back there. So I nominated it for deletion as one of Eric Weisstein's neologisms (as you'll have gathered, I don't think the existence of a MathWorld article speaks particularly well in favor of it; it's not a strike against it per se, but certainly not enough support for an article by itself).
2. During the discussion it emerged that there was more than a not-so-interesting definition involved, but rather an actual putative theorem, which (if true) goes as follows: Consider all numbers that can be expressed by starting with the naturals and closing under addition, multiplication, subtraction, division, and extraction of natural-number roots. Intersect that class with the algebraic integers. Then any number in the intersection can be expressed by starting with the naturals and closing under the previous operations, without division.
3. That theorem, if it is one (which I think it probably is), is very interesting, and clearly justifies the creation of a term for an element of the class. Unfortunately at the current time the theorem cannot be sourced, except to MathWorld, which IMO is not reliable. Moreover I think it's a reasonable principle that sources for putative theorems ought to point the reader to an actual proof, and the MathWorld source does not do that. --Trovatore 17:26, 25 May 2006 (UTC)

It might be posible to get a better source, the theorem was discussed on the math-fun mailing list, which I presume is on the web somewhere. In an email to me Rich Schroeppel said he would try to dig up the archive when the tax season was over. If anyone is interested this would be great to follow through. --Salix alba (talk) 17:35, 25 May 2006 (UTC)

Oh, one more small point: What I said about "sourced only to MathWorld" is not strictly true; I'm including Weisstein's encyclopedia of math as part of MathWorld. With that addendum it's true. --Trovatore 17:35, 25 May 2006 (UTC)

• It seems to me if I understand the claim that Schroeppel's theorem is too trivial to use as a reason for an article. If μ is an algebraic integer, then it has a monic polynomial, and expressing it as a root expresses it without division. Expanding on that, the ring of integers in any number field has an integral basis; it can be written as c₁ μ₁ + ... + c_n μ_n, where the c's are ordinary integers and the μs are algebraic integers in the field, so in terms of this basis everything in the ring of integers is precisely everything which can be expressed without division.

• So, what exactly is the statement of this theorem? Gene Ward Smith 19:47, 25 May 2006 (UTC)

I think I've already stated it exactly; here's the example that came up as to why it's not trivial. The golden ratio is a root of x²−x−1=0, so it's an algebraic integer. It's also obtainable from the naturals by iterating the operations listed, including division, as

${\frac {1+{\sqrt {5}}}{2}}$

However it's not immediately obvious that you can get it from the naturals by iterating the operations not including division. But you can. It's

${\sqrt[{3}]{2+{\sqrt {5}}}}$

(Thanks to Lambiam for that representation.) Unless I've misunderstood it, the argument you give does not prove this. --Trovatore 19:55, 25 May 2006 (UTC)

Here's a sketch of an almost-proof. "Almost" because I'm left with a denominator of at most 2.

Let S be those numbers obtainable from the natural numbers by addition, subtraction, multiplication, division, positive integer roots. (I want to call this the maximal radical extension of Q, but I'm slightly concerned about roots of unity. Never mind.) Let R be the "radical integers", i.e those numbers obtainable from naturals by addition, subtraction, multiplication, and positive integer roots (but not allowing division). First I claim that any x in S is of the form y/d for some y in R and some integer d. This is done by induction on the structure of x. Clearly addition, subtraction, multiplication pose no problems. Integer roots also fine (i.e. $(y/d)^{1/n}=y^{1/n}d^{(n-1)/n}/d)$). Division is slightly more troublesome, you need some kind of "rationalising the denominator" trick.

So now suppose we have x = y/d as above, and suppose further that x is an algebraic integer; we want to prove that x is itself a radical integer. Let K = Q(y), and let O be the ring of integers of K, so x is in O. As Gene pointed out above, O has a finite Z-basis, and the basis elements are polynomials in y with coefficients in Q, so for a large enough integer m we find that mO consists entirely of radical integers. Split m into a product of powers of prime ideals in O, say $m=\prod _{P}P^{r_{P}}$. By looking at the rings $O/P^{r_{P}}$, we can find some large integer n such that xⁿ is congruent to either 0 or 1 modulo each $P^{r_{P}}$. Then $x^{2n}-x^{n}$ is in mO, so is a radical integer, say z. Then we have $x=\left({\frac {1\pm {\sqrt {z}}}{2}}\right)^{1/n}={\frac {2^{(n-1)/n}(1+{\sqrt {z}})^{1/n}}{2}}$, which is a radical integer possibly divided by 2.

Anyone buy that? Getting rid of that last 2 seems a little problematic. Dmharvey 00:26, 26 May 2006 (UTC)

Oh yeah, by the way you can apply that proof to the golden ratio case quite easily. We already have $x={\frac {1+{\sqrt {5}}}{2}}$ presented in the right form. Let O be the ring of integers of $\mathbf {Q} ({\sqrt {5}})$. Then the ideal (2) is inert in O because the polynomial $x^{2}-x-1$ is irreducible mod 2. So the quotient O/2 is GF(4), so cubes of anything nonzero are congruent to 1. So $x^{3}-1$ is in 2O, so is a radical integer. And indeed $\left({\frac {1+{\sqrt {5}}}{2}}\right)^{3}-1=(1+{\sqrt {5}})$ is twice an algebraic integer, so must be a radical integer, which is I suppose where Lambian's formula comes from :-) Dmharvey 00:33, 26 May 2006 (UTC)

OK, here's the rest of the proof to handle that annoying factor of 2. You need to treat the residue characteristic 2 a little carefully.

Again suppose x = y/d where x is an algebraic integer. Let $\theta =(1+{\sqrt {5}})/2$ be the golden ratio. Consider the extension $K=\mathbf {Q} (y,\theta )$, let O be its ring of integers. Again we can find some m so that mO consists entirely of radical integers. Consider all prime ideals P of O of residual characteristic 2, suppose their multiplicites in m are given by r_P. Take some high power of x, call it x₂, which is = 0 or 1 modulo each $P^{r_{P}}$. Then x₂ + θ is not in any $P$, because θ is not 0 or 1 modulo 2 (i.e. neither θ nor θ−1 is twice an algebraic integer). So some high power of x₂+θ, let's call it x₃, is congruent to 1 modulo every $P^{r_{P}}$. Then x₃−1 is = 0 modulo every $P^{r_{P}}$. Now consider all the other primes Q of various other residue characteristics, which have multiplicities $r_{Q}$ in m. Then some high power of x₃−1, let's call it x₄, is either 0 or 1 modulo each $Q^{r_{Q}}$, and is still 0 modulo every $P^{r_{P}}$. Now look at x₄+1; it's either 1 or 2 modulo each $Q^{r_{Q}}$, and it's 1 modulo each $P^{r_{P}}$. Since the residue characteristics of the Q are not 2, some high power of x₄+1, say x₅, is 1 modulo all of the $Q^{r_{Q}}$ and all of the $P^{r_{P}}$. So x₅−1 is in mO, and therefore a radical integer. If you unroll your way through x₅, x₄, x₃, x₂, back to x itself, you get that x is a radical integer. Whew! Dmharvey 02:48, 26 May 2006 (UTC)

Applause. Now get that published in the Journal of Number Theory and we can write an article about it :) --Lambiam^Talk 16:21, 26 May 2006 (UTC)

Update on the lists of missing math topics

The lists at Wikipedia:Missing science topics#Mathematics now contain entries from MathWorld, Springer Encyclopaedia of Mathematics, Charles Matthews' maths lists (thanks Charles!), St Andrew's, and PlanetMath. There are 15465 redlinks and 9700 bluelinks (in separate lists), which is a progress of 38.55% towards eliminating the redlinks. For many redlinks it is likely that the information exists on Wikipedia but under a different name, so creating redirects is a good way to advance that project forward. The harvest is great and the workmen are few[19] (since it's Easter today :) Oleg Alexandrov (talk) 22:21, 16 April 2006 (UTC)

And I finally got permission from Springer to use their lists in our project. Oleg Alexandrov (talk) 03:25, 25 April 2006 (UTC)

Really? That's very generous of them, I didn't think they would. I think mathworld wasn't willing. Neat! -lethe ^{talk +} 03:32, 25 April 2006 (UTC)

If Mathworld was not willing, how come the Wikipedia:Missing science topics was created to start with? Before I got there, all the math entries from there were copied from MathWorld, all the way to incomplete entries, like Archimedean Spiral Inv.... Oleg Alexandrov (talk) 03:37, 25 April 2006 (UTC)

I seem to recall a discussion here on the wikiproject talk page, where someone created a carbon copy of the mathworld index of topics, and someone emailed them, and they indicated that it was indeed a violation of their copyright. In fact, my recollection is that you were in this converation, though I could be mistaken. Anyway, I don't know where the content of Wikipedia:Missing science topics comes from, but unless I'm misremembering something, to have their index is a copyright violation. I guess I should see if I can find that old conversation. -lethe ^{talk +} 07:37, 1 May 2006 (UTC)

That's really good news. I'm not so surprised though, that Springer was willing but MathWorld not. There are people at Springer that are truly committed to what they're doing and I've seen Springer do things that strictly speaking, they did not need to do. --C S (Talk) 07:27, 1 May 2006 (UTC)

listing variable names after formulas

I wonder what people think of these multiply-indented lists to define all the variables that appear in a formula. An example is found here. It is claimed that this format is somewhat standard here at wikipedia and is found in hundreds of articles, but I've never seen it, and furthermore don't really like it, I prefer instead a regularly indented paragraph of text. What are your opinions of this format? -lethe ^{talk +} 00:52, 22 April 2006 (UTC)

It takes too much space. -- 127.*.*.1 03:26, 22 April 2006 (UTC)

Yes, that is quite an unfortunate presentation style. A simple paragraph of explanation would be much better.  — merge 08:07, 22 April 2006 (UTC)

From a dyslexic point of view I have problems parsing large blocks of text and tend to find lists easier to read. I had a play about with a more compact format using tables. Compare

---

The Schrödinger equation is:	i		the imaginary unit,
	t		time,
$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$	${\partial \over \partial t}$		the partial derivative with respect to t,
	$\hbar$		reduced Planck's constant (Planck's constant divided by 2π),
	$\psi (t)$
	H(t)		the Hamiltonian - a self-adjoint operator acting on the state space.

---

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$   

where i is the imaginary unit, t is time, ${\partial \over \partial t}$ is the partial derivative with respect to t, $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π), $\psi (t)$ is ...., H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

---

--Salix alba (talk) 09:27, 22 April 2006 (UTC)

If a list seems necessary, why not use a list?

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$,

where:

• i is the imaginary unit
• t is time
• ${\partial \over \partial t}$ is the partial derivative with respect to t
• $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π)
• $\psi (t)$ is ....
• and H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

---

 — merge 09:42, 22 April 2006 (UTC)

I wonder if those explanations of the symbols make this equation any more comprehensible to someone not familiar with the notation. If you don't know what the symbol is for partial differentiation then IMO it is very likely that you don't know what partial differentiation is and the same goes for the imaginary unit.--MarSch 09:55, 24 April 2006 (UTC)

I don't think it's necessary to explain certain things, such as the imaginary unit, time, or the partial derivative. Articles assume some basic knowledge, so we should rely on this (however, we should clearly attempt to make the number of assumptions as smallest as sensibly possible). Dysprosia 10:05, 24 April 2006 (UTC)

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$

where H is the Hamiltonian, ψ is the state and t is time,

but even better is probably

A physical system with Hamiltonian H and initial state vector ψ₀ can be described at time t by the state vector ψ(t) which is a solution of the initial condition ψ(0) = ψ₀ and the differential equation called the Schrodinger equation

$H(t)\psi (t)=i\hbar {\partial \over \partial t}\psi (t)$

--MarSch 10:09, 24 April 2006 (UTC)

I'm in favor of lists for equations. The main reason is that I don't like to read the whole article - and lists of variables show a clear spot where I can find all the information I need. This is of course provided that its written properly. If the variables in the equation are fully clear, then theres no need. However, in the case of the schrodinger equation, almost none of the variables and symbols are familiar to most people. Also, most always, all variables do need description. Leaving out variables leaves the equation incomplete, and even a reader who assumes the right meaning might question himself, and end up having to double check the formula somewhere else. Stuff like simple operators probably don't need explaining, but I've found a good compromise in that respect to define the derivative of something rather than the dervative operator (for example: "dp/dt is the instantaneous rate of change of the momentum").

Another main consideration is consistancy. If equations are written in 5 or more different forms, users will have a harder time sorting through the formats to find what they need. Almost always, variables are written below the equation, and when they're not - I find it difficult to follow. The list format makes it easy to find the perhaps one or two variables you don't know, and refer back to it without losing your place.

We as editors should consider that wikipedia isn't only used by people wanting an in depth overview of a subject, but may also want a quick reference. Articles that distinguish different parts of the article (like equations, subject headers, examples vs generalities) are much easier to read and use. The faster a reader can find the information they are looking for is (in my opinion) far more important than making the page compact. Fresheneesz 07:25, 2 May 2006 (UTC)

AFD - How to get the prime factors of a number

I have nominated How to get the prime factors of a number for deletion. Comments welcome. -- Meni Rosenfeld (talk) 16:46, 26 April 2006 (UTC)

It seems like useful information, although it could be better written. Is this info in some other article? If not, maybe the article should stand. PAR 16:58, 26 April 2006 (UTC)

Please take comments on the merits to the AfD page. --Trovatore 17:04, 26 April 2006 (UTC)

Deleted. -lethe ^{talk +} 05:17, 1 May 2006 (UTC)

May 2006

"Tone", pronoun use, etc. in math articles

The other day, I left a pretty extensive comment on Talk:Knot theory, in response to two editors who complained about the article's tone. One specific complaint was the use of pronouns and that the article sounded like a teachger giving a lesson. Now, I just noticed that Braid group has been tagged (by someone else) with a "tone" tag, and the talk page mentions for example, that the use of "we" is bad and that it sounds too much like a "math lesson instead of an encyclopedia".

My thought is that while some of the pronoun use could be favorably excised, I am definitely starting to get the feeling (especially after examining the articles in question) that these particular editors do not understand the conventions in mathematical writing, e.g. "We consider blah as doing blah..." is ok. They also may not understand that sometimes a procedural description should be given, e.g. "take such and such and do such and such...". See my long comment linked above. I would like to know what those who normally work on mathematics articles think about all this, so please drop by those pages and make some comments. --C S (Talk) 03:58, 1 May 2006 (UTC)

We is pretty much mathematical jargon; one is better for the general reader. Charles Matthews 11:45, 1 May 2006 (UTC)

I believe the passive is the preferred thingy. "We consider..." becomes "... is considered". --MarSch 14:08, 1 May 2006 (UTC)

But then... "is considered", er, by whom? By a deity? (Igny 15:33, 1 May 2006 (UTC))

This reflects a certain diference about using We. In a statement like We can deform a knot in 4D it can easily be rewitten as a knot can be deformed in 4D and the prounoun can easily be dropped. However We consider... are subjective statments and in a paper the we is used to indicate the opinion of the authors. In wikipedia such subjective statements need appropriate qualification most mathematicians consider 4D knots to be very boring. --Salix alba (talk) 19:04, 1 May 2006 (UTC)

I've responded where requested; see for details. Passive is not preferred; just the opposite. Overuse of "one" also makes reading drag. Technical writing has a tradition of such conventions, not to its credit. --KSmrq^T 19:15, 1 May 2006 (UTC)

A MIT style guide says to use "we" in the active voice. I see now that I was mistaken in thinking it too personal, and yes, I did not understand mathematical writing conventions as pointed out by Chan. I will try to not be an ignoramus in the future. --Reader12 03:57, 2 May 2006 (UTC)

Well, you live and learn! I tried to carefully explain how the situation appeared to me without being patronizing or rude; I hope you weren't offended. At any rate, I think it's been a very fruitful discussion thus far with a variety of people voicing their thoughts and it's still ongoing! --C S (Talk) 08:08, 2 May 2006 (UTC)

No, no offense taken. This has been very instructive to me. Thanks! --Reader12 21:40, 2 May 2006 (UTC)

I've just come across a great book on Algebraic topology by Allen Hatcher which can be downloaded [20]. To my mind he has a very good writing style, which avoids the problems of overly technical writing, whilst still being technically correct. I fell there is quite a bit which could be learnt by examining how he structures his writing. I think a lot of illustrations help, the sub project /Graphics has reciently been set up to try to improve the illustrations of the maths articles. --Salix alba (talk) 09:21, 2 May 2006 (UTC)

Naming: "fixed-point" vs "fixed point"

Several articles are named inconsistently. I prefer "fixed point". Any opinions? Post here or at Category talk: Fixed points. Staecker 21:18, 1 May 2006 (UTC)

It's my experience that "fixed point" is way more common in the literature, so we should stick with that.--Deville (Talk) 22:25, 1 May 2006 (UTC)

Not so fast; there's a grammatical distinction. As a noun phrase, we would write the "fixed point" of a recursive function, without the hyphen. But as an adjective, we often write "fixed-point" thingy, with the hyphen. In the case of theorem names, the former applies, as in "Brouwer fixed point theorem". And what about "Kleene fixpoint theorem"? It should redirect. --KSmrq^T 22:59, 1 May 2006 (UTC)

I don't mind making the distinction, but I don't think I understand as you've stated it. In "Brouwer FP Theorem," it sounds like an adjective phrase to me (modifying "theorem"). Is this an exception? When would the hyphen be appropriate? Something like "fixed-point set"? That sounds like an adjective phrase to me, but I never write it that way myself. Come to think of it, I don't ever use the dash regardless of context. (Except when I have to link to Lefschetz fixed-point theorem) Staecker 23:19, 1 May 2006 (UTC)

You want me to explain why punctuation conventions make sense?! I wish. I can say that I would never hyphenate in a situation like "Every rotation has a fixed point." The article on hyphen discusses some common rules. So why not "Brouwer fixed-point theorem"? I suppose because it's a ritual thing, with "theorem" doing the modifying. Or it's an example of the general guideline that hyphens are for clarity, and if we don't need them we don't use them. The still more general guideline is to tread carefully in this territory, and don't rush to accuse anyone of doing it wrong just because their choice is not yours. (But you knew that already, yes?) --KSmrq^T 02:47, 2 May 2006 (UTC)

My usage would be like KSmrq's. The underlying reason may be that a "fixed-point set" is a set which consists of fixed points (or is a fixed point, if you're doing category theory); but a "fixed point theorem" is a theorem about fixed points: a more distant relationship, analogous to the difference between mathematics and metamathematics. Septentrionalis 18:58, 5 May 2006 (UTC)

Are you sure there's an inconsistency? A fixed-point theorem (with a hyphen) asserts the existence of a fixed point (with no hyphen), and it is completely appropriate to use a hyphen in one case and not in the other, because of the difference in the way the phrase is being used. That is not an inconsistency. Michael Hardy 20:09, 5 May 2006 (UTC)

hyphens generally

By the traditional conventions concerning hyphens,

• A man-eating shark (with a hyphen) scares people away from beaches, whereas
• A man eating shark (with no hyphen) is a customer is a seafood restaurant.

The traditional usage is still followed by nearly all newspapers and magazines and in novels, and people are accustomed to seeing it. But many educated people, including many authors of scholarly papers and books no longer follow the traditional rule. I've tended to be conservative about it and I moved the Wikipedia article titled "light emitting diode" (with no hyphen) to light-emitting diode (with a hyphen) and have done the same with various other articles. I think in some cases, the hyphen is a magnificently efficient disambiguation device. Michael Hardy 20:14, 5 May 2006 (UTC)

Nice example, copied from hyphen:

semantic changes caused by the placement of hyphens:

• Disease causing poor nutrition, meaning a disease that causes poor nutrition, and
• Disease-causing poor nutrition, meaning poor nutrition that causes disease.

Michael Hardy 20:18, 5 May 2006 (UTC)

A fixed point theorem is a point theorem that was found to contain an error, which now has been repaired. Lambiam^Talk 21:13, 6 May 2006 (UTC)

Blahtex and wikimania

The poster deadline for wikimania is fast approaching. I think it would be really good if we could have some presence there as a step to getting meta:Blahtex integrated into the main encyclopedia sites. Neither User:Dmharvey or myself are able to attend, but posters can be submitted without having a physical presence. Questions: is anyone here planning to go to wikimania Aug 4-6, in Cambridge MA? Anyone happy to spend some time standing next to a Blahtex poster? For those who don't know Blahtex is a extension which converts LaTeX maths into the MathML XML markup which allows for improved rendering of mathematics in MediaWiki with moder browsers. --Salix alba (talk) 10:05, 2 May 2006 (UTC)

Bogus AfD of proof article

Loom91 has been goaded by Melchoir into nominating "Proof that 0.999... equals 1" for deletion, on the grounds that Wikipedia should not contain proofs like this. The archives of sci.math currently show well over a thousand postings related to this topic, which is therefore included in the sci.math FAQ; yet it appears that Wikipedia covers the topic far better. Those who are interested can register an opinion here. Caution: This topic (and perhaps this vote) attracts, um, non-standard thinkers, to put it delicately. (See the talk page archives for examples ad nauseam.) --KSmrq^T 10:31, 5 May 2006 (UTC)

Yeah, I feel bad about that; sorry, everyone! (In my defense, though, I did try to explain why the AfD would fail, after which I didn't think Loom91 would actually go through with it.) Well, at least it's attracting some fresh constructive attention, and it'll be useful to have on record. Melchoir 20:09, 5 May 2006 (UTC)

By the way, in case anyone hasn't seen it yet, the AfD closed with a keep. Melchoir 22:58, 5 May 2006 (UTC)

That's a understatement; it closed with a speedy keep, with overwhelming support and complaints about the nomination as violating WP:POINT. --KSmrq^T 22:31, 6 May 2006 (UTC)

Rewrite of Mode (statistics)

I rewrote the article Mode (statistics). Please review and correct errors, rewrite awkward sentences, simplify, embellish, supply sources, etc. It would further be nice to have some illustrations, both for a continuous density function and a histogram. Lambiam^Talk 20:40, 5 May 2006 (UTC)

AfD for List of Mathematical Formulas

Should this be kept, deleted, merged, or should there be a category of "mathematical formulas"? (I wonder what the morphisms would be.) Visit Wikipedia:Articles for deletion/List of Mathematical Formulas and contribute your two cents. Lambiam^Talk 21:04, 6 May 2006 (UTC)

As far as I can see, the chemists don't need Category:Formulas. We might not need it either, though. Charles Matthews 19:09, 7 May 2006 (UTC)

WAREL back?

See [21]. I don't read Japanese so I can't tell if the change is correct, but it's exactly the type of change we might expect from WAREL if he came back. --Trovatore 15:24, 10 May 2006 (UTC)

OK, I hate machine translation but it has its points. He changed the article to point to a nonexistent article on ja.wiki, called "Commutative field". It's WAREL alright; please block him with all deliberate speed. --Trovatore 15:41, 10 May 2006 (UTC)

KLIP (talk · contribs) blocked. -lethe ^{talk +} 17:20, 10 May 2006 (UTC)

James Stewart

Just created the page on Stewart, James Stewart (mathematician), your contributions would be most appreciated.--Jersey Devil 09:08, 11 May 2006 (UTC)  

TeX font size

There is a discussion at the Village pump that might interest a few people here. —Ruud 01:09, 12 May 2006 (UTC)

Koszul-Tate

Is there anybody here interested in tackling the Koszul-Tate derivation topic listed on the "wikipedia:Articles requested for more than two years"? Thank you. — RJH 15:45, 12 May 2006 (UTC)

WAREL

is back again at Field (mathematics). --Trovatore 02:39, 13 May 2006 (UTC)

JLISP (talk · contribs). -lethe ^{talk +}

Zeration

Can someone please review zeration? Thanks. Samw 03:28, 13 May 2006 (UTC)

I'd give it thumbs down, in regard the Δ numbers. That is just wrong, even if referenced in the paper. The rest is more-or-less accurate, although I believe it falis WP:N.

As for hyperexponentials, my first paper (in 1966) references an earlier paper by Donner and Tarski which discusses hyperexponentials on the ordinal numbers. I doubt the primacy of the 1987 paper. — Arthur Rubin | (talk) 04:29, 13 May 2006 (UTC)

Referencing something from 2004 makes it a bit young and possibly fails "established research". Dysprosia 08:44, 13 May 2006 (UTC)

Duly sent to AfD, see Wikipedia:Articles for deletion/Zeration. -- Jitse Niesen (talk) 08:47, 13 May 2006 (UTC)

Spanish category

I wrote the following on Category talk:Mathematics; copying here.

An anon recently changed the Spanish link to es:Categoría:Matemática from es:Categoría:Matemáticas, or perhaps the other way around. It seems that both categories exist and are populated. Would someone whose Spanish is better than mine like to go tell them? I don't know how they handle these things over there; I think things like {{cfm}} are set up language-by-language. --Trovatore 14:54, 13 May 2006 (UTC)

It looks like es:Categoría:Matemática was created just today, by one es:Usuario:Ingenioso Hidalgo, who then took it upon himself to go around recatting over a hundred articles, then apparently got tired. Unless this was discussed somewhere this doesn't strike me as good behavior; someone should let them know. I don't know if they have any equivalent to WikiProject Mathematics. --Trovatore 15:21, 13 May 2006 (UTC)

On second thought, I suppose someone will notice, as the recats will surely show up on some watchlists. --Trovatore 15:35, 13 May 2006 (UTC)

P-adic numbers

There is a discussion on decimal-style notation for p-adic numbers, and what would be appropriate to use, on the talk page Talk:P-adic number which we would like comments on. I added a section which uses a notation which is unusual but not unprecedented, in the section intended to convey the intuitive idea of a p-adic number. It seems to me the notation I used does that more successfully than any alternative for people used to decimal notation. Gene Ward Smith 21:14, 13 May 2006 (UTC)

Real number

User:Oleg Alexandrov seems to me to be engaging in abusive reverts on this page, to a previous verison which is arguably incorrect mathematically and which removes a lot of new material, material for which he has given no argument for removal. He also says, falsely, that my attempt to satisfy his previous criticims amounted to "writing a one-liner" which seems to prove he hasn't even seriously looked at the version he is reverting from. I think we need other people to weigh in at this point. I am very much opposed to simply allowing it to say the real numbers have a number line and calling that a definition. My proposal to say they have a number line, with no "room" to fit additional numbers in, is an attempt to make the one-line introduction correspond to an actual rigorous definition, which will not be the case if we allow Oleg's revert. Gene Ward Smith 22:32, 13 May 2006 (UTC)

Comments at talk:real number are encouraged. My version of things is that Gene is convinced enough that he is right that he is prefers repeatedly reverting to his version to discussing things on the talk page. Oleg Alexandrov (talk) 22:51, 13 May 2006 (UTC)

I think you need to take your own advice; your reckless reversion was done without any discussion. Gene Ward Smith 23:28, 13 May 2006 (UTC)

Regardless of who did what, there is a discussion running at the talk page now. Please engage yourselves there. -- 127.*.*.1 23:35, 13 May 2006 (UTC)

Islamic mathematics

User:CltFn has proposed to move Islamic mathematics to Middle-Eastern mathematics. Please comment at the talk page. —Ruud 02:36, 15 May 2006 (UTC)

A typesetting subtlety

See if you can spot the difference between this:

$a+b+c+d\,$

$+e+f+g+h\,$

and this:

$a+b+c+d\,$

${}+e+f+g+h\,$

without looking at the TeX code, and guess how and—perhaps more subtly—why the difference was achieved.

I think perhaps this should be borne in mind in editing math articles. Michael Hardy 02:37, 15 May 2006 (UTC)

This is presumably because TeX does not apply its operator spacing rules in the first case, while since you've forced an empty group in the second, it does. Preferrably if you're continuing a sum onto two lines, one would add a \quad of space in the second or add a text indent (via a ":"), instead of relying on empty groups. Dysprosia 03:02, 15 May 2006 (UTC)

Sadly, I spotted the difference instantly, and even knew exactly where to look. This has been with TeX for decades, and Knuth explicitly calls attention to it in The TeXbook (ISBN 0201134489, p. 196). You'd never guess he was the type to pay extraordinary attention to detail, now would you? ;-D

• "An extra ‘{}’ was typed on the second line here so that TeX would know that the ‘+’ is a binary operation."

The difference is a consequence of the operator handling rules. --KSmrq^T 04:27, 15 May 2006 (UTC)

Personally, I never noticed this until recently. I once asked Donald Knuth why he had issued an infallible pontifical decree about minute details of the design of the lower-case letter delta. He said it's because the design he prescribed was just obviously the right one. Anyway, in non-TeX mathematical notation, I've been something of a stickler about proper spacing with binary operations and binary relations, thinking all the while that there's no need to think about that in TeX, but in cases like this, there is. Michael Hardy 23:55, 15 May 2006 (UTC)

Dysprosia: How does a text indent via an initial colon achieve this result? It only adds space to the LEFT of "+". Michael Hardy 23:57, 15 May 2006 (UTC)

I wasn't exactly precise in what I was meaning above -- what I meant is that if one wants to continue a sum on two lines, one should add space to the left somehow, instead of keeping both lines of the sum aligned, for example

$a+b+c+d\,$

${}+e+f+g+h\,$

as opposed to

$a+b+c+d\,$

${}+e+f+g+h\,$

I probably should have added "and keeping the same indent" to the end of my comment. It's a shame that the TeX system in use here ignores initial spacing via quads and such. Dysprosia 08:46, 16 May 2006 (UTC)

Math error right on this page?

On this page there is a box telling us that hyperreal numbers, superreal numbers, and surreal numbers are "complex extensions"; in fact, they are all real closed fields. Gene Ward Smith 04:34, 15 May 2006 (UTC)

Zero-eigenvalue bifurcation

Could someone take a look at zero-eigenvalue bifurcation? It is proposed for deletion, but it do find some uses of this term on google scholar. —Ruud 00:17, 16 May 2006 (UTC)

The deletion, rather than redirection, seems summary and not necessary. Charles Matthews 11:03, 20 May 2006 (UTC)

I agreed with the deletion because I think that the term "zero-eigenvalue bifurcation" is hardly used by itself (in constract to more complicated phenomena like the "double zero-eigenvalue bifurcation", used as a synonym for "Bogdanov-Takens bifurcation"). But if you want to create a redirect, be my guest. -- Jitse Niesen (talk) 13:07, 20 May 2006 (UTC)

p-adic numbers notation

A debate is in progress at Talk:P-adic number about whether p-adic numbers should be written from right to left or from left to right. The article used to use the right-to-left notation, but was recently rewritten with the left-to-right notation. Contributions to the debate from a wider pool of wiki mathematicians would be helpful, to see if we can reach a concensus. Gandalf61 08:21, 16 May 2006 (UTC)

Okay, after some discussion on its talk page, I have now changed the p-adic number article to consistently use the right-to-left notation, but with a new section that mentions other alternative notations. Any comments on the partial re-write are welcome at Talk:P-adic number. Gandalf61 09:34, 26 May 2006 (UTC)

Moore closure

I propose to delete the bits about Moore closure in the article Kuratowski closure axioms; see Talk:Kuratowski closure axioms#Moore closure. --Lambiam^Talk 09:05, 16 May 2006 (UTC)

Fine topology (suggestion needed for better name)

I have created a new page on fine topology (as in classical potential theory), but as the title "fine topology" already seems to be taken by a page about general topology (i.e. 'finer topology' rather than "THE fine topology"), I have called my page "classical fine topology" - seems like there ought to be a better solution - any ideas? —The preceding unsigned comment was added by Madmath789 (talk • contribs) .

(Copied from my talk page, I don't have a good answer to this. Oleg Alexandrov (talk) 23:30, 16 May 2006 (UTC))

Call the page Fine topology (potential theory) and use a

{{dablink|[[Fine topology]] redirects here. For the use in potential theory, see [[Fine topology (potential theory)]]}}

at the top of Comparison of topologies? Kusma (討論) 23:43, 16 May 2006 (UTC)

Thanks for that suggestion - I have renamed the page. In a similar vein, I am tempted to write 2-3 articles on the subject of 'thin sets' and 'polar sets' (as used in potential theory, subharmonic functions etc.) and find that these terms also link to pages mainly about set theory. Would it be sensible to call my new pages 'thin sets (potential theory)' etc. What do more experienced wikipedians think? Madmath789 10:10, 17 May 2006 (UTC)

Nothing links to Fine topology, so it might be better to turn this into a disambiguation page rather than redirect to Comparison of topologies, thereby avoiding an awkward disambiguation phrase in Comparison of topologies. Nothing links to Thin set either. --Lambiam^Talk 11:07, 17 May 2006 (UTC)

Idea: when user clicks on an equation wikipedia explains it

Sorry if this is the wrong place / its already been suggested (I searched :-\), please direct me to the right place if here is incorrect (or tell me its not a worthwhile idea if you think so). This is a suggestion that when a equation is displayed (for example the one on this page) the user can click on the equation and is taken to a special page that explains the contents of the equation and what it means.

OK, let's try it:

$\int _{0}^{\infty }1\,dx.$

Weird! What I see is this:

UNIQ5f19c7bc44ccc704-math2f6e29f1133d184200000001

What I "should" see is this:

$\int _{0}^{\infty }1\,dx.$

When I click on it, it takes me to the right place.

Is this browser-dependent? Michael Hardy 01:50, 20 May 2006 (UTC)

You are seeing artifacts of one of the intermediate interpretation passes that mediawiki does during math markup. When all goes well (e.g. properly formed or properly messed up math syntax) you'll either see the math, or some nice error note. If something unexpected happens (e.g. math in links, math in image captions, etc) then mediawiki will mysteriously dump out that garbage. Basically, you're causing an error that isn't specifically handled by the markup engine, so it gets confused. It's totally browser-independent.

As for the suggestion, I think such a thing would overly burden the database and the authors. It sounds like you're suggesting that a new page be created to explain every equation. That's a lot of new pages to store, and a lot to write. That style of writing probably wouldn't be very popular, since most of us are used to explaining equations in neighboring text. Plus, it would be quite a large programming task to add that functionality into mediawiki. Staecker 02:07, 20 May 2006 (UTC)

Ahh no I meant something automatically generated. By definition a mathmatical equation is exact and parsable by a computer. It will be a bit of work by someone to make it function, but I thought I'd put it out there as an idea.

In the page I referenced above, the reason for the equation is explained, but at the level of someone who understands equations already, not to someone who has no idea what the $\sum$ means. I thought it would make wikipedia more accessible to non maths experts and require the time of one developer (and not the time of every maths editor).

See User:RickiRich\Math_Example for an example of what I think could be programatically created, and a description of How it could be created without too much fuss. After exams I'll have a go at this if no one else has.

--RickiRich 01:01, 22 May 2006 (UTC)

I don't think this is a good idea, I doubt it will get used by anybody if it gets implemented, and I doubt the developers will ever bother implementing that. You should at least get some support for this feature before you decide to do anything about it. But again, I don't think this wil lead anywhere. Oleg Alexandrov (talk) 04:07, 22 May 2006 (UTC)

What Oleg said. Dysprosia 06:31, 22 May 2006 (UTC)

I think it won't work. A significant obstacle is that mathematical symbols can have many different meanings, and a computer just ain't smart enough to distinguish which one you mean. For example, the + symbol could mean addition, or it could mean the span of two vector spaces, or the concatenation of two strings, etc. So much depends on context. (Also you probably wanted a forward slash in the title of that page, not a backslash. See Wikipedia:Subpage.) Dmharvey 21:43, 24 May 2006 (UTC)

Intriguing idea, but I don't think its right for wikipedia. There have been some development along similar ideas both MathML and OpenMath formats have had some aspect of representing the meaning of an equation rather that its purely visible representation. OpenMath in particular has seen a lot of work with people developing Content Directories which are domain specific collections of mathematical definitions. There has been numerous papers on the subject, but I don't think its gained much acceptance apart from as a means of converting from one computer algebra system to another. In the wikiworld meta:Semantic MediaWiki is a wikipedia extension which allows some form of semantic markup.

Why its not right for Wikipedia: basically the wiki concept follows KISS principle (Keep it simple stupid) and this sort of system gets rather complex. Hopefully all the relevant terms should be linked in the text anyway. --Salix alba (talk) 22:17, 24 May 2006 (UTC)

Massive edits foil comparison operation in article history

Sometimes an editor goes thru an article and changes many minor things at once. For example: spelling corrections; deleting unneccessary spaces; replacing & alpha ; with α; etc.. When this is done, the function which shows changes in the history often fails. It may begin matching an old paragraph to the wrong new paragraph and then it never gets back in synch (until one reaches a section header, if that was not changed). Of course, this makes it very difficult to check that the change was done appropriately.

I think that it is probably impractical to correct this bug in the comparison. So I am suggesting that you-all try to avoid this situation in the first place. When you do such massive edits, please first do every other paragraph (to allow the software to get back in synch with an unalterred paragraph). Then do a separate edit to change the remaining paragraphs. Thank you. JRSpriggs 06:06, 20 May 2006 (UTC)

I think you'll need to provide a concrete example of this happening. Dysprosia 09:39, 20 May 2006 (UTC)

The most recent occassion on which this happened to me was in the 18 May 2006 edit of Constructible universe by UkPaolo, called clean up +spelling correction using AWB. See http://en.wikipedia.org/w/index.php?title=Constructible_universe&diff=53858793&oldid=53818751 and scroll down to the section named "L is absolute and minimal". JRSpriggs 09:05, 21 May 2006 (UTC)

For this example it would have helped if the diff algorithm ignored blank lines, that is, tried to match up the two versions after filtering out the blank lines (which should be re-inserted for the final presentation). I suppose there is a backlog of all kinds of wishes for the developers, and I don't know how important this really is, but it is relatively simple to implement. --Lambiam^Talk 18:48, 21 May 2006 (UTC)

I think that the problem is more difficult than Lambiam thinks it is. In the section to which I referred, the only blank line was the next to last paragraph. Yet the mismatching of paragraphs began at the first paragraph in the section. Apparently the diff-software cannot measure the similarity of the contents of two paragraphs until after it has decided irreversably that they are matching paragraphs. That matching of paragraphs appears to depend only on whether they are identical, followed by interpolation (guessing) between identical pairs of paragraphs. JRSpriggs 07:12, 22 May 2006 (UTC)

Blank lines were removed in the edit following each and every section title. This doesn't show up clearly in the diff, but start an edit on both versions and compare the contents of the edit boxes, and it will be obvious. If then the next paragraph is also modified, the diff algorithm can't line them up. The silly thing in this massive edit is that many of the changes have no substance and consist of replacing two spaces after a full stop by a single space. --Lambiam^Talk 10:06, 23 May 2006 (UTC)

You may want to mention this on Wikipedia:Village pump (technical) or check the bugZilla where there are currently 93 bugs related to the diff. In this case the edit summary gives some clue, the edits were done using the WP:AWB tool, they are mainly minor edits and it would be hard to break this up into smaller edits, by limitations of the software. --Salix alba (talk) 07:16, 23 May 2006 (UTC)

The problem is apparently caused by a feature of AWB, "Apply general fixes", which removes "excess white space" to which the diff algorithm is sensitive (Wikipedia:AutoWikiBrowser#"Set options"). --Lambiam^Talk 10:15, 23 May 2006 (UTC)

resolve a revert war at dual space

I find myself in a revert war at the article dual space. It's mostly about style; how much information is too much, whether material looks good or fits. this diff shows the difference between the two users preferred revisions. See also this old version for a much longer revision that I reverted. I am pessimistic with how talks on the talk page are going. We seem not to see eye-to-eye. I would like to get some more opinions. -lethe ^{talk +} 04:42, 23 May 2006 (UTC)

Compound Poisson process question

Probabilists out there, I wonder if you could answer a question posted at Talk:Compound Poisson process. Oleg Alexandrov (talk) 17:25, 24 May 2006 (UTC)

looks right to me. (and the changes i made were mostly cosmetic.) Lunch 19:10, 24 May 2006 (UTC)

I added a final line to the moment generating function calculation, which should clarify matters further. The variance result looks OK, by computing them in terms of the moment generating function. — Arthur Rubin | (talk) 20:27, 24 May 2006 (UTC)

Looks OK to me, too. Michael Hardy 21:17, 24 May 2006 (UTC)

... and generally, the nth cumulant of the compound Poisson distribution, following the notation now in the article, is λt times the n moment of the distribution of the random variable that the article (in its present form) calls D_i. This can be shown via the law of total cumulance. The cases n = 1 and n = 2 are just what now appears in the article. Michael Hardy 21:20, 24 May 2006 (UTC)

Widespread mathematical delusions

I'd like to hear some opinions about the new article Widespread mathematical delusions. At the moment, the article lists only one delusion, and I am not sure what the delusion actually is, but it has something to do with statistical independence. In fact, the article Widespread mathematical delusions criticizes the lead section of statistical independence. Can somebody make sense of the new article?

The user who created the article has also written some articles on eventology, a theory which I haven't heard about. The article on eventology lists ten references, all by the same author, including some papers in good Russian journals so we might want to keep the article even though it violates the Wikipedia:Vanity guidelines. -- Jitse Niesen (talk) 05:12, 25 May 2006 (UTC)

0.999... ≠ 1 must be pretty widespread. And misconceptions about infinity are pretty common. -lethe ^{talk +} 06:58, 25 May 2006 (UTC)

I can't make much sense out of this rant. The "intuitive" meaning offered in the article Statistical independence appears to me to be an informal way of saying P(B|A) = P(B). Using the standard definition of conditional probability, this means P(A ∩ B)/P(A) = P(B), or P(A ∩ B) = P(A) P(B), in other words: events A and B are independent. Where is the delusion? There is no shortage of delusions, including mathematical ones, and the field of statistics and probability theory is particularly rich, but this doesn't seem to be one of them. Its like having a diatribe against saying that 1 < 2 means that 1 is less than 2, while it means nothing except "1 < 2". To AfD? --Lambiam^Talk 11:16, 25 May 2006 (UTC)

I find it hard to understand exactly what this guy is ranting about, mainly because of the poor translation of his thoughts (presumably from Russian) into English. His maths seems to be correct, but only seems to show that conditional probability can be different in different situations. If this page is to be kept, it surely needs a different title? (and a lot of work on wording) I cannot believe that this really is a *widespread* delusion Madmath789 11:46, 25 May 2006 (UTC)

Whatever else it it is, it is surely OR. Paul August ☎ 11:51, 25 May 2006 (UTC)

The delusion consists in popular attempts to justify or to prove or to deduce the definition of independence of events: P(AB)=P(A)P(B) from other assumptions. Mathematical definitions do not demand proofs, especially in a preamble to encyclopaedic paper on probability theory. The criticism is directed only on style of a preamble. All other sections of paper “Statistical” are quite correct. Thanks for discussion. - Helgus 12:28, 25 May 2006 (UTC)

Helgus: I think you misunderstand what the lead section (what you are calling the "preamble") of Statistical independence, is saying. It is not trying to "prove the definition" rather it is simply trying to provide an intuitive understanding of the concept. In any case any criticism of that article belongs at talk:Statistical independence not in some other article. Paul August ☎ 15:52, 25 May 2006 (UTC)

Probably you are right. Especially it concerns the second section of paper. However the first section without doubts keeps within a well-known encyclopaedic category “Paradoxes in mathematics”. Russian mirror of this paper contains, for example, popular delusions which often meet at discussion on “Fermat's last theorem”, “Parallel lines in Lobachevsky's geometry”, “Events with zero probability”. Can be it is necessary to open a new category “Paradoxes in mathematics” into which this paper could enter? - Helgus 21:58, 25 May 2006 (UTC)

Yes AfD unless its moved to a different name and cleaned up to be less like Orignial Research, give it a bit of time though the page is less than a day old.

Also the eventology page is now proposed for deletion, although the other sub articles and the category are not. Either it should be all or none and I think AfD might be better than prod in this case. --Salix alba (talk) 12:58, 25 May 2006 (UTC)

If the page is to be kept, it should probably be renamed -- "delusions" is not quite neutral, perhaps "misconceptions" would be better. Dysprosia 13:03, 25 May 2006 (UTC)

The eventology pages look suspicious to me. The only reason I created Category:Eventology is too keep them all in one place. I agree that an AfD vote on all of them could be the things to do. Oleg Alexandrov (talk) 15:37, 25 May 2006 (UTC)

It really is OR and a rant. The title reads pretty bad as well, it probably should be deleted.--Jersey Devil 17:37, 25 May 2006 (UTC)

I've removed the prod tag from eventology, If we are to believe the references there, it isn't OR, although it may be non-notable. So I agree with Jitse's, I'm not sure we should delete this. Paul August ☎ 18:09, 25 May 2006 (UTC)

But User:Helgus is Oleg Vorob'ov, the author of 10 out of 11 of the references. Sounds like OR to me. Staecker 02:44, 26 May 2006 (UTC)

No, OR means writing about something which has not yet been published elsewhere. Paul August ☎ 02:48, 26 May 2006 (UTC)

You're right- sorry, I confused it with WP:AUTO. Not surefire grounds for deletion, but it gives me the willies. Staecker 02:57, 26 May 2006 (UTC)

Yes writing about your own work is problematic. And we should take special notice of such. Paul August ☎ 17:10, 26 May 2006 (UTC)

eventology, but not sub-pages now on AfD. --Salix alba (talk) 10:45, 28 May 2006 (UTC)

Lebesgue spine

Being a newcomer here, I would appreciate some brief advice: Lebesgue spine is listed somewhere as a missing link, but when I look at 'what links here', I only find things like Wikipedia:Missing science topics/Maths16. I could write a page about the Lebesgue spine, but would it be any use? Madmath789 20:35, 25 May 2006 (UTC)

Sure it would be useful. Paul August ☎ 02:45, 26 May 2006 (UTC)

Non-negative v. nonnegative

OED lists "non-negative" but Webster's lists "nonnegative". Is this a British/American usage split? I've looked through a few textbooks, but there doesn't seem to be any particular consistency (not all American books use "nonnegative" and not all European ones use "non-negative"). Any opinions? There seems to be a mix among Wikipedia articles (even within a single article) and titles. Thanks. Lunch 22:05, 25 May 2006 (UTC)

I use either when the mood strikes me. If there's no standard, what's the difference? Ryan Reich 22:39, 25 May 2006 (UTC)

I s'pose I was thinking consistency would make things easier to find, and any source I found was always self-consistent whereas the Wikipedia isn't. And now that I look through the textbooks sitting in front of me, four have "nonnegative" (five American authors) and only one has "non-negative" (two Frenchmen). Lunch 23:11, 25 May 2006 (UTC)

In my experience, in American papers and textbooks "nonnegative" is by far the most common. Older works may use "non-negative" to a greater frequency. --C S (Talk) 01:52, 27 May 2006 (UTC)

Stone-Cech compactification name

Most of the references I've seen have a symbol over the "C", which I can't figure out exactly how to generate. (Also, there seems to be a convention that the "-" should be replaced by an n-dash "–".) — Arthur Rubin | (talk) 00:28, 26 May 2006 (UTC)

How about this: Čech? Dmharvey 02:51, 26 May 2006 (UTC)

When I open an edit window, below the Save page button is a box that says "Insert:", followed by numerous special characters. The character in question is one of them, and clicking on it causes it to be inserted into the edit box. JavaScript must enabled in the browser for this to work. --KSmrq^T 03:52, 26 May 2006 (UTC)

What a mess. We have Stone-Cech compactification and Stone-Čech compactification, and Čech points to neither, and probably we need Cech as a redirect as well. Dmharvey 02:56, 26 May 2006 (UTC)

Hm, apparently the redirect at Stone-Čech compactification is my fault; don't really remember doing it. Stone-Cech compactification should be moved to Stone-Čech compactification, but it won't let me move it because the redirect is to a different place. I'll tag the redir for speedy. --Trovatore 03:05, 26 May 2006 (UTC)

OK, fixed now. This time the endash thing came in handy. --Trovatore 03:12, 26 May 2006 (UTC)

How about Štone-Cech compactification? :-) -lethe ^{talk +} 04:01, 26 May 2006 (UTC)

Added. Hey, you never know. --Trovatore 22:34, 26 May 2006 (UTC)

Maths AfDs

A certain User:Mathguru has AfD'd Quasi-Hopf algebra and Quasi-bialgebra. I think it is notable, but as the author, I may be biased.Blnguyen | Have your say!!! 06:39, 26 May 2006 (UTC)

I'm a hair away from closing them both speedy keep. -lethe ^{talk +} 10:48, 26 May 2006 (UTC)

Too late now ... I closed them. -- Jitse Niesen (talk) 12:00, 26 May 2006 (UTC)

well, mathguru, Afd' the Australian Mathematics Competition as well.Blnguyen | Have your say!!! 08:00, 31 May 2006 (UTC)

Also closed as a speedy keep. -- Jitse Niesen (talk) 08:36, 31 May 2006 (UTC)

A query

Does anyone have a reference or proof for Kronecker's lemma? This has been bothering me, mainly in case absolute convergence of Σ x_n ought to be included. Charles Matthews 13:07, 26 May 2006 (UTC)

I think the statement is true as is stands, but I don't have a reference. Using summation by parts,

${\frac {1}{b_{n}}}\sum _{k=0}^{n}b_{k}x_{k}=S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{n-1}(b_{k+1}-b_{k})S_{k},$

where $S_{k}$ are the partial sums of the x's. Pick any epsilon > 0, choose N so that $S_{k}$ is epsilon-close to s for k > N. Then the right hand side is

$S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{N-1}(b_{k+1}-b_{k})S_{k}-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})S_{k}$

$=S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{N-1}(b_{k+1}-b_{k})S_{k}-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})s-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})(S_{k}-s)$

$=S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{N-1}(b_{k+1}-b_{k})S_{k}-{\frac {b_{n}-b_{N}}{b_{n}}}s-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})(S_{k}-s)$

Let n go to infinity. The first term goes to s, which cancels with the third term. The second term goes to zero. Since the b sequence is increasing, the last term is bounded by $\epsilon (b_{n}-b_{N})/b_{n}\leq \epsilon$. Dmharvey 13:41, 26 May 2006 (UTC)

Now transcribed to that controversial category Category:Article proofs. linas 01:43, 13 June 2006 (UTC)

Indiscriminate collection of information?

Don't pages like this, Derivative (examples), break with WP:NOT?--Jersey Devil 02:32, 27 May 2006 (UTC)

I have put it up for afd, your input would be appreciated.--Jersey Devil 02:36, 27 May 2006 (UTC)

Mathematics is Article Improvement Drive collaboration

Ladies and Gentlemen! Did you know that the article Mathematics is the current Article Improvement Drive collaboration? --Lambiam^Talk 22:40, 27 May 2006 (UTC)

Voted for it on the AID page. One user commented that it is in the top ten most viewed pages on Wikipedia and therefore must be a featured article.--Jersey Devil 23:01, 27 May 2006 (UTC)

Eventology AfD

The article Eventology (by the same author as Widespread mathematical delusions) has been nominated for deletion. --Lambiam^Talk 13:21, 28 May 2006 (UTC)

Delusions in probability theory and statistics on AfD

I've nominated the article Delusions in probability theory and statistics (earlier called Widespread mathematical delusions) for deletion. --Lambiam^Talk 22:31, 28 May 2006 (UTC)

Disambiguation of sinc function

There are two possible definitions of the sinc function, namely

$\operatorname {sinc} \,x={\frac {\sin x}{x}}\quad {\mbox{or}}\quad \operatorname {sinc} \,x={\frac {\sin \pi x}{\pi x}}.$

One possible way to handle this is to split the article sinc function in two, sinc function (normalized) and sinc function (unnormalized), similar to the usual disambiguation process. We are having a discussion on Talk:Sinc function (unnormalized) whether this is the proper way to go about it, and I'm solliciting others to join. -- Jitse Niesen (talk) 05:21, 31 May 2006 (UTC)

Possible confusion over 'subadditive'

There is an article Subadditive which discusses functions satisfying $f(x+y)\leq f(x)+f(y)$, and there is a link to this article from Sigma additivity in the category measure theory. There seems to be a different definition of 'subadditive' (and also 'countably subadditive') in use in measure theory:

$\mu (E\cup F)\leq \mu (E)+\mu (F)$

(used in developing the theory of 'outer measure'). My question is: do we need a separate page for subadditve set functions, or should we incorporate it into the existing subadditive page? (Or are subadditive set functions not notable and we do not need them?). I might be in a position to write something on the set function version of subadditive (if needed), but would appreciate some views about what might be done - and there are probably others better qualified to write such stuff anyway.Madmath789 11:27, 31 May 2006 (UTC)

I think you're right, subadditive (measure theory) deserves its own article. I don't know any measure theory, but I recall there being interesting theorems about set functions which are additive (on finite collections of sets) and countably subadditive. Dmharvey 11:37, 31 May 2006 (UTC)

Be bold! Write stuff, we move and fix later. Charles Matthews 11:46, 31 May 2006 (UTC)

Barry Simon article

The piece on Barry Simon is from a fan, it seems. Important guy for mathematical physics, and this should be better expressed and sourced, and have more technical stuff about the work. Charles Matthews 11:46, 31 May 2006 (UTC)

A good example of hagiography I guess. --CSTAR 18:54, 1 June 2006 (UTC)

Jun 2006

E9 (Lie algebra)

My knowledge of Lie algebras is a single course, but this potentially confusing notation was never mentioned. Has anyone else heard of this? Septentrionalis 18:40, 1 June 2006 (UTC)

I have never heard of this notation. I note that my references list the notation as E₈⁽¹⁾. The subscript here is, as always, the rank. -lethe ^{talk +} 18:51, 1 June 2006 (UTC)

Please review

I have extensively revised and cleaned up Divisibility rule, so please take a look and help to improve it more. As I'm not fully experienced at all the editing tools, I'm sure the formatting and adherence to guidelines and standards could be improved.

I'd like to create a number of other pages related to mental math, so I'd like to get feedback on this one, the first I've heavily edited. (The current mental arithmetic has only the most basic, simple of techniques.

Walt 01:59, 2 June 2006 (UTC)

Category:Billion and cousins up for deletion

See Wikipedia:Categories_for_deletion#Category:Thousand. Oleg Alexandrov (talk) 18:57, 3 June 2006 (UTC)

Poincaré conjecture

Some Chinese news sources have picked up a story about a recent journal article by Cao and Zhu, experts on the Ricci flow, who have written what they (and the journal editors) claim is a "complete" proof of the geometrization conjecture, by giving more details of Perelman's work. Slashdot has also picked up on this. As a consequence, there has been several editors who have insisted on placing mention of Cao and Zhu's paper in the lead section. I have disagreed (see talk page discussion and also some of my edit summaries for extensive reasons). Please continue discussion there. I would also appreciate if people could pop in and check that things don't get out of control. Thanks. --C S (Talk) 02:15, 6 June 2006 (UTC)

American Institute of Mathematics

The article on American Institute of Mathematics has been nominated for deletion by someone. R.e.b. 13:02, 6 June 2006 (UTC)

PlanetMath Exchange project milestone

The PlanetMath Exchange project has today reached a new milestone, with 40% of all PlanetMath articles reviewed.

For those of you who have not been following the project, I thought I would take this opportunity to report on the status of the project, and the progress which has been made to date. The purpose of the project is to review all PlanetMath (PM) articles (which are licensed under GFDL) and to incorporate any appropriate PM content not adequately covered on Wikipedia (WP).

There are over 4800 PM articles listed, of which over 1900 of which have been reviewed so far. Of the reviewed articles, 143 PM articles have been copied to WP, creating entirely new WP articles, and 121 have been merged into already existing WP articles. Additionally, a further 75 PM articles have been identified as needing to be copied, and 349 needing to be merged.

The project maintains 49 lists of PM articles grouped by topic (e.g. 11 Number theory, 26 Real functions, 54 General topology). The entire list of lists is compiled into a "Article lists" table, and statistics are maintained for each topic's list.

19 editors have identified themselves as participants, and 26 have reviewed at least one PM article (see Editor contributions).

Oleg Alexandrov, has provided several excellent tools to facilitate the project. He and Mathbot created the original 49 lists (first created in Feb 2005, and updated with new PM articles in March 2006). They also perform daily updates of statistics in the "Article lists", and "Editor contributions" tables. In addition, Oleg has created a convenient tool to assist in converting a PM article to wiki markup.

I heartily encourage everyone to join the fun.

Paul August ☎ 02:06, 8 June 2006 (UTC)

Direct logic up for deletion

See Wikipedia:Articles_for_deletion/Direct_logic -Dan 15:36, 8 June 2006 (UTC)

Another misguided nomination for deletion

Please vote at Wikipedia:Articles for deletion/American Institute of Mathematics. Michael Hardy 23:33, 9 June 2006 (UTC)

Yeah, R.e.b. told us already. -lethe ^{talk +} 00:48, 10 June 2006 (UTC)

I closed that AfD. -lethe ^{talk +} 00:54, 10 June 2006 (UTC)

Functional analyst needed

Hi, I left a question regarding the correct statement of the Ryll-Nardzewski fixed point theorem at Talk:Ryll-Nardzewski fixed point theorem. Cheers, AxelBoldt 04:10, 11 June 2006 (UTC)

As stated it's wrong. The semigroup is required to satisfy another property, that it be "distal". Also I don't think it can be used to prove existence of Haar measure on general locally compact groups, although I think for compact groups yes. I think this is in Rudin's functional analysis book for instance. Also see Frederic Greanleaf's little book (now horribly outdated) on "Amenable Groups".--CSTAR 12:41, 12 June 2006 (UTC)

Rewrite Poincaré_conjecture?

I invite interested parties to make comments at Talk:Poincaré_conjecture#Peer_review. --C S (Talk) 12:48, 11 June 2006 (UTC)

Jaques Hadamard or Jacques Hadamard?

An anon recently redirected the wikilink in Chaos Theory from the first to the second. Is this legitimite? Are these the same person? — Arthur Rubin | (talk) 15:30, 11 June 2006 (UTC)

Yes, same person. Correct spelling is Jacques [22]. I have changed the Jaques page to a redirect and fixed the link in the single remaining article that used the wrong spelling. Gandalf61 15:53, 11 June 2006 (UTC)

Zipper theorem

I wanted to {{prod}} this article. But to be sure I thought I'd check. Is this article nonsense or not? I couldn't google the name, but that doesn't always mean anything. Garion96 ^(talk) 00:20, 12 June 2006 (UTC)

The theorem and its proof in the article are correct. The theorem was not known to me under this or any other name. --Lambiam^Talk 00:53, 12 June 2006 (UTC)

Thanks, so I won't {{prod}} it. Anyone here wants to clean that article up? Cause the way it looks now, it's not understandable for the non mathematician reader. Like me. :) Garion96 ^(talk) 12:04, 12 June 2006 (UTC)

Hmm, perhaps I should have looked at at the article again. It already is cleaned up. Thanks. Garion96 ^(talk) 12:05, 12 June 2006 (UTC)

I think it's a neologism. I think it should be deleted without some evidence of that name having widespread currency. Dmharvey 12:15, 12 June 2006 (UTC)

I've heard it referred to in that way ("zipper theorem"); dunno if that's enough evidence for you. I also can't think offhand of a place I've seen it in print, though. I could ask around. Lunch 18:53, 12 June 2006 (UTC)

I'm skeptical that the name is very common. I can't imagine the theorem would even have a name amongst mathematicians. So I think the term would only be used in certain kinds of introductory course work. Google gives no results (off Wikipedia), so nobody that has mentioned it, for example, in a course webpage. The only place I can think the term may exist is in some textbooks somewhere. Even in that eventuality, I don't know if it's worth having an article based on that amount of usage. I guess it does no harm, but I'm also hard-pressed to imagine a situation where we would want to link to it. --C S (Talk) 19:18, 12 June 2006 (UTC)

Merge it into Limit of a sequence#Properties? —Blotwell 17:01, 13 June 2006 (UTC)

I've asked a few people around, and none other than me have heard this result referred to as the zipper theorem. I guess it's not as popular a term as I thought. Maybe zipper lemma instead?  ;) Maybe it'd qualify for a list of some sort of elementary properties of limits; if not, maybe stick it in the article on limits. BTW, this theorem is true for any metric space, but is it true for non-Hausdorff spaces? How much can the requirements of the theorem be relaxed? Lunch 21:57, 20 June 2006 (UTC)

The exact same proof, translating epsilons into open sets, proves it in every topological space. This result has about the same significance as, say, the linearity of differentiation, and should probably go in a list of limits like the list of derivatives. Ryan Reich 22:48, 20 June 2006 (UTC)

Sure, a list of limits article would be a good idea. And I guess you can just replace balls with neighborhoods; I think I was confusing myself with the non-uniqueness of limits in non-Hausdorff spaces. Lunch 23:33, 20 June 2006 (UTC)

Sorry if I was curt with that reply. I'll be happy to put together a basic list of limits. Actually, following the model of the list of derivatives, there isn't any need to touch zipper theorem, just link to it from the list. Unless we really don't like it for some reason. Ryan Reich 00:22, 21 June 2006 (UTC)

looks good! Lunch 17:58, 22 June 2006 (UTC)

integrable systems

Over at Talk:Constant of motion, I've been reduced to babling and waving my hands to the effect that a "system of differential equations with constants of motion == integrable system == system with symmetries" and conversely, "non-integrable system == system with no constants of motion". However, it occurs to me that I know of no grand theorems making this claim. Are there any? Is this in fact a collection of small results in narrow fields that have accreted into a grand truth? Guidance? How can one make this clear at a college-math level? It doesn't help that the article integrable system is somewhat foreboding in its current form. linas 01:30, 13 June 2006 (UTC)

Maybe I'm being lame? Maybe its just the Frobenius theorem coupled to the idea that the submanifold has a natural symmetry, ergo by Noether's theorem has constants of motion? I've never had formal skoolin in this matter. linas 03:13, 13 June 2006 (UTC)

I think I'm grasping for Liouville's theorem (Hamiltonian). I swear this stuff goes in one ear and out the other. I'm babbling even now. linas 03:27, 13 June 2006 (UTC)

You make a good point about the current article being somewhat forbidding. I would go a step further. I don't think integrable system should redirect to integrability conditions. An integrable system usually (?) refers to a Hamiltonian system with a full set of Poisson-commuting flows. Naturally, integrability conditions do play a role, but there is more structure a priori in an integrable system. For the point about conserved quantities for an integrable system, since the Hamiltonian flows commute, there should be loads of conserved quantities. (As you ask, is there a general theorem here? Does Noether apply? etc). Hence a system without "enough" conserved quantities will be non-integrable. I'm not so sure about the converse. Silly rabbit 13:15, 13 June 2006 (UTC)

Thanks. What I've been reading gives the name completely integrable system to the case of a full set of commuting Poisson brackets. Your "not being sure about the converse" would imply that there are non-integrable systems with a "full set" of conserved quantities. That certainly sets my mind wandering in wild directions. linas 23:27, 16 June 2006 (UTC)

Nice start on integrable systems. It certainly has helped me organize some of my own wild wanderings. I'm clearly not an expert, but it seems to be tricky to give a good definition of an integrable system. (Ok, so first off, yes I meant what you call completely integrable: which is unarguably a better term ;) In particular, there are issues of local versus global integrability. What does global integrability mean anyway? Do the all the level submanifolds have to be closed? Do the constants have to be found explicitly, or can they just be given in some implicit sense? Can a locally completely integrable system have degenerate Poisson brackets on some small dimensional locus, and still have functionally independent integrals? (Here is the "lack of converse" possibility -- if it exists to begin with.) Silly rabbit 23:37, 17 June 2006 (UTC)

Thanks. I'd say a Lie group is the prototype for something that is "globally integrable". I don't know of any systems that are "provably integrable" (constants of motion implicitly given), but whose solution is unknown (no explicit form). I suspect one can find level manifolds that are not closed, certainly things like the horocycle flow ( aka Anosov flow on tangent space of SL(2,C)) has the flavour of being non-compact but this is an off-the-cuff remark. I believe that the whole area of sub-Riemannian geometry is permeated with integrable systems that have cuts and isolated singularities and the like. Next, chaotic systems have "regimes" of regular and chaotic motion that's interspersed; the KAM torus being the famous example, although the easy-to-understand variants are in difference equations. Then there's all this stuff about homoclinic orbits, and stuff like Axiom A, which I dimly understand. Or things I dont:Smale's spectral decomposition theorem. I'm sort of learning this stuff as I go along.linas 04:57, 18 June 2006 (UTC)

Mathematicians for Wikipedia:Version 0.5 Nominations

On Wikipedia talk:WikiProject Mathematics/Wikipedia 1.0 there is a request for the most notable mathematicians whos biographies could be included in Wikipedia:Version 0.5 Nominations. Suggestions for celebratity mathematicians welcome. Possible also assesments of the quality of their article also welcome. --Salix alba (talk) 07:45, 15 June 2006 (UTC)

Thanks to great work by Lethe we now have a fairly comprehensive list of the the giants for mathematics on Mathematics/Wikipedia 1.0. A new template Template:maths rating has also been created together with a set of categories listing the quality and importance of mathematics articles. Mathbot will included these articles in Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality on a daily basis. Help is now needed in identifying the important maths articles and assigning then a grade (Feature Article/A/Good Article/B/Start/Stub), which can be done by including the template on the talk page. There are a few biographies which may be suitable for listing as good articles and several other on some key figures which are barely more than stubs and could do with expansion.

I'm also thinking that the list of mathematicians could make a good article in its own right, either as a section in Mathematicians or its own article, possible Influential mathematicians. --Salix alba (talk) 09:25, 16 June 2006 (UTC)

We already have list of mathematicians, but I guess you are thinking of a selective subset. I don't know if it is worth its own article. Oleg Alexandrov (talk) 15:37, 16 June 2006 (UTC)

Yes I was thinking of a more selective list, probably anotated as well, briefly describing their main acheivments. It could be an interesting way to tell the history of mathematics through the people involved and the new areas of study they started. This sort of presentation, is quite popular in science books aimed at the general reader and might appeal to certain wikipedia readers. --Salix alba (talk) 20:20, 16 June 2006 (UTC)

Well If you want a selective list one place to start would be Bell's Men of Mathematics. Paul August ☎ 20:55, 16 June 2006 (UTC)

Might I also suggest the obvious web site, MacTutor? --KSmrq^T 04:53, 17 June 2006 (UTC)

Probability/Measure theory glossary?

Does WP have a glossary that translates the language of probability theory to measure theory? I've got a complaint on my talk page that I'm trying to decipher; I don't understand Score (statistics) and Fisher information, although I suspect I would, if they were restated in terms of measure theory. The root of this interest is the rather astounding edit here, which is so remarkable, I abstract it here:

Fisher information is a powerful new method for deriving laws governing many aspects of nature and human society. B. Roy Frieden sets out in detail how Fisher information can ground a great deal of contemporary physical theory, including Newtonian mechanics, virial theorem, statistical mechanics, thermodynamics, Maxwell's equations, Lorentz transformation, general relativity, EPR experiment, Schrodinger equation, Klein-Gordon equation, Dirac equation, Rarita-Schwinger equation, and the fundamental physical constants. Frieden and coauthors have also used EPI to derive some established principles and new laws of biology, the biophysics of cancer growth, chemistry, and economics.

Surely, the ommission of M-theory and intelligent design is just an oversight? linas 00:38, 17 June 2006 (UTC)

See Talk:B._Roy_Frieden for a little bit of discussion and some links to external reviews of Frieden's work. He has some interesting ideas but, it seems, not quite the revolution he makes out for himself. The IP address of the edits is assigned to [http:/csc.canterbury.ac.nz Christchurch College of Education] in New Zealand. Maybe Frieden's been travelling? Lunch 03:49, 17 June 2006 (UTC)

user mathisreallycool

A new user mathisreallycool (talk · contribs) has made several edits which to my mind betray a fundamental lack of knowledge in certain mathematical topics. I have reverted several additions by this user, and I want to vet some other things by the user. For example, the article Konfisakhar space seems unobjectionable, it's referenced. However I've never heard of this idea, it's not in any of my texts, nor is it in my EDM2, and frankly, I find the idea of a fractal vector space hard to believe. Can someone (maybe with access to the book by Schaeffer) verify this concept? Otherwise, I shall want to AfD is. And maybe also this definition of semidirect products for monoids? -lethe ^{talk +} 07:14, 17 June 2006 (UTC)

A web search for Igor Konfisakhar suggests the work of a creative student, violating WP:NOR. The citation of the Schaeffer book is also not quite correct; the second edition (ISBN 978-0-387-98726-2) has two authors. I have no personal knowledge of the topic or the book, but I share your reservations.

PS: I've begun using 13-digit ISBNs, since the official transition is not far off. On online converter is available. --KSmrq^T 10:40, 17 June 2006 (UTC)

I've listed Konfisakhar space for deletion. "Professor Igor Konfisakhar" appears to be an undergrad, notable only for being a 3rd place winner in a Putnam prize contest, which is better 'n me but not good enough for this. linas 03:54, 18 June 2006 (UTC)

I know Igor Konfisakhar personally (or did), and can confirm that he is (at present) an undergraduate. Tesseran 03:21, 19 July 2006 (UTC)

The reference work listed is searchable online at Amazon (see [23]). I find no reference to "fractal" or "Konfisakhar". Paul August ☎ 04:35, 18 June 2006 (UTC)

Problems at Propositional Calculus

(Copied from my talk page. Oleg Alexandrov (talk) 07:51, 17 June 2006 (UTC))

JA: Hi, could you help sort out the continuing tangles at Propositional calculus? First there was that improper name change last month, and I let it go because the user who did it seemed fairly competent and added some good stuff, but now the word "logic" seems to be inviting anonymous users to take the article out of the mathematical logic designation and add any sort of half-baked exposition that they can cook up. I don't know my way around the procedures well enough to keep dealing with sort of stuff. Much appreciated, Jon Awbrey 05:15, 17 June 2006 (UTC)

There had been some noise in the past about moving propositional calculus to propositional logic or classical propositional logic. The move to propositional logic was affected by Charles Stewart via WP:RM last month, then reverted by a history-destroying copy-paste by Jon Awbrey this week. I reverted the copy-paste (restoring the history), then reverted the proper move (preserving the history), so now we're back where we started. If the move is to happen, a case will have to be made again. -lethe ^{talk +} 07:59, 17 June 2006 (UTC)

Use "iff", not "if", in definitions!

Some editors appear to believe that there is a convention which requires the use of "if" in definitions rather than "iff" (short for "if and only if"). A definition is a proposition which equates a new term to a compound expression composed of old terms. So using "if" is wrong. One should use "iff" or an equivalent, such as: "if and only if", "is", "is the same as", "means", "is equivalent to", "when and only when", etc.. JRSpriggs 08:20, 17 June 2006 (UTC)

Though you are technically correct, I don't think it's such a problem to use just an "if" in a definition. It's tedious to always write "if and only if" (and the abbreviation is esoteric), and the full meaning can always be inferred. Of course to require "if" in definitions is certainly bad. -lethe ^{talk +} 08:29, 17 June 2006 (UTC)

I am complaining because thrice recently someone has changed "iff" to "if" in a definition. JRSpriggs 10:03, 17 June 2006 (UTC)

If I saw that happen, I would probably revert. -lethe ^{talk +} 10:25, 17 June 2006 (UTC)

Well, "if" is brief, commonly understood, and colloquial; "iff" is brief, not commonly understood, and precise. What to do? Personal, I dislike "iff", so I either write out "if and only if" or use a phrase like "exactly when". My feeling is that anyone who understands the meaning of "iff" and feels comfortable with it also has enough of that fabled "mathematical maturity" to not misinterpret a definition using "if". I am not aware of a WikiMath guideline, nor a Wikipedia guideline that speaks to this slightly delicate issue involving both accessibility and formal correctness.

A recurring challenge with a multinational pool of editors is melding one's own training and taste with that of others. I cringe whenever I see the word "ditto" in an article, as to me it screams of informality, not suitable for an encyclopedia. I'd love to see both "iff" and "ditto" banned, but I have no sense of how much agreement I would find for that view. --KSmrq^T 11:01, 17 June 2006 (UTC)

I would agree with abolishing "ditto" but not with abolishing "iff". Anyway, I agree with Ryan below. The precision afforded by the usage "iff" is useful for theorems, but not so much for definitions. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

This doesn't follow any mathematical practice I've ever seen, so why should we insist on it simply because it's technically right? We don't make policy here, just record it. Besides, to counter your argument, "iff" is logically absurd in this context since the term to be defined has no prior meaning; whether or not it applies is determined by the text of the definition. In other words, "only if" is vacuous if the term is unique, and if not, it is erroneous. Someone reading an "iff" definition for the first time will wonder if they've missed some other discussion of the term, and anyone else will be annoyed because it departs from the usual style. I agree with lethe, though: any change of one to the other should be reverted. This is a personal preference. Ryan Reich 10:57, 17 June 2006 (UTC)

We are certainly allowed to make policy here. What we don't do is invent subject matter for our articles. So we can't invent terminologies, but we can certainly decide on conventions for our terminologies. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

I'd argue more but apparently you agree with me. My objection to inventing policy in this sort of case is that the choices are not all equally acceptable; it's not like choosing an indentation style for C code, where many different styles all have their widespread adherents. I've simply never seen "iff" in a definition. Ryan Reich 11:30, 17 June 2006 (UTC)

I can't quote chapter and verse, but I remember seeing a mathematical style guide recommending "if" in definitions. Personally I prefer "when", to distinguish it from the notion of logical consequence (as in: You are in a dilemma when you don't know which way to turn), although some may decry the temporal connotation. --Lambiam^Talk 12:07, 17 June 2006 (UTC)

I much prefer "if", and that's what I observe as common mathematical practice. Dmharvey 12:57, 17 June 2006 (UTC)

I think "if" is somewhat unclear, but I have no problem with "only if", "if and only if", the equivalency arrow ($\Leftrightarrow$) and other such language. The term "iff" I object strongly to, at least in basic math articles, on the grounds that it is jargon that is unfamiliar to many basic students of mathematics who have not done proofs. But don't take my word for it - I've seen countless edits where amateurs have "corrected" iff to "if". Deco 13:53, 17 June 2006 (UTC)

Something unseemingly asymmetrical about accepting "only if" (⇐) and rejecting "if" (⇒). I must say I do not understand your position. -lethe ^{talk +} 14:04, 17 June 2006 (UTC)

The words "only if" do not imply "given the sufficient condition that", and it is a myth that "if and only if" is the conjunction of "if" and "only if". It is merely a way of clarifying "if" using the additional qualifier "only if" that only serves to strengthen that "no we don't mean this is just a necessary condition" but in fact an equivalency is intended. If I say "a number is prime only if it has exactly two factors", the intepretation is clear; it does not even suggest that there might be a prime which doesn't have two factors. Deco 17:23, 17 June 2006 (UTC)

Indeed, "only if" implies "given the necessary condition that", and "if" means "sufficient". And in mathematics, "if and only if" certainly is their conjunction, at least in a formal context, but since this is a formal phrase that is to be expected. Using it in an informal context evokes its formal meaning and is just confusing when you start to split hairs about what it really means, especially given that syntactically, it definitely looks like the conjunction of "if" and "only if". Stating "only if" in a definition is redundant, since the term is intended to be deciphered, not encoded: if I see a long string of conditions which happen to have a nice definition but I don't know it, I will not go looking for one until it's necessary; on the other hand, if I see an unfamiliar term I will go looking for its definition. Putting "only if" in the definition would just mean "whenever you see this term, you can be sure it means this phrase", which is exactly what the process of defining the term means anyway. Combined with the common-sense reason that people just don't talk like that, I say "only if" should stay out. Ryan Reich 18:03, 17 June 2006 (UTC)

Oops, I switched necessary and sufficient, that's not what I meant. I don't object to leaving out "only if" if you find it unclear. I'd like to avoid "if" due to ambiguity if possible, but my main concern is that that we avoid "iff", which people generally assume is a typo if they don't know about it. Deco 21:01, 19 June 2006 (UTC)

I strongly support the use of "if" in definitions over either "iff" or "if and only if". By the way this has (of course) been discussed before. I will now provide for your reading pleasure this oldie but goldi, this blast from our past:

(Start of copied text from talk page archives)

Can I raise the question of whether we want iff in definitions? I don't. I think it's offputting to those not pure-mathematical 'native speakers'. And the idea that it's more rigorous is surely shallow.

Charles Matthews 16:28, 21 Oct 2003 (UTC)

In the absence of an explicitly-stated convention, I think it's marginally more rigorous than "if". I have occasionally used "if" in a definition and meant "if but not only if", although not on Wikipedia as far as I remember. I'd suggest that if "iff" is undesirable, the best replacement for the non-specialist reader is "if (and only if)", since the rigorous alternative is to ensure that "if" is never used other than to mean "iff". Onebyone 16:49, 21 Oct 2003 (UTC)

I don't accept the 'rigour' argument, anyway. Using 'if' there is an implied 'one can assert' in front of mathematical propositions - which no one writes unless in a very careful formal treatment. Those who care about this can imagine it all anyway. Better, I think, just to use normal language: 'an X is a Y with property P'. I haven't checked whether the definitions of legal terms on Wikipedia make a point of this type of care. On the whole I think it's wasted: it's hard to imagine the user who needs it. Charles Matthews 17:58, 21 Oct 2003 (UTC)

Well, I agree that the pedantry is not worthwhile if it is off-putting for readers. On the other hand, I'll take no part in any kind of global edit to deliberately introduce ambiguity, even if that ambiguity can generally be resolved from context. You say "I think this care is wasted", but I suspect that for most mathematician authors it will require extra care to remember not to do this rather than extra care to do it!

"An X is a Y with property P" sounds good to me, especially in the standout definition at the top of the article. Nobody writes articles on topics other than maths saying "a person is a saint if and only if they have been canonised by the Church" or whatever. If there's a more formal section of maths in the article, I do think that "iff" and other jargon words should be used in that section exactly as the author would use them in any mathematical writing.

Onebyone 10:35, 22 Oct 2003 (UTC)

So, my understanding is that the Project isn't trying to prescribe, but is looking for some harmonisation. Charles Matthews 19:02, 22 Oct 2003 (UTC)

(End of copied text)

Paul August ☎ 18:38, 17 June 2006 (UTC)

In regards to Lambiam's comment on a style reference, a popular one is Nick Higham's "Handbook of Writing for the Mathematical Sciences." On page 20 of the second edition it says:

By convention, if means if and only if in definitions, so do not write "The graph G is connected if and only if there is a path from every node in G to every other node in G." Write "The graph G is connected if there is a path from every node in G to every other node in G" (and note that this definition can be rewritten to omit the symbol G).

In my own experience, I cannot recall ever seeing "if and only if" in a definition in formal mathematical writing. Can someone supporting the use of "if and only if" cite a current journal article with this usage or give reference to a style manual that advocates its use? Lunch 20:44, 19 June 2006 (UTC)

Oh, in definitions. I didn't realise this was regarding definitions and not theorems. My apologies for my dissent - of course it's redundant in a definition to state that it's an equivalency. I would not use any more verbose language in this case. Deco 21:03, 19 June 2006 (UTC)

If the consensus is that "iff" may be confusing because some lay-persons do not know what it means and it might be mistaken for a misspelling of "if", then I will not object when other editors change "iff" to "if and only if" or an equivalent. However, I still object to using "if" by itself between the definiendum and the definiens. JRSpriggs 03:52, 20 June 2006 (UTC)

Using a conditional rather than a biconditional in a definition is wrong

"Often ... the definition is a statement that expresses a logical equivalence between the definiendum and the definiens." When we define a mathematical symbol (constant, function, or relation), the definiendum (symbol defined) is a new word being added to our language; and it has no meaning other than that given to it by the definition. The definition is a postulate which gives meaning to the new word. Since it is not normally our intention to add strength to our set of axioms (as the axioms of ZFC), this must be a conservative extension. And we should be able to translate any sentence involving the new word into one which omits it and has the same meaning. If you put a conditonal ("if") rather than a biconditional ("if and only if") between the definiendum and the definiens, then you are doing one of three things:

• Using "if" to mean "if and only if" when in the context of a definition. This is potentially confusing to the readers. First, they may not realize that "if" is being used for "if and only if". Second, they may learn to read "if" as "if and only if" in other circumstances where it is mistake to do so.
• You are using "if" to mean "if", i.e. you really intend the postulate which is the definition to be a conditional rather than a biconditional. In this case, one could not prove the negation of the new word was ever appropriate. For example, if we defined "measurable cardinal" via "κ is a measurable cardinal if it is an uncountable cardinal with a <κ-additive, non-principal ultrafilter.", then we could not prove that 17 was not a measurable cardinal.
• You are assuming that anything which is not provably true is false. Surely, since Gödel's incompleteness theorems, it is clear that this is not a tenable position.

In conclusion, definitions should not be conditionals. JRSpriggs 03:52, 20 June 2006 (UTC)

If you were working in a formal logic, you would not be phrasing your definitions as English sentences at all, and this would not be an issue. The use of "if" in definitions is just one of many places that context is conventionally used to establish the meaning of a symbol. If you did want to make a definition that was not biconditional (for some reason) you could simply use more explicit language such as "A implies that B", "A is a sufficient condition such that B", or implication arrows. Finally, I think the language "B if A" should be avoided in theorem statements in favor of "if A, then B" or "Given A, we have B" or "Whenever A holds, it follows that B", or something a bit less vague; such use would preclude confusion about the meaning of that sentence structure. Deco 04:18, 20 June 2006 (UTC)

The "if" in a definition is not a conditional. It's an assignment, like the = sign in C. This is a well-established linguistic convention (and it doesn't mean "if and only if"; as I said, it's an assignment, and not any sort of proposition at all).

Moreover I have a strong antipathy to using "iff" in formal writing (in any context, not just definitions). It's acceptable on a blackboard, like "wrt", but it should not appear in articles. --Trovatore 04:27, 20 June 2006 (UTC)

Agree with Trov on both counts. That being that "if" in deffintions is perfectly acceptable, while "iff" in definitions is a bit iffy. :) Oleg Alexandrov (talk) 04:39, 20 June 2006 (UTC)

In a context that makes clear we are offering a definition, "if" works for me.

We say that a foo is a bar if it satisfies mumble.

In a context which is not clearly a definition, we must be more careful.

… A foo is a bar if it satisfies mumble. …

Can a foo be a bar even when it does not satisfy mumble? Here I don't know!

So now we come to the question of what to write in Wikipedia articles. Often definitions are not highlighted as such, but appear inline in a form that is ambiguous about the intent. I myself would never use "iff". I would try to word the statement carefully so that it was clear what I meant. When we write, we know what we mean, so we don't always see the possible confusion our words may cause a reader. But when we see a potential problem, the better solution is to reword to make our intent clear, not to throw in jargon like "iff". Flag a definition as a definition, and our readers will thank us. (Well, no. Actually they'll read happily along, never knowing the confusion we spared them. Bad writing is what gets noticed.) --KSmrq^T 14:33, 20 June 2006 (UTC)

I guess I am agreeing with Oleg and Trovatore here. I am happy to go along with pretty much all the authors I respect (Rudin, Lang, Halmos, Ahlfors, ...) and NOT use 'iff' or 'if and only if' in a definition. Either would looks stilted and also be more confusing than helpful to less experienced readers. Madmath789 14:47, 20 June 2006 (UTC)

As KSmrq said "Often definitions are not highlighted as such, but appear inline in a form that is ambiguous about the intent.". For that reason, if no other, we should use language the same way in definitions that we do elsewhere to avoid confusion. JRSpriggs 05:43, 21 June 2006 (UTC)

When KSmrq said In a context that makes clear we are offering a definition I took it to mean that a phrase such as we say that or a foo is called bar if or we define a foo to be a bar if is used. This doesn't mean that Definition. has to appear in front of the sentence. By wording the sentence carefully, it can be made clear that a definition is occuring. If it isn't clear, putting in if and only if won't make it clear; that will only make it look more like a theorem if it already looked like one. I agree with several others, by the way, that common usage avoids the phrase if and only if in a definition. CMummert 12:36, 21 June 2006 (UTC)

We should also make definitions clear by italicising what we are defining. Dysprosia 12:39, 21 June 2006 (UTC)

I can't believe this is still going on. I've already made all the arguments I think are necessary to oppose "if and only if", but I do have two questions: is there anyone, anywhere, who has become confused due to the use of "if" in definitions? Would you actually want to read an article so reeking of pedantic formalism? Also, to respond to your comment above: a more important consistency principle than internal consistency is external consistency; our articles must follow common English writing practice. As KSmirq said, it is always possible to set apart definitions from the text (and this would constitute better writing), thus obviating the internal consistency problem, but it is never possible to set apart Wikipedia from the experience of a native English reader. Ryan Reich 12:50, 21 June 2006 (UTC)

Redirects in the list of mathematics articles

Currently we have 12102 articles in the list of mathematics articles. Out of them, 1070 are redirects (see the complete list). Redirects get created in several ways

1. Plugging in some redlink in the list (not anymore, as all redlinks are removed automatically)
2. Merging an article to a bigger article
3. Renaming an article.

In my view it is the third which makes for most redirects.

While redirects are very important, I see no good reason for why they should stay listed in the list of mathematics articles (I estimate that there are at least 2000 math redirects which are not there).

I wonder what people think of a big purge, removing all redirects from the list of mathematics articles. Of course, if at some point a redirect becomes back an article, my bot will add it back to the list. Thanks. Oleg Alexandrov (talk) 22:37, 17 June 2006 (UTC)

So if I create a redirect to a math article, but the redirect isn't already a redlink from the list, then it doesn't get added to the list? -lethe ^{talk +} 22:57, 17 June 2006 (UTC)

No. The bot adds to the list of mathematics articles via categories. So, if your redirect is made to be in a math category (which it won't, most of the time), the bot will add it to the list. Otherwise it won't. The primary purpose of list of mathematics articles is to list articles I think, not redirects, although a separate list of redirects to math articles may be found useful by some people. Oleg Alexandrov (talk) 23:55, 17 June 2006 (UTC)

Well whatever uses there may be for a list of math redirects, this list cannot serve, since it doesn't contain them all. Therefore, you have my full endorsement to remove them. There is simply no reason to have only some of the math redirects in a list, right? -lethe ^{talk +} 00:00, 18 June 2006 (UTC)

I'm not sure what purposes the list serves. Take Circular arc, which is currently a redirect to Arc (geometry), but the concepts are distinguishable and Circular arc might eventually grow into a separate article. In an index it would be reasonable to include it. If the purpose is to have a way to visit every maths article to check if its conforms to a new policy, then you'd prefer to skip it. (By the way, it currently is not categorized.) Perhaps math-categorized redirect pages could be listed, but rendered in italics, like with the All pages search. (<-This comment was by User:Lambiam who forgot to sign it. JRSpriggs 11:08, 18 June 2006 (UTC))

OK then, so if a redirect is important enough, it should be categorized, and then my bot will add it in. About making redirects italic, that is harder to do, as I would need to daily download a lot of articles to see which are redirects. Oleg Alexandrov (talk) 16:25, 18 June 2006 (UTC)

Done. The log is at User:Mathbot/Changes mathlist. Oleg Alexandrov (talk) 02:39, 19 June 2006 (UTC)

MathML / improved TeX support

Hi people. For those of you who have been watching developments concerning m:blahtex, MathML support on wikipedia, etc, I'm sure you've noticed nothing much has been happening for a while. Well, for the past few months, Jitse and I have been trying pretty damn hard to push buttons in the background to make things happen, but sadly the core developers simply haven't taken the bait. It seems to be a case of "yeah, it looks interesting, but we've got like 10,000 other things we're trying to do, and we just haven't got around to checking out the code yet...". It seems that wikipedia just doesn't have enough engineer-hours to give us the attention we need to get this going, and there's only so much pushing that Jitse and I can do without becoming annoying pains in the arse.

The status now is that I'm certainly not spending any more time on the code until I have some indication that there's a chance wikipedia is going to use it. And I've had enough of all the promotional "hey everyone isn't blahtex wonderful and y'all should be using it". It's tiring and not really my style. I enjoy writing code, not selling it.

So unless the people who hang out on this page somehow band together and make the developers realise that MathML is something that people want, the project is going to die a serene death. I took the initiative about a year ago, and wrote 13,000 lines of code to prove that it was possible. I'm happy to help out some more, and of course I look forward to the day when there is good mathml support in wikipedia. But someone else needs to take the initiative now, because I'm through.

Anyway, I think I'll go to bed now, make sure I'm bright and fresh to watch Australia defeat Brazil 6-0 tomorrow.

Good luck guys. Dmharvey 03:57, 18 June 2006 (UTC)

Perhaps a petition signed by the user community? Which is then passed up to Jimbo? This is an important chunk of code that is being laid at the feet of the sysadmins; surely its something that should be picked up. A few words of caution: (1) although the code may work well for you, sysadmins concerned with high-availability servers have a very very very different view of what it means "to run reliably". You might not have given them warm fuzzies on this issue. (2) The WP servers seem often overloaded, there may be unvoiced concerns about impacting performance. If you think these issues are under control, then a public appeal may be the right route to get attention. If they're wobbly, you might get blown out of the water. linas 04:18, 18 June 2006 (UTC)

I've explored the BlahtexWiki and I have to say, I'm quite impressed. I just have two main concerns for implementing MathML on Wikipedia, if those were fixed, I would gladly push the developers to implement it.

1. Browser compatability. Almost nothing works for me in IE 6.0
2. Fonts. It appears as if you need to download special fonts for MathML to display correctly. I'm not sure how many people would want to do that. Also, the radical symbols do not display correctly in Firefox for me.

I would be glad to push for the implementation of MathML in WP if we can somehow figure something out for those two problems. —Mets501 (talk) 04:26, 18 June 2006 (UTC)

There is no way around the issue of downloading fonts. As far as I can tell, Firefox often lacks some fonts by default. For IE I think one needs the MathPlayer extension.

It is no surprise the developers are weary at accepting a huge chunk of outside code, especially there is not really a huge demand for MathML from users. Any ideas of how to convince the developers to take this step would indeed be much appreciated. Oleg Alexandrov (talk) 05:14, 18 June 2006 (UTC)

Thank you, thank you, thank you for all of your work. Having written some mathematical typesetting code myself at one time, I have a feeling for what a challenge it is to do a good job. There are so many subtle issues of fonts and stretching and spacing and symantics and positioning and compatibility and on and on, that only someone who has been in the trenches can really appreciate the magnitude of this endeavor. It really takes a champion, like Roger Sidje on the Mozilla project or David Harvey on BlahTeX.

I believe I can speak to systems programmers with some credibility, and I would be happy to do so on behalf of BlahTeX. A noisy outcry from Wikipedia's technical writers might also prove influential. Beyond mathematicians, we have physicists, chemists, biologists, and engineers of all stripes, all of whom could benefit.

The latest word from the STIX Fonts Project is

"After reviewing the tasks required for completion of the project, September was established as a revised target for the beta test. The final production release will likely occur in December, but the TeX package may not be ready until January 2007."

Although the STIX project has not been exemplary in meeting its targets, it does appear that it is real, it is happening, and in a matter of months there will be little excuse to complain about a lack of fonts for MathML.

I cannot imagine that server load is a realistic concern. Currently MediaWiki converts <math> mkup to images, which requires parsing, pseudo-TeXing, image generation, and then serving the images. Unless BlahTeX is very poorly written indeed, it is unlikely to be more of a load. All BlahTeX has to do is transcribe TeX syntax to MathML syntax; and bloated as it is, MathML is still much smaller to serve than the equivalent image. Caching may be used currently to amortize the cost of image creation, but there is no good reason the same could not be done for BlahTeX. And, again, storing cached images requires more space than storing cached MathML.

That leaves the concern of bullet-proofing. For that, we have the empirical argument that the code has been tested against every single equation currently used at Wikipedia, of which there are hundreds of thousands. Yes, a few hundred do not translate; but that's a small matter of manual conversion because they depend on the bastardized TeX currently supported (texvc). In compensation, future editors will have use of a broader range of TeX features, something arrow-pushers will appreciate.

It occurs to me that if the developers are recalcitrant, perhaps Jimbo Wales might be persuaded. Pressure from the top could then be more effective than pressure from the bottom.

Thanks again for all the hard work so far. Given Wikipedia's culture of consensus, it seems only fair that others now help shoulder the burden. --KSmrq^T 10:33, 18 June 2006 (UTC)

But so what is the next step? Campaign to get it installed on test.wikipedia.org? What can we do to help? Send messages to mediawiki-l? I notice searching through the archives, that you have previously announced releases of blahtex to that mailing list, and they have never had any response. Have you ever had any dialogue with anyone from mediawiki development about this code? Whom do we talk to? -lethe ^{talk +} 10:43, 18 June 2006 (UTC)

---

At the risk of sounding too critical, how difficult would it be to make things work for the current "bastardized TeX"? The idea of breaking old revisions of articles without it being obvious why that is makes me kind of queasy ...

Is this a major issue? How do things fail after the change? Backwards compatibility is something that needs to be addressed, even if it cannot be guaranteed.

Not that I think this is a huge problem, if the scope is that small.

Otherwise, I'm with lethe. Whom do we talk to, and what's their favourite ice cream flavour (for bribes, you know)?

RandomP 11:00, 18 June 2006 (UTC)

We have a list of all the broken bastardized tex instances. There are a couple of hundred, which we've slowly been fixing, one at a time. We would obviously want to finish them off before we went live. -lethe ^{talk +} 11:21, 18 June 2006 (UTC)

---

I'd just like to qualify my remarks: it seems that even today, "history" won't get you anything like the old version of an article, at least when that article uses images from the commons.

I think it would be really cool if someone wrote, essentially, a simulated wayback machine for wikipedia, that went back to the wikicode, images, and math layout as they were when the revision was created. I thought that's what history was, but apparently, not so.

So that's not an issue either, and can we please have mathml now?

RandomP 14:09, 18 June 2006 (UTC)

Brief replies to above questions

• Linas's question about server overload. This is a complete non-issue for several reasons, some already mentioned by KSmrq. I haven't done any benchmarking for a while, but here's what I remember. Both blahtex and texvc spend almost all of their time (at least 90%) on PNG generation. Blahtex is somewhat faster at PNGs, maybe 2 or 3 times faster, since I switched to dvipng instead of using imagemagick+dvips. (And Brion Vibber has endorsed the use of dvipng in the past, ask Google for more information.) MediaWiki already has code for caching the images, so this time only gets spent during the first edit, not on subsequent page views or edits. Second, I haven't directly compared the parsing and mathml generation time of blahtex to the parsing time of texvc, but I do know that my desktop machine can generate mathml for the entire wikipedia corpus in about 30 minutes. There's 200,000+ equations in there, so it's not lightning speed, but you ain't gonna overload their servers. And MediaWiki also has code already for caching the mathml, so again that only happens on the first edit. Third, some tests Jitse and I ran a while back suggested that texvc's parsing is unbearably slow on long input data; blahtex on the other hand processes that kind of input really fast.
• Linas's point about reliability. Of course it's got bugs. All software has bugs, especially software that hasn't yet been exposed to the real world. Someone mentioned above that it's been tested against all the input in wikipedia and doesn't pretty darn well, which is a start, but of course that's not the point. The real question is whether it survives a determined adversary with source code access. Well, I don't know, I suppose most likely it's not secure. But all software has to start somewhere. I'm not asking to have the code installed tomorrow and force everyone to use it. Heck, at this stage I'm not even asking for the "minimal interesting configuration", which is that it's only available for registered users who select MathML in their preferences, and that we stick to texvc for all PNG output, and only allow mathml for the equations for which texvc can already generate graphics. All I'm asking for is that some core developer gives us more than ten seconds of their time to render an opinion. If they tell me the code is crap and I'm a chump, that's fine, I can live with that, at least it's an answer. If they tell me I need to rewrite it in COBOL, that's fine, it gives me something to do. If they tell me I need to write a comprehensive test suite, that's great, I can do that. But so far the longest reply I've had from people like Brion Vibber, Tim Starling, etc, is a one-line email from Brion:

It sounds great, but I've not had a chance to look at it yet...

He also replied on the mailing list once, here's what he said:

Neat!

I understand 100% where he's coming from, but it's still incredibly frustrating.

• Mets501's question about fonts. As KSmrq points out, the STIX fonts project is going to get there eventually, not tomorrow or the next day, but eventually. I believe it will solve all the font problems, because e.g. Firefox will just be able to bundle the fonts in the default installation and it will all Just Work. So for now, no good answer, but eventually, yes.
• Mets501's question about browser compatibility. Short answer: it sucks. Firefox/Mozilla is the best out there in my opinion, and it's not quite good enough yet. (I've heard about your problem with broken radical signs; I believe it's a recent regression.) I think the reason browsers haven't quite made it yet is because there just isn't the content out there yet. Well, we can change that, because if wikipedia switched on mathml support, it would overnight become the largest repository of mathml on the web. (I don't have stats for that, it's just a guess.) And here's something else: when I first mentioned to the firefox people, like roger sidje, that wikipedia was planning mathml support, suddenly a whole raft of mathml-related bugs in firefox got fixed, bugs that had been lying around unattended for 2-3 years. These open-source guys love wikipedia. If we deliver, they will follow. On the other hand, I don't have any illusions about MSIE.
• RandomP's question about backward compatibility. It's a minor problem in my opinion. See http://blahtex.org/errors.html for a complete list, as of March. Maybe that list looks long, but remember it's across 13 languages, and represents about 0.1% of the total. We could fix them all in a few days. And anyway, Jitse's glue software falls back on texvc if blahtex fails, so it's easy to make the problem vanish entirely.
• Everyone's question about who to talk to. I don't know. I've run out of ideas and energy. That's why I'm turning the initiative over to all of you. If enough of you make enough noise, and if the powers that be are hearing voices other than that of the guy who wrote the program, maybe something will happen. Dmharvey 12:28, 18 June 2006 (UTC)

Caching: As KSmrq suggests, the MathML is cached and hence it needs to be generated only once.

Backward compatibility: To expand on what David says, the code as currently written uses texvc to generate HTML and PNG and blahtex for generating MathML. If texvc fails, then blahtex will also generate PNG. Therefore, the few formulae that are not understood by blahtex (for instance because they use invalid latex syntax) will still be rendered as PNG, but there won't be any MathML. In other words, just like the present situation. -- Jitse Niesen (talk) 13:02, 18 June 2006 (UTC)

my email

I sent this email to mediawiki-l just now:

---

From: lethe at charter dot net
Subject: Blahtex: what's the next step
Date: June 18, 2006 8:08:37 AM CDT
To: mediawiki-l@Wikimedia.org

David Harvey and others has been working hard on Blahtex, the next generation in MediaWiki math rendering technology. Visit http://www.blahtex.org/ for more information and http://wiki.blahtex.org/go/Main_Page for a running demo hosted by Jitse Niesen.

Harvey suggests that blahtex will afford a significant performance advantage, but the main impetus is the ability to render MathML. Support for MathML is not widespread at the moment, so the need for Blahtex is not urgent, but it is the future, and we have reason to believe that Wikipedia's adoption could goad browser developers to speed their efforts (the answer to the old chicken and egg of who comes first, browser support or use by web pages could be: Wikipedia comes first).

It has to happen someday, and today is as good a day as any. Harvey says the software is ready for the next step, and wants to move forward, but doesn't know whom to talk to in order to make this happen. I'm writing you to voice my full support for Harvey's and Niesen's efforts, to find out what needs to be done to take the next step towards rolling this software out, and to ask if there is anything I can do to help the developers to get this software ready for deployment.

Thanks
lethe

---

I was hoping that several others of you would chime in on the mailing list. If we had a chorus of complaining voices, we would be harder to ignore. Currently, the developers watching that mailing list have ignored me completely. What should I do? Send another, more plaintive, email? -lethe ^{talk +} 11:51, 20 June 2006 (UTC)

Are you sure this is the right way to go? I'm not sure about the relation between mediawiki, the software that actually serves wikipedia, and that mailing list. Is the authoritative version of mediawiki the one serving en:? Are decisions about changes to that software, beyond bugfixes, made on that mailing list, the meta wiki, wikipedia (en) talk, or where?

RandomP 11:56, 20 June 2006 (UTC)

The short answer is, I don't know. Where is the right venue to discuss changes in the software, and who is the right person to talk to? I don't know. Does anyone know what is the right course of action to take? How to we get software changes evaluated and committed? As for whether en runs the official version, the answer is yes. They rollout new versions on test.wikipedia.org first, I think. But then they roll it out for en.wikipedia.org. Should I email Brion Vibber or Rob Church or something? I don't want to be a nuisance, but I think Dmharvey's request to get a response from them at least to say "sorry, we can't accept this" is not unreasonable. -lethe ^{talk +} 12:20, 20 June 2006 (UTC)

Hmm. This is a problem. I've looked around for a good place, but the best I've found is the MediaWiki bugzilla, which currently has two bugs [24] [25] matching blahtex, and I don't think either is what we want.

Can someone create a new feature request there and link to it (I'd also suggest linking back to a Wikipedia page from the new bug, so we can have discussions without all getting out to get accounts on yet another bugzilla)?

That might be a first step to, at least, documenting we're trying to get it in through the official channels ...

Again, I'm just confused by the whole thing. There's a wiki, a mailing list, a bugzilla, and apparently an IRC channel, and I still don't know where and if development discussions happen. However, at least a bugzilla is permanent and will get someone's attention, one would hope ...

Can we move the discussion to Wikipedia:Blahtex or something? It's of interest to physicists, economists, biologists, etc, too! (Or should be.)

RandomP 12:53, 20 June 2006 (UTC)

m:Blahtex would be a place to have a centralized dicussion, after we sent spam to all the physicist, economist, etc Wikiprojects. But that would only be necessary if we are completely unable to open up a discussion with developers in one of the developer channels. If we can do that, then let's just have the discussion there. -lethe ^{talk +} 13:02, 20 June 2006 (UTC)

I have submitted a bug report and sent another email to mediawiki-l. You can vote for the bug at this location. I have no idea what voting for bugs accomplish; I wouldn't be surprised to find out accomplishes nothing. -lethe ^{talk +} 13:23, 20 June 2006 (UTC)

I'm told that most discussions take place on IRC, but I haven't seen any. There are two relevant mailing lists: mediawiki-l for the software as used on Wikipedia, other Wikimedia sites, and other wikis not related to Wikimedia; and wikitech-l for technical matters (hardware and software) involving Wikimedia (Wikimedia is the foundation running Wikipedia, Wikibooks, Wiktionary, Wikisource etc). Either list would be appropriate, and I think they mostly have the same readership. Then there is bugzilla, as mentioned by Lethe, and we also have Wikipedia:Village pump (technical) here. There are also two central wikis, http://meta.wikimedia.org/ which used to contain everything related to the software, and http://www.mediawiki.org/ where the documentation is being brought over to. So it is rather confusing.

I put the items in the order that seems to be best to get the attention of the powers to be (with IRC on top). However, in the end it boils down to an individual developer taking a decision. The concept of consensus plays rather a small role on that level.

I'd advise against emailing the developers individually. -- Jitse Niesen (talk) 14:02, 20 June 2006 (UTC)

I guess the response you may get from IRC depends on who's in the room. I went there first, before anything else, a few days ago as soon as Dmharvey posted his request, and got no biters there. They suggested I might have better luck on the mailing list. Perhaps I try IRC again at a busier time. -lethe ^{talk +} 14:08, 20 June 2006 (UTC)

Discussion continued

I'm not a developer, nor am I Jimbo, but putting myself in their shoes I'd be much more worried about the font issue than about accepting an apparently well-tested huge chunk of outside code. In fact, not being in their shoes this worries me. Many people access Wikipedia from computers they have no control over, and are in no position to download and install fonts for, even if willing to do so. Others may try to and fail. Most wouldn't even try, and miss out on all Wikipedia has to offer that involves formulas. I think it is important to keep blahtex alive, but aim at introduction after the availability of the required fonts has become common. --Lambiam^Talk 13:53, 18 June 2006 (UTC)

Thus MathML won't be enabled by default. Only people who know what it is, have capable computers, and want to see it, will see MathML. When the day comes that every windows, mac, and linux computer has by default MathML able browsers and plenty of fonts, then we can have MathML by default. But for today, let's have Blahtex which is smarter in all ways. This is a non-issue. -lethe ^{talk +} 14:22, 18 June 2006 (UTC)

Yes, I agree. I will help push for this to be implemented as much as I can. I do think, however, that the default should not be MathML (yet). Users who sign up for an account should be able to select MathML from the preferences page, but the option should link to a page called Wikipedia:MathML, which would say what MathML is, which browsers support it, and which fonts/whatever is needed for MathML to work. I would definitely not give up on this project and I hope that it will be implemented soon (I love experimenting on the BlahTeX wiki!) —Mets501 (talk) 16:54, 18 June 2006 (UTC)

We've really got to stomp out some myths. The most important fact is that BlahTeX only adds capability to MediaWiki, it does not force removal or breakage of anything that already works. A complete set of mathematics fonts will be available Real Soon Now to everyone on every platform with every browser. Don't have the necessary fonts on the computer you happen to be using? Not a problem; stick with the old-fashioned images and HTML hacks. Browser not set up to support MathML? Not a problem; don't ask for MathML. In other words, adoption of MathML is strictly voluntary.

So why BlahTeX? Because it offers so much more than texvc, which is old and seriously deficient. BlahTeX handles a broader range of TeX input, including things that are currently a real pain to work around. Even when it generates PNG output, not MathML, BlahTeX is superior to texvc.

And why MathML? Because it is the future of mathematics on the web, for reasons such as the following.

• A text-to-speech processor can read MathML aloud for vision-impaired users, or for ordinary folks who merely want to know how a formula is spoken.
• All the fonts and layout of a MathML display can be scaled up or down, just like the rest of the text on a web page, to either zoom in on a detail or zoom out for an overview.
• MathML can include arbitrary Unicode characters, something texvc is unlikely ever to do.
• A MathML formula is smaller and faster to serve than a PNG.
• MathML can allow internal line breaks, while images cannot.
• Programs like Mathematica allow cutting and pasting MathML formulae, so an equation can be transfered easily for evaluation or graphing.
• MathML has already found favor on technical blogs, like The String Coffee Table.
• Because MathML is built on XML, it can be processed with XSLT and used across diverse media. In particular, MathML will be much more compatible with print than any fixed-resolution PNG rendering.
• One of my favorite benefits is that the contents of a MathML formula are available to search in my browser, whereas a PNG is an opaque monolith.

Note that the MathML 2.0 Recommendation from W3C was released on 2001 February 21, and the 1.0 version dates back to 1998 April 7. That's an eternity ago in web time!

But to reiterate: BlahTeX offers considerable benefits even for those who do not choose to view MathML. It can't hurt. It can only help. Please support its rapid adoption by MediaWiki, in whatever way suits you best. --KSmrq^T 19:22, 18 June 2006 (UTC)

I think you should put that in an email to the mailing list. Perhaps wait until mine shows up and make it a reply so it's all in one thread though. We want to generate some noise so that it seems like there is a whole rabble of us clamoring for this. And of course we have to quelch the false assumptions that people will make to justify not using the software. -lethe ^{talk +} 19:29, 18 June 2006 (UTC)

Thanks, KSmrq, that's a nice piece of writing. Not for the first time, I admire your writing skills.

Apparently, the best way to contact the developers is via IRC (#mediawiki on irc.freenode.net). Another thing we haven't done is to contact our colleagues at the other language Wikipedias. I imagine that especially editors writing in a different script than ours would be interested. -- Jitse Niesen (talk) 04:23, 19 June 2006 (UTC)

Hey, KS, I think maybe this nice list of yours should be copied over to m:Blahtex where it would be the skeleton of a FAQ. A central repository that we can refer to easily to stop out myths. What say ye? -lethe ^{talk +} 14:38, 20 June 2006 (UTC)

If you like it, use it. --KSmrq^T 20:14, 20 June 2006 (UTC)

Do you think that we should write an email to Jimbo about this? Do you know how aware he is of BlahTeX? If we could convince him, it would definitely get implemented. —Mets501 (talk) 20:40, 20 June 2006 (UTC)

Let's try to confine our efforts to those people who will actually have a hand in the software direction, which I don't think Jimbo does. Anyway, the latest correspondence sounds like Vibber is going to set up Jitse with an SVN account. We might be in business, so let's wait to hear from Jitse and Dmharvey what happens with that. -lethe ^{talk +} 20:47, 20 June 2006 (UTC)

[via edit conflict] Hang on for the moment guys. Brion gave a more positive reply to one of Lethe's recent emails, see here. Jitse and I will work out what to do with this development, and we'll keep you all posted. Dmharvey 20:49, 20 June 2006 (UTC)

Yay! Good luck guys! Make sure to let us know about any developments. —Mets501 (talk) 13:11, 21 June 2006 (UTC)

Some progress has been made

See here. I'm not precisely sure about terminology here, but perhaps this makes Jitse a Developer. This is good news, but I don't promise mathml tomorrow. Still some work to do. We'll keep you posted. Thanks guys for your encouragement, and especially lethe for the insistent emails on mediawiki-l :-) Dmharvey 12:00, 22 June 2006 (UTC)

Or perhaps he's saying that he's responding to Jitse, and he will be adding the BlahTex extension (because he put in a comma). Either way, its good. —Mets501 (talk) 12:35, 22 June 2006 (UTC)

It only makes me a minor developer. The standard tariff is to sacrifice one virgin every full moon as otherwise Bad Things Happen. However, I can also be placated with papers on which I can put my name as co-author. ;) -- Jitse Niesen (talk) 13:19, 22 June 2006 (UTC)

Well, I can give away my virgin mathbot as a groom to the brand-new bride-to-be Jitse's bot (who am I am sure is a she, or otherwise can be made so just by flipping a bit). Oleg Alexandrov (talk) 16:10, 22 June 2006 (UTC)

So who is "jitsenielsen" anyway? Dmharvey 14:11, 22 June 2006 (UTC)

I'm pretty sure Brion Vibber made a spelling error :-) —Mets501 (talk) 14:30, 22 June 2006 (UTC)

Request for book recommendations

Maybe this is not the place for this (I am aware that this is not un all-purpose forum), but here it goes. I intend to order some math books from Amazon, but I'm not sure what to get. As it seems to me that there are some very good mathematicians here, I think you could help me a lot with some recommendations. Now for some background, to understand what I specifically need: I'm an undergraduate math student (though also an economics graduate and working economist) and I pursue math mostly for my own curiosity and because I truly enjoy it (more than economics :D). I need something mainly appropriate for self-learning, so I'm targeting good classic texts on major fields or other good books. I prefer books that don't shy away from advanced/abstract concepts, but preferably give motivation for concepts and some intuitive explanaition/interpretation. Also, I learn the most from books which include examples worked-out in detail and/or solved relevant problems. Also, note that unfortunately cost is an issue, so don't recommend too many books that are only somewhat helpfull (though by all means recommend books that you consider good, even if they are not very popular). Hope that you will have some advice for me... AdamSmithee 20:48, 18 June 2006 (UTC)

A great place to ask this question, which is indisputably appropriate (unlike here, which is apparently disputably so :)) is the sci.math newsgroup. You can get there through Google groups if you don't already know. This page is really just for discussing the Wikipedia mathematics project. Ryan Reich 20:57, 18 June 2006 (UTC)

I am sure that we could give a great deal of advice (though some of us will contradict each other!), but we do need a bit more info about your mathematical interests and level: which branches of maths are you most interested in? what sort of level are you at in that level? Perhaps it might be best if you could tell us some maths books that you believe you have mastered, and we could suggest some books that would make a "good next step"? Madmath789 21:02, 18 June 2006 (UTC)

Myself, I'm a graduate student and I like algebraic geometry and sometimes number theory. Or did you mean him? :) Ryan Reich 21:42, 18 June 2006 (UTC)

LOL! I did mean 'him', but our edits crossed, and I got the indentation wrong :-) (but if you want some suggested reading on algebraic geometry, I can probably oblige :-) ) Madmath789 21:46, 18 June 2006 (UTC)

The most affordable route is used books, especially if you live in or near a decent university or college. Some of the much older books are easier to learn from, because not so long ago mathematics texts had a bad habit of being horribly written for learning, though packed full of detail for reference. More recently there may have been a corrective swing, so that one can benefit from both a modern viewpoint and decent pedagogy. But in a field like algebraic geometry, the really old stuff has lots of geometry while the modern stuff has almost none. Depending on your tastes, one may appeal more than the other. Another fact about older books is that often recent books try not to duplicate the work of the early masters, so if you want to get the original insights from the folks who had them you have to step back in time. It reminds me of something that was said about the programming language ALGOL, that it was an improvement on many of its predecessors, and also on many of its successors. Lastly, it is vital to choose books at the right level at the right time, lest an otherwise great book become a doorstop. --KSmrq^T 22:39, 18 June 2006 (UTC)

Well, first of all tx for replying! As I said, I know this is not the place (and I'll probably try sci.math, which I didn't know about), but I tried it because I came to trust many of you guys. As for my background and interests: I'm an undergraduate student in math at this time. So far, my exposure was almost entirely to Romanian textbooks, which are very tightly written and unfortunately are generally very good for reference but not for learning (this is somewhat of a characteristic of Romanian academic books). On the other hand, I've read quite a few American graduate level textbooks in economics and I noticed that, generally, they are much better for learning (also, reading some freely available online math books lead me to believe this is also true for math). To give an example, at this time I'm struggling with linear connections and covariant derivative, but my (Romanian) books insist to much on tightely written modern coordinate-free stuff, giving virtually no motivation and no explanation, and I'm having trouble understanding why the stuff is defined that way, what does it mean and what is it good for.

At this moment my interests are rather wide and I just want to get a reasonable background in the main fields. However, I do have a sweet spot for abstract algebra, and I'm interested in probability and statistics (including links to measure theory, numeric analysis etc.) for the aplications to economics. But I'm also very interested in stuff like differential geometry for instance. As an example of one book that I have heard about, and I might get, I know about Jacobson's 'Basic Algebra' (though I don't know how that is), but I have no idea what else is there.

Regarding level, it is hard to say what undergraduate in Romania means compared to other education systems, but it is possibly more advanced than American undergraduate level (?maybe?). AdamSmithee 23:25, 18 June 2006 (UTC)

Hi, I suggest browsing Dover Publications online catalogue (use Google to find, I am lazy :P). They republish a lot of classical and important texts. By rule of thumb, eastern Europe is more advanced in beggining of undergraduate studies. -- 127.*.*.1 01:14, 19 June 2006 (UTC)

Poussin proof

I have just had a brief look at the page Poussin proof, and apart from being a short stub, at least half of it seems to be mathematical rubbish. I would like to have a go at making this into a sensible article - but about the Dirichlet divsor problem (the first sentence of the Possin page), as I can't find anything about this elsewhere. If I have missed it, and there really is a page about the Dirichlet divisor problem, plase let me know before I waste too much time ... Madmath789 12:11, 19 June 2006 (UTC) (OK, having read it again, it is not total rubbish, but badly worded.)

Change of project scope at Wikisource

(I've copied the following from Talk:Mathematics. — Paul August ☎ 16:56, 19 June 2006 (UTC))

I would like to call the communities attention to and personally protest a decision at Wikisource to exclude and delete a significant portion of the material that was part of its original charter. Prior to April 29 of this year, Wikisource:What is Wikisource? listed the following as included material:

"Some things we include are:

• 1. Source texts previously published by any author
• 2. Translations of original texts
• 3. Historical documents of national or international interest
• 4. Mathematical data, formulas, and tables
• 5. Statistical source data (such as election results)
• 6. Bibliographies of authors whose works are in Wikisource
• 7. Source code (for computers) that is in the public domain or compatible with the GFDL"

On that date the project page was changed to explicitly exclude:

• Mathematical data, formulas, and tables
• Source code (for computers) that is in the public domain or compatible with the GFDL
• Statistical source data (such as election results)

Obviously, this represents a major change in the scope of the project. It is based on a single poll conducted between April 4 and 27, 2006 Wikisource:Scriptorium/Archives/2006/04. Previous discussions had been held with opposite results Wikisource:Wikisource talk:What Wikisource includes. A primary reason given for the new change is that the editors participating do not feel competent to maintain this material and have little interest in it. However apparently no effort was made to notify participants in the previous discussions, nor to recruit new editors that might have an interest. Note that there are many active projects pages in mathematics and the sciences where such people might be found.

There was also no discussion of methods for reducing the load on editors, such as locking material after review. In general, reference material does not need or benefit from frequent edits.

I certainly respect the efforts of the regular editors on Wikisource and agree that their views should be shown some deference. However the process they chose is not sufficient. At the very least, I think there needs to be broader community input into such a massive change in the scope of a Wikimedia project. Even if this material is best excluded from Wikisource, I believe it deserves to be part of an encyclopedia and that any material already contributed should be moved elsewhere rather than be deleted. The simplest solution would be to move mathematical and scientific reference material to Wikipedia, where there are large communities to evaluate and protect this information. An argument could be made that mathematical data belongs in Wikicommons because it is, or potentially can be, language neutral. Or perhaps there should be a new Wikireference project. Computer source code deserves a separate discussion, since there are so many other open source code repositories available.

At this point hundreds of articles have been marked for deletion. See Wikisource:Category:Deletion requests/Reference data Some material has apparently aready been deleted. There is nothing left in Category:Mathematics. I would propose that all article deletions on Wikisource based on this change be frozen until a fuller, community-wide discussion can be held.

I have also posted these comments at Wikisource:Scriptorium, where I think the primary discussion should be held.--agr 16:01, 19 June 2006 (UTC) --agr 16:01, 19 June 2006 (UTC)

This call to arms would look better at Wikipedia talk:WikiProject Mathematics. It is about mathematics at wikipedia, not about the article Mathematics on wikipedia. -lethe ^{talk +} 16:12, 19 June 2006 (UTC)

(end of copied text)

It was actually my intent to post the here. I just messed up. I am removing the link from the math talk page.--agr 20:16, 19 June 2006 (UTC)

(Cross-posted from Wikisource)I would like to quote my own remarks on opening up this disscusion back on April 3:

I realize this has been discussed several times in the past, to the agreement of accepting such material. However, the current state of reference data on Wikisource is unacceptable. The community members who are active on this site have little interest, and in some cases understanding, of the data we have been hosting. Although there have been editors that were adamant that this material should be included here, they have not remained active in the organization nor matainance of it. Much of this material is beyond the active administrators ability to even distinguish vandalism from corrections. Because of this current state of affairs there have been nominations for deletion for some of this data. However I feel we need discuss the larger questions of the place of reference material on Wikisource before we make any deletions.

It is disingenuous to suggest we ignored previous discussions or made no efforts to find other solutions short of deletion. In fact I opened up the discussion back then to put a stop to this material being brought up piecemeal at Proposed Deletions. In all honesty, at the beginning of the April disscussion I expected that we would arrive at a solution for keeping a portion if not a majority of this material. No one who was interested in this material bothered to even suggest any alternatives much less volunteer to implement any solutions in over 2 months since then. As for calling this to the "community's attention", you imply we are trying to hide it or be secretive. This is false. I personlaly have left notes on WP talk pages of people showing recent interest, as well as mentioned the decision in passing on foundation-l. Not to mention the write up done by Pathoschild in Wikisource news during and after disscussion. The decision was also mentioned on wikisource-l. The idea that this was "based on a single poll" is also misleading. It is based on consensus taking into account ideallistic comments made in prior disscussions as well as the pragmatic reality of maintaining this site. (Added Note: Not a single person spoke up for inclusion) My negative opinions about inviting in the entire Wikimedia community into these sorts of decisions are given in much detail at the foundation-l archives. The thread begins with this post (Note this thread is not about Wikisource, but deals with the subject of alerting other Wikimedia projects to dissucions of policy changes within one sister project). I will quote myself from a later email in that thread:

I think [Ec has] hit the nail on the head with "Good rules support existing practice rather than shape it." The problem with the original suggestion is such advertisement would atract people who have no understanding of existing practice. That is my concern. I feel anyone familar with existing practice will be aware of policy disscussion through the normal in-project channels.

The deletions are proceeding slowly and carefully with any wanted info being moved to other sites. There were no mass deltions on April 29th. If you can find a home for anything we could not I will restore the pages for your access, please give me a list. I think the topic of this post is out of line and [agr's] proposal has little merit. Especially the idea that we should hold this material until and new sister project of "Wikireference" gets off the ground--Birgitte§β ʈ Talk 18:16, 19 June 2006 (UTC)

Added Note. This disscussion as seen by those unfamilar with Wikisource may be misleading in our inclusion policy. I just want clarify that if there is an otherwise acceptable publication with apendices of Mathmatical tables, the enitre work including the tables is accepted at Wikisource. The exclusion only regards standalone data which is not a transcription of an acceptable publication such as s:Trinary numbers.--Birgitte§β ʈ Talk 18:27, 19 June 2006 (UTC)

Yes, I would like a list of the material that has been deleted. I think it is totally reasonable to expect some notice and time for us to decide what should be kept and where. I get the message that this material is not wanted at Wikisource, but that is no excuse for simply deleting it without informing anyone who might be interested. The fact that no supporter of the material spoke up during the April discussion should have been a clue that there was not adequate notice. --agr 20:16, 19 June 2006 (UTC)

I find your topic header both here, and on the Scriptorium, to be inflammatory, inappropriate, and wildly out of place. To quote from our own article on book burning: "Burning books is often associated with the Nazi regime." Jude (talk) 00:14, 20 June 2006 (UTC)

I certainly was not trying to suggest that anyone is behaving like Nazis and I apologize if the title is too harsh. As I said in my original post, I believe the regular editors at Wikisource are due some deference in their decision making. But I find the wholesale deletion of articles belonging to topics no longer in favor, Mathematics in particular, to be very disturbing. It is one thing to change the scope of a project, another to simply discard material submitted and accepted in good faith.--agr 00:38, 20 June 2006 (UTC)

Just to clarify, nothing was deleted because the topic fell out of favor. I would love to see mathmatical texts added. We actually have some being worked on now. Data is being excluded no matter the topic. --Birgitte§β ʈ Talk 00:58, 20 June 2006 (UTC)

The entire category of mathematics was wiped out. Absent a list of what was deleted there is no way to tell what might have been of interest.--agr 11:54, 20 June 2006 (UTC)

Of the 1741 pages that have been deleted since April 29, 2006, on Wikisource, and June 18, 2006, 1381 of them were in the main namespace. Of those 1381 deletions, 152 pages contained "efer" or "ref" in the deletion summary. You can find the complete list of them here. Jude (talk) 13:26, 20 June 2006 (UTC)

(edit conflict)Categories are currently little used at Wikisoucre (i.e. s:Category:Epic poetry lists 5 poems, believe me there plenty more), that one is empty does not mean we have nothing on the topic. I do not know how narrowly you define Mathmatics but some projects currently underway are s:A Treatise on Electricity and Magnetism (the proofreading of OCR is being done on the image pages); s:The New Student's Reference Work#Arithmetic; s:1911 Encyclopædia Britannica/Infinitesimal Calculus These are just a few example of current work. Most anything listed on this website would also be a welcome addition as I believe they are all out of copyright. The topic of Mathmatics has not fallen out of favor!

You are complaining that pages you might have been interested in (if you had a list of them to examine, as you do not seem to know what actually existed) were deleted by people who examined and disscussed them on project's main discusssion page as well as at Proposed Deletions. This complaint's scope is based on an empty category on a project that does not currently use categories in an organized fashion. This complaintent despite speaking for the inclusion of data at Wikisource in November, never made a single edit towards the maintanence or organization of that material in the 5 months between then and the April disscussion. Despite your strong interest in the deleted data, you refuse to do the legwork on compilng a list of titles for me to restore. Titles which you did not put up, did not edit and did not add to your watchlist. I dislike turning this in your direction, but I really dislike the the misrepresentations being made about what happened at Wikisource. I will repeat that this topic heading is quite out of line and would appreciate it if you struck it. I imagine you realize the Plan on phasing out reference data will procede without interuption, please make any requests for temporary restoration on my talk page.--Birgitte§β ʈ Talk 14:15, 20 June 2006 (UTC)

To cool things down a bit, I have changed the topic heading here and at scriptorium. User:Bookofjude has finally provided a list of the material deleted after others told me to search through the logs. That is a big help. I really don't want to make this personal, but I must point out that after the November discussion led to a clear consensus on keeping reference material, I submitted a detailed proposal on what tabular material to include to the discussion page on January 18, 2006. It received no further comment. I think I had every reason to think the matter was settled. --agr 14:52, 20 June 2006 (UTC)

Thank you for the alteration. I sympathize that you believed things were settled, but I have learned that settled doesn't exist on a wiki.--Birgitte§β ʈ Talk 15:13, 20 June 2006 (UTC)

Although I am a bystander in the debate, though in favour of keeping math tables on wikisource, I would like to remark that I read Wikipedia Signpost regularly and I don't remember any remark about voting about massive deletions of existing material on Wikisource. Considering that fact that Wikisource is not so high profile and people here could be interested in the voting, I think it's a bit unfair. Samohyl Jan 16:47, 20 June 2006 (UTC)

I read the Signpost regularly as well. Although they seem to report very well on Wikimedia Foundation issues, I think their coverage of other projects and other languages is quite minimal. I don't know that I would say it is unfair of them, after all the Signpost a product of the English Wikipedia. Anyone interested in Wikisource policies should regularly read the Scriptorium. There is nothing of importance that is not at least mentioned there. I think the archives are quite nicely organized as well for those interested.--Birgitte§β ʈ Talk 17:08, 20 June 2006 (UTC)

Deleted math articles

As best I can determine, here is a list of the math-related articles that have been deleted. Birgitte§β has kindly restored them temporarily:

• Wikisource:Prime deserts - a fairly short short list of gaps in the primes
• Wikisource:Fibonacci numbers 1-500
• Wikisource:Mersenne primes - up to number 30, 2^132049−1
• Wikisource:Phi to 30,000 places - There was also an article listing Phi to 20,000 places

Also there were computer source code articles with the following titles:

• Wikisource:Fibonacci sequence
• Wikisource:Euclidean algorithm
• Wikisource:Prime factorization

I'm not sure these have mcuch value. Finally, I believe there were once articles listing pi and e to a million places. These would be easy to reconstruct if anyone wants to make a case for them.

I think a case can be made for moving at least the first two or three articles above to Wikipedia, presumably retitled as "Table of..." Comments?--agr 18:35, 20 June 2006 (UTC)

Babylonian mathematics, Ibn al-Banna

The section Old Babylonian Mathematics (2000-1600 BC) of this article seems to be a copy of this page (starting with "Perhaps the most amazing aspect of ..."). It's especially funny in sentences like "In our article on Pythagoras's theorem in Babylonian mathematics we examine...", where in reality, no such article exists on Wikipedia. What should be done about it?

On a somewhat related issue, User:Chem1 has created the article Ibn al-Banna (1256-1321), to whom he attributes the invention of the iterative process $x_{n+1}={\frac {1}{2}}(x_{n}+{\frac {N}{x_{n}}})$ for finding the square root of a number - aka the "Babylonian method". This doesn't seem right. -- Meni Rosenfeld (talk) 14:41, 21 June 2006 (UTC)

I'll take a shot at a re-writing and wikifying the Old Babylonian Mathematics (2000-1600 BC) section. Gandalf61 14:54, 21 June 2006 (UTC)

I've removed that section from Babylonian mathematics as well as and following section as possible copyright violations, leaving a notes on the talk page of that article, and the editor who added it. Paul August ☎ 15:31, 21 June 2006 (UTC)

Okay, I've now trimmed, re-written, wikified and re-ordered the offending section. I think it is now sufficiently different from the source to be no longer copyvio, so I have put the re-written version back into the article. Gandalf61 13:17, 22 June 2006 (UTC)

Iff in formal writing

I would like to propose that all usages of "iff" to mean "if and only if" be replaced by "if and only if", as iff is not a very common abbreviation. Thoughts? (I actually did a bit of this but Oleg Alexandrov advised me to ask here – if there is a consensus for me to remove those edits it will be no problem for me to do it.) —Mets501 (talk) 20:24, 21 June 2006 (UTC)

I disagree that iff isn't very common, but I support removing it in favour of "if and only if", particularly in articles that might be of use to people who aren't expert mathematicians. RandomP 20:28, 21 June 2006 (UTC)

I would say that iff is quite common in textbooks, and I use it all the time, personally, but this is an encyclopedia, and I believe (quite strongly) that iff should be avoided everywhere (especially in definitions, whether formal or informal!) Madmath789 20:45, 21 June 2006 (UTC)

Yeah, iff is a bit of a neologism (which I think fell out of fashion by now :) and should surely be avoided in defintions. Is it a good idea however to just do a mass iff removal from all math articles? Makes me wonder if it is worth the trouble. Oleg Alexandrov (talk) 21:05, 21 June 2006 (UTC)

It's not really trouble. It just takes a bit of time, but I'll put the time in if we get enough consensus here to remove it. —Mets501 (talk) 21:08, 21 June 2006 (UTC)

I prefer "if and only if". Life is short, but if your life isn't that short, I say go ahead and change them. Just be careful with articles like if and only if and IFF. Dmharvey 21:14, 21 June 2006 (UTC)

(Edit conflict) Well it may not be trouble for you to do it, but you have kind of washed out my watchlist. This is slightly annoying, but tolerable for a good cause. Is there any precedent for bot flags for people using AWB? -lethe ^{talk +} 21:15, 21 June 2006 (UTC)

No precedent that I know of. I'm sorry about the watchlist, I know what you mean (my watchlist is full of math articles too). Hopefully I can get it all done today so that only one day's watchlist is screwed up :-) —Mets501 (talk) 21:18, 21 June 2006 (UTC)

If I recall, "iff" is allowed in any Springer book or journal. It is in the Merriam-Webster dictionary (supposedly). I think that disqualifies it from being a neologism. I personally never use it, but I wouldn't impose a moratorium. Don't you think this is a bit heavy-handed? Silly rabbit 21:39, 21 June 2006 (UTC)

It's there. At least it's in their online version, and I predict that iff (heh) it's there, it's either in their print edition, or will be in the next print edition. --Jay (Histrion) (talk • contribs) 17:33, 22 June 2006 (UTC)

I support making this change, with the exception of "iff" used in definitions which should be changed to "if". In fact I think we should expand the Math Manual of Style to discourage the use of "iff".Paul August ☎ 21:56, 21 June 2006 (UTC)

I support editing out all uses of "iff" from Wikipedia, and augmenting the MSM to discourage future use. However, I think a more delicate touch is required. In definitions that are clearly such, change to "if". Elsewhere, it is often better to rewrite the sentence rather than merely changing "iff" to "if and only if". I realize that may be much more labor intensive, and require more insight and judgement on a case-by-case basis, but the alternative could look ugly. Uglier than "iff", I don't know. My practice has been simply to make this kind of change as I encounter instances, and as the mood strikes me. A note in our conventions, a note in the Manual of Style, and widespread awareness among mathematics editors may be enough to stamp out the problem.

I also go after a few other issues as I see them. I've mentioned "ditto" previously. Others are the Latin abbreviations "i.e." (id est, "that is") and "e.g." (exempli gratia, "for example"). Although I know what they mean and am perfectly comfortable with them, I think they pose an unnecessary barrier to many readers; and since the English glosses are perfectly good substitutes, I see no reason to use the abbreviations here. The list goes on, but that's enough for today. --KSmrq^T 23:40, 21 June 2006 (UTC)

So what is the proper rewrite for "a triangle is right if and only if its sides satisfy a² + b² = c²"? -lethe ^{talk +} 23:49, 21 June 2006 (UTC)

Depends whether you're defining the term "right" or whether it's been defined previously. Dmharvey 23:55, 21 June 2006 (UTC)

I'm asking KSmrq how to rephrase a theorem whose converse is also true, so assume "right" has been previously defined as, say, "contains a ninety degree angle". -lethe ^{talk +} 01:27, 22 June 2006 (UTC)

I'd need more context to be sure; good writing doesn't happen one sentence at a time. Since this is a theorem asserting an equivalence, I would not object to "if and only if", and perhaps not feel the need to edit it. However, if I were writing this ab initio myself, I might choose different language. For example, if I wanted to highlight the assertion I might write

• Theorem. Let a triangle have side lengths a, b, c, with c the longest side. Then the following two statements are equivalent:
  1. The triangle is a right triangle.
  2. a² + b² = c².

For an inline statement, but still feeling the double implication is important, I might write

• For any right triangle with sides a, b, c, the sides satisfy a²+b² = c², where c is the longest side. The converse is also true: any triangle whose sides satisfy the equality is a right triangle.

But it really depends on the topic, the audience, the assertion, and the context. For example, in a larger context where this is a minor point, and the paragraph in which it appears is building a more important concept, I'd try to keep it as short as possible consistent with clarity. Does that answer your question? --KSmrq^T 12:53, 22 June 2006 (UTC)

It does answer my question. But I don't like it. You want to double the length of the assertion so that you can mention the statement and its converse explicitly? I would really much rather stick in an "if and only if". Listing the equivalent conditions is nice when there are three or four equivalent conditions, but rather burdensome for only two. Therefore I cannot support the idea to revise the MSM to suggest that "if and only if" be avoided (for theorems, that is. I'm on board avoiding this turn of phrase for definitions though). -lethe ^{talk +} 03:54, 23 June 2006 (UTC)

Yes, I described two variations that are longer. But the last thing I said was that in certain contexts I'd prefer to keep it as short as possible, so as not to detract from a larger point.

Here's one way to think about it. I have an assertion in mind. It's a nifty little assertion and I quite like it. But my first question is, does it help the article? Is it important either as an end in itself, or as support for a larger goal? Or perhaps as entertainment or enrichment? If it does not help the article, no matter how much I like it I shouldn't use it. OK, I decide it stays. Is it a brief aside, or is it something the reader really should understand? If the latter, then brevity is less important than clarity. Both of the longer versions I offered are predicated on the assumption that each direction of the implication is important for the reader to absorb. If it's that important to say, then spend a few extra words and do it right. If it's not that important to say, then maybe we don't really need it.

Prose that packs five major ideas in one paragraph is not reader-friendly. We tolerate it in mathematics texts if we must, but we don't enjoy learning from it. (I'm reminded of a graduate algebraic geometry class that spent the better part of a term covering the first chapter of the text: Hartshorne, ISBN 978-0-387-90244-9.) That kind of density intimidates mathematics graduate students; surely it is inappropriate for an encyclopedia.

As for the MSM, my proposal was to ward off "iff", not "if and only if". --KSmrq^T 23:03, 23 June 2006 (UTC)

OK, since it seems like no one is opposed to changing iff to if and only if, I'm going to continue. As far as replacing some with just "if", that can be done afterwards. —Mets501 (talk) 01:24, 22 June 2006 (UTC)

I think that's a misreading. Both Paul August and I explicitly objected to making the change in the context of a definition, a view widely supported by others in prior discussion. Is there some reason you can't be careful about that? --KSmrq^T 13:00, 22 June 2006 (UTC)

Basically, what I've gotten out of this discussion is that nobody objects to changing "iff" to "if and only if" (they do mean the same thing), but that you both support removing some of the "if and only if"s and making them just "if"s, or removing them altogether and rephrasing definitions. It will be no harder for you to do that when it says "if and only if" than when it had said just "iff". If you want to go back and do that, well, all the pages that have "if and only if" are now grouped in my most recent contributions. —Mets501 (talk) 13:18, 22 June 2006 (UTC)

I also would like to add that through my going through all the "iff"s I came by very few definitions. —Mets501 (talk) 13:21, 22 June 2006 (UTC)

I don't think this is a big problem. Paul August ☎ 17:54, 22 June 2006 (UTC)

I would point out, however, that this is one of the reasons we have a link for iff; so if someone doesn't understand it, it can be explained.Septentrionalis 00:15, 2 July 2006 (UTC)

Fraction refraction. :-)

I've never poked my head into the Math WikiProject before, but a few months back I did some work on Fraction (mathematics) before I had to take a break to tend to both Real Life and my proper job. Looking around, I can't help feeling there's a lot to be done, and it's not just a matter of the one article:

• If Vulgar fraction and fraction (mathematics) are not to be merged, then duplicate material needs to be excised. If they are to be merged, then let's merge 'em!
• Fraction (mathematics), while slowly improving, needs cleanup, and needs it badly, but the lengthy material on the arithmetic of fractions really belongs in an article all its own. Or, for that matter, in a Wikibook, but...
• the Wikibooks material is scant, sometimes incorrect, and things are often hard to find, or can be found in more than one place. Looking for fraction arithmetic, for instance, I found it under both Algebra/Arithmetic and Applied Math Basics, but not under Beginning Mathematics. Are Wikibooks out of the scope of this WikiProject?
• Amongst the mess, there's probably more duplicated material about Egyptian fractions than there needs to be.

I'd keep going, but another task is calling me from my PC. I know that fractions might not be a hip'n'trendy subject, but I work as a tutor at a community college and there are a few math topics that come up a lot, and manipulating fractions is one of them. :) I'd be willing to take the lead on this, as long as I have the support of the Project. --Jay (Histrion) (talk • contribs) 21:09, 21 June 2006 (UTC)

New template

I just created a new template, {{In sqrt}}. It basically displays the radical (√) and the the number with an overline. For example, if you enter {{In sqrt|x}}, it will produce √x. It works great for all CSS capable browsers, otherwise it just displays a radical sign. I was wondering, should we put this in the mathematics manual of style as a recommendation for all inline square roots? —Mets501 (talk) 01:15, 23 June 2006 (UTC)

"it will produce √x." Jɪmp 04:26, 31 May 2007 (UTC)

otherwise it just displays a radical sign

So what happens if I enter √x+2 in a non-CSS capable browser? Is it going to appear as √x+2? Dysprosia 01:50, 23 June 2006 (UTC)

"if I enter √x+2" Jɪmp 04:26, 31 May 2007 (UTC)

Yes, I think it will. However, there are so few non-CSS capable broswers that this is not an issue. Or if people here think it is an issue, then don't use this template for polynomials. —Mets501 (talk) 01:56, 23 June 2006 (UTC)

If it's going to fail and effectively look incorrect for any number of users, then it's not a Good Thing. As KSmrq said, √(x+2) is always correct. Dysprosia 03:57, 23 June 2006 (UTC)

I take it the benefit is the vinculum (overline)? Otherwise, &radic;2 produces √2 just fine.

I'm leary of this for a few reasons. One is that a browser that doesn't support CSS properly doesn't have a graceful fallback to show the grouping, so readers can't distinguish √x+2 from √x+2, whereas with &radic;(x+2), √(x+2), they can. The second problem is that the radical sign doesn't stretch up or down, so that something like √^x⁄_y or √x²+y² won't look right. It seems I can't write the fraction using the {{fraction}} template, because there is no nesting; still, I suppose this doesn't come up often. But template use incurs extra server overhead; is it worth it?

My last concern involves the arrival of BlahTeX. Currently the notation <math>\sqrt{x^2+y^2}</math> produces a PNG, ${\sqrt {x^{2}+y^{2}}}$. BlahTeX can serve this as MathML that renders beautifully inline. However, this creates a predicament for the template. How should the template adapt? Should it be revised to produce the <math> form, or continue to produce the Unicode/CSS form which is now less attractive for many readers?

Your thoughts? --KSmrq^T 03:45, 23 June 2006 (UTC)

"can't distinguish √x+2 from √x+2, ... something like √^x⁄_y or √x²+y² won't look right" Jɪmp 04:26, 31 May 2007 (UTC)

On my machine (Firefox on Mac OS) it renders like this: . Honestly, if I saw something like that in an article, I would change it to <math> straight away. I think it looks awful. I looks like "square root of the conjugate of x+2". It's marginally better in Safari. Dmharvey 11:04, 23 June 2006 (UTC)

I really dislike the idea. Sure, presentation is important for Wikipedia, and we all (or at least some of us) are looking forward to seeing a beautiful print version of wikipedia in the library one day (or just a nicer version on a high-resolution display with large fonts).

However, at least as far as I'm concerned, the real value's in the database being created. I'm already somewhat skeptical of the guideline to avoid using inline math. Templates make it even harder to understand what's going on, are limited in their applications, and I'm not sure they'll ever do exactly what you want with screen readers. Blahtex promises to be a better way out, for now, with MathML salvation on the horizon.

(I don't think Wikipedia should be using TeX-derived syntax forever, though. An advanced language that would allow us to specify not only what our formulas should look like, but also what they mean, and allow wikilinked symbols, might be a good idea when MathML has become accepted).

RandomP 12:08, 23 June 2006 (UTC)

Thanks everyone for your input. I will stop using the {{In sqrt}} template (it appears as if that's what everyone above thinks), and have removed the changes to the square root article (the only one which I changed. Oh god, we need BlahTeX! It's so ugly with inline PNG square roots and even uglier with the √ sign. —Mets501 (talk) 12:51, 23 June 2006 (UTC)

While we're on the topic, something else I should mention is that blahtex knows how to get the vertical alignment of a PNG equation correct (thanks to dvipng). That is, it aligns the baseline of the equation with the surrounding text. This is not enabled on the demo wiki, because it requires some (minor) changes to mediawiki's database schema, and we don't want to be pushing our luck yet. It is however enabled on the interactive demo. Things like inline square roots become a lot less uglier when the baseline is correct, especially if the font size is approximately correct. Dmharvey 13:20, 23 June 2006 (UTC)

Yes, I forgot to mention baseline issues as one of the advantages of BlahTeX. MathML display, of course, automatically gets it right without clever hacks. --KSmrq^T 14:21, 23 June 2006 (UTC)

Yes, I've experimented more with the interactive demo, and it does render much better. How long do you guys think it will be before it's implemented? (or is not quite finished yet?) —Mets501 (talk) 17:53, 23 June 2006 (UTC)

Don't know. We're working on it. (In between the real lives that we sometimes pretend to have.) Dmharvey 18:02, 23 June 2006 (UTC)

What, you're not still faking that whole doctoral thing, are you? Or do you mean serious pursuits like sleep and beer? Oh, now I remember; you were planning to spend time celebrating Australia's 6–0 win over Brazil! Ah, well; at least you didn't have to play Ghana. ;-) --KSmrq^T 20:26, 23 June 2006 (UTC)

In case the function of the template is changed in the future (which would be a good thing seeing as it's otherwise unwanted) I've made copies of the text which transcludes it and added subst: so that the text as it originally looked will still be able to be read. Jɪmp 04:26, 31 May 2007 (UTC)

Category:Degenerate forms up for deletion

Wikipedia:Categories for deletion/Log/2006 June 23#Category:Degenerate forms Oleg Alexandrov (talk) 01:48, 23 June 2006 (UTC)

Need third opinion at Operation (mathematics)

JA: Could use a third opinion at Operation (mathematics), a page that was created as a gloss on the generic concept but is now being converted into "hwk-helper" with material that either belongs or is pretty much already covered at Binary operation and other places.

JA: Looking down the road, in both directions, I am seeing here a more generic issue for the WP math community. For instance, the article in question was categorized as Mathematical Logic, and is now being recategorized as Elementary Mathematics. I think that there needs to be a standard operating procedure for sorting out and coordinating "tutorial" and "standard" articles. I notice that the physics folks already have a template for doing this. Anyway, something to think about. Thanks, Jon Awbrey 17:56, 23 June 2006 (UTC)

As the other editor in this dispute, let me summarize my position. "Operation" is an elementary term in mathematics. Someone helping their kid with his or her homework would likely end up at Operation (mathematics). The term belongs in Category:Elementary mathematics. In editing the article I preserved the full formal definition. The entire article fits on one screen. There is no need in this case (though there certainly may be in others) for "tutorial" and "standard" articles. (I gather by "standard" JA means aimed at specialists.)

No specialist is harmed by having to skip over a dozen or so lines of introductory material to get to a formal definition. If there were a need for a specialized page for the mathematical logic community (and I fail to see why since they are using the ordinary meaning), a proper name for such an article might be "Operation (mathematical logic)." According to Wikipedia policy WP:NAME: "Generally, article naming should give priority to what the majority of English speakers would most easily recognize..."

I agree with JA that a broader discussion would be helpful. I have no problem with highly technical articles that treat their subject rigorously, but where it is possible to do so introductory sections should be included that speak to a wider audience. I have tried to do this in several places and I consider it some of my best work. See homotopy groups of spheres for example. Wikipedia should try to demystify math, not obfuscate it. --agr 17:28, 23 June 2006 (UTC)

My personal opinion that the article requires a general definition as well as examples. In this version, the examples are nicely covered in introduction (one more example: operations on sets and functions, which I have just added). Operations in math logic is just one of the examples, and I think that elementary mathematics is more appropriate. (Igny 19:10, 23 June 2006 (UTC))

In this specific case I see no reason not to combine an elementary treatment with one for the specialist. And let's be honest, a specialist has no need to look up such basic stuff, so actually general understandability is more important. One thing that is not made clear and may be confusing, is that there is no clear distinction in mathematics between the meanings of function, operation, and operator. For example, the article Operation (mathematics) now mentions square root as an example of a unary operation, while the article Square root itself only mentions "function". It is largely a matter of historical convention when which term is used. --Lambiam^Talk 19:26, 23 June 2006 (UTC)

JA: This is like deja vu of discussions that we had on Function and Relation, and so I'd rather focus on the generic problem, as I'm fresh out of ergs to be caring about this stuff unless others do. I created this article because of a recurring need in other articles — check the "what links here" page — for a quick gloss to a suitably general concept of k-adic operations. And now anybody chasing those links is likely to skip the whole darn thing before getting past the TOC. What we have now is two articles whose front ends are devoted to Binary operations, and so it seems like the whole thing is better dealt with by way of a 1-liner up top like: {{for|an introductory treatment|Binary operation}}. Jon Awbrey 19:48, 23 June 2006 (UTC)

First of all, the present intro to operation (mathematics) does not just deal with binary operations. It also describes unary operations. The common mathematical use of the word "operation" includes both. The binary operation page is not that elementary and goes off to discuss groups, monoids and the like, as it should. The unary operation page devotes a lot of its space to computer programming operations. So there is a need for the current version of "operation." This is an encyclopedia, not a glossary, and specialists can put up with a little intro material. Regarding "what links here," I came to this article in the first place when I was editing exponentiation and wanted to link the word "operation.' What I found when I looked there was totally inappropriate. I suspect other editors of elementary articles have come to the same conclusion.

As for the relation (mathematics) article, it already has a long introductory section. It would take very little editing to make its intro beginner friendly, eliminating the need for an initial redirection. Basically defer the jargon for sentence or two. And that I think is the broader issue here. Where it is possible to do so, editors should be able to add short introductions to articles that make them more accessible to non specialists, without a big battle each time. Long tutorials deserve their own article, of course. But an average reader landing on a basic mathematical topic should get an initial explanation they can understand before being redirected.--agr 21:44, 23 June 2006 (UTC)

I suggest creating operation (elementary mathematics), function (elementary mathematics) and relation (elementary mathematics) which would have content aimed at the primary-school/secondary-school/high-school level. This might solve the edit-warring over these articles. linas 00:19, 2 July 2006 (UTC)

Span.texhtml

Please see my proposal here. —Mets501 (talk) 22:20, 23 June 2006 (UTC)

Doesn't anyone want to comment? It's very relevent to all math pages on Wikipedia. —Mets501 (talk) 23:49, 24 June 2006 (UTC)

We've seen it before. There's little enthusiasm for a global stylesheet change for two reasons (at least).

1. For an inline formula using <math> tags that happens to force a PNG, the "x" will appear in a serif font, which is also the way it appears in most displayed equations (since the typical display is a PNG); consistency in this case dictates that the HTML should use a serif font as well.
2. Anyone who really cares about using a sans-serif font can do so using using their personal stylesheet, just like the users you noted.

No matter which choice is taken, so long as the monobook body text uses sans-serif and TeX PNGs use serif, we have a conflict. Nor is that the end of it; look at the difference in other characters, such as Greek symbols and operators.

This conflict is unlikely to end with the release of the STIX fonts, as suggested by the following statement:

“Most of the glyphs in the STIX Fonts have been designed in Times-compatible style. Times was first designed under Stanley Morison's direction by Victor Lardent at The London Times in 1932. Many variations of this design have been produced since the original.

“In addition to Times-compatible glyphs, some portions of the STIX Fonts include other design styles such as sans serif, monospace, Fraktur, Script, and calligraphic.”

Thrilling; all of the extra styles except sans serif are essential for TeX. So get used to serif mathematics; it looks to be with us for a long time to come. --KSmrq^T 00:27, 25 June 2006 (UTC)

How about "span.texhtml {font-size=14px}"? That will at least get it to be the same line height as the sans serif.

Will it? For which OS, browser, fonts, and settings? This kind of hair-pulling madness is a tiny fraction of the issues Dmharvey and Jitse Niesen have been wrestling with over in BlahTeX-land. --KSmrq^T 22:38, 25 June 2006 (UTC)

he's baaaacccckkkkk..... "made it clear"

[26] Dmharvey 18:35, 24 June 2006 (UTC)

He never seems to tire, does he? Blocked again... -- Fropuff 05:35, 25 June 2006 (UTC)

In defense of our clarificator, there is an apparent contradiction between the Real number article, in which "a [presumably meaning any here] real number can be given by an infinite decimal representation", and the article Decimal representation, which has: "Every real number except zero has a unique infinite decimal representation" (which is true the way things are defined locally). Instead of blocking, it might be better to smooth away the contradiction. --Lambiam^Talk 10:00, 25 June 2006 (UTC)

I just removed that section in "decimal representation". It was probably also put there by WAREL and missed by others. JRSpriggs 11:00, 25 June 2006 (UTC)

Actually, if you read that paragraph again, you will notice that it is correct. Every positive real number has exactly one decimal expansion which doesn't end with all 0's, and one decimal expansion which doesn't end with all 9's (usually, these two are the same). That paragraph emphasized the first of these - which looks unusual, so I don't object to the removal. -- Meni Rosenfeld (talk) 18:05, 26 June 2006 (UTC)

The first sentence of the removed paragraph said was "Every real number except zero has a unique infinite decimal representation, that is, one in which not all of its digits become zero after a while. ". Although the subordinate clause tries to rescue it, the main clause is false. Some real numbers have more than one infinite decimal representation. It is senseless to discriminate against a terminal string of zeros in favor of a terminal string of nines. If anything, I would do it the other way around. JRSpriggs 10:22, 27 June 2006 (UTC)

The subordinate clause clarifies what was the meaning of "decimal expansion" in the main clause. The main clause would have been false on its own - but it is accompanied by the subordinate clause to form a whole sentence - a correct one. It is the same as saying "every real number a has a unique cube root, that is, a real number b such that b³ = a". The first part could have been seen as false on its own, if we see it in the context of complex numbers - but the second part clarifies that we are only concerned with real numbers. Not much point in arguing about this, though - I do agree that ther article is better off without that section. -- Meni Rosenfeld (talk) 10:35, 27 June 2006 (UTC)

It is more like saying "Every positive real number has a unique square root, i.e. a negative number which when multiplied by itself gives the positive number.". He is treating the abnormal case as the normal. JRSpriggs 11:01, 27 June 2006 (UTC)

That is something I certainly agree with. -- Meni Rosenfeld (talk) 11:28, 27 June 2006 (UTC)

I would agree with all this, but I have to say that I do recall situations in proofs, where it is more convenient to use the version of a real number which ends in a string of 9's (it means that every strictly positive real has a non-terminating decimal representation) - but in this instance, I agree that he is advocating the 'abnormal'. Madmath789 11:48, 27 June 2006 (UTC)

Here is an attempt to say something that is (a) true, and (b) not a manifent consequence of what is already in the article:

Every non-negative real number has an infinite decimal representation. It is unique, except for those positive real numbers that also have a finite decimal representation: these have two infinite representations. For example, the number 5/4 = 1.25 has the two infinite decimal representations 1.24999… and 1.25000….

Is it worth adding this? --Lambiam^Talk 17:23, 28 June 2006 (UTC)

If you do add it, add it to the existing section "Multiple decimal representations" rather than making a new section. JRSpriggs 04:55, 29 June 2006 (UTC)

Request from non-mathematician

When I do "random article" I occasionally come across mathematical formulae (and sometimes with general science books etc). It would be useful for those of us who are not mathematically informed if there was a "basic explanation" as to use and purpose.

See the examples I put on Wikipedia:Requests for expansion for what I mean. Jackiespeel 16:54, 26 June 2006 (UTC)

In reference to boolean-valued function, boolean domain, and finitary boolean function. Those are pretty short stubs. They need lots of work (or perhaps even to be merged somewhere). In response to your general query: yes, I will try to make every math article I write have explanations, examples, context, and everything else that makes for brilliant writing. Sometimes a stub is better than nothing though. -lethe ^{talk +} 17:37, 26 June 2006 (UTC)

On the request for expansion page, you wrote:

Finitary boolean function, Boolean domain and Boolean-valued function and some of the links thereof - can someone give an explanation in "ordinary English" as to what these functions are. I can see that they are complex mathematical functions - but "what are they"? Perhaps a brief standard text could be added. "This mathematical function is used in xxx, and does yyy." (add more detail as required) Jackiespeel 23:14, 24 June 2006 (UTC)

The article "finitary boolean function" describes a simple generalization of a boolean function. There's not much else to write. Perhaps that article needs to be merged into the "boolean-valued function" article. The article "boolean domain" is just a definition, and is already marked as a stub. The article "boolean-valued function" gives what you ask for: it describes the function and gives several fields where it's used. Could you explain why that doesn't meet what you want? Lunch 18:32, 26 June 2006 (UTC)

Finitary boolean function is not a generalization but a specialization of boolean function. The situation is a bit messy. There is also the article Boolean function, which never defines what a boolean function is. Is there a difference between the concepts of "boolean function" and "boolean-valued function"? What is sorely missing here are examples. There is further an article Logical connective, which treats operators like AND and NOR, the redirect page Boolean operator redirecting to Logical connective, and the redirect pages Boolean operation, Logical operator and Logical operation, which instead redirect to Boolean function. --Lambiam^Talk 20:03, 26 June 2006 (UTC)

Conventions in graph theory : strongly regular graph

I was busy trying to make a Strongly regular graph separate article, and I was wondering : what will we agree on the conventions.

Graph theory can really be annoying when you really want to do it right. For instance my syllabus agreed on not including disconnected graphs and their complements, which in turn implied $v-1>k>\mu >0$.

The spectrum also changes when you allow disconnectedness: the degree of disconnected graphs becomes an eigenvalue with more than dimension one.

What is your opinion?

Evilbu 18:22, 26 June 2006 (UTC)

My advice would be to have a look at the other graph theory articles to see if their conventions seem reasonable, and try to follow those if so. You can of course use your own conventions too — the most important part right now is to write the article; we can discuss your conventions later. Just be sure to explain what your conventions are in the article. - Gauge 02:39, 28 June 2006 (UTC)

Research first, write afterwards. Halmos, a widely respected mathematics author, says:

"A good, consistent notation can be a tremendous help… Bad notation can make good exposition bad and bad exposition worse; ad hoc decisions about notation, made mid-sentence in the heat of composition, are almost certain to result in bad notation."

Try to conform to standard conventions. But especially, be explicit about what conventions you choose; don't leave the reader guessing. This is essential within Wikipedia, where readers and editors come from different disciplines, different schools, different continents, and different levels of experience.

Graph theory is mathematics applied to many tasks, and the conventions that are helpful for one may be an impediment for another. Since we cannot know why someone is reading an article, we cannot assume that for their purposes all graphs are connected. However, it is fair to introduce a discussion by saying something like, "Here we restrict attention to connected graphs." That's not only good for the reader, it also makes it easier for another editor to come along, see the restriction, and expand the coverage.

You will find this done throughout the mathematics articles. In fact, it can help to start an article that includes both introductory material for a general audience as well as much more abstract material for an advanced audience. First give the accessible and common cases to build intuition, then later remove restrictions.

Specifically with regard to strongly regular graph (and note: don't capitalize the first word just because it's linked!), nothing in the definition of regular graph implies or depends on having a connected graph. If some of the results you want to state only apply with that restriction, say so.

A fine point of TeX usage is that it is incorrect to write

$srg(v,k,\lambda ,\mu ).\,\!$

TeX typesets this as if s, r, and g are three single-letter variables being multiplied. I mention this here instead of on the article talk page because it's a common mistake. Instead, try

$\operatorname {srg} (v,k,\lambda ,\mu ).\,\!$

The special notation here, "\operatorname{srg}", does several good things; use it. This is not highlighted at Help:Formula, but many other helpful suggestions are; read it. Especially note the trick (which I've used here) to force displayed equations to use a PNG image (which is large and uniform) instead of an approximation in HTML.

I'll also use this opportunity to point out that since there is no reason to capitalize the first letter of a link, there is also no reason to write, say, "[[Adjacency matrix|adjacency matrix]]" instead of merely "[[adjacency matrix]]". The MediaWiki software also performs other background magic, such as simplifying plurals like "[[complete graph]]s", which comes out looking like "complete graphs". Something that often proves handy in mathematics articles is that trailing parentheses in a link, needed for disambiguation, can be automatically removed by using the "pipe" character, "|". Thus we can write "[[graph (mathematics)|]]s" to get the word "graphs" with a disambiguated link, like this: "graphs". --KSmrq^T 04:27, 28 June 2006 (UTC)

Okay, well first of all, I checked my syllabus and found that followig THOSE conditions works out eventually. But I don't want to get into any trouble with my own University for copying very explicitly. The problem is that the University of Ghent is such a big 'player' in the field of incidence geometry, that a lot on the internet (and that is assuming you find something) comes from their sites I bet you also disapprove then of my pg(s,t,\alpha) notation in the partial geometry article? I read that Formula page and even applied one of the guidelines on Paley graph. But I am totally confused with HTML/Tex/PNG, especially since I was instructed very recently to switch my Preferences to 'Always render PNG'. Evilbu 13:09, 28 June 2006 (UTC)

Explicit copying is a bad idea anyway, because this is an encyclopedia, and written for a much wider audience. It's not enough that you understand what you write, or that a university lecturer understands; the goal is that anyone in the world with an interest in the topic (and sufficient background or determination to learn) can understand. We have a mathematics style manual that is helpful. Much more could be said. My personal guidelines remind me to try to include, among other things,

• intuition
• examples
• counterexamples
• connections
• pictures
• humor

Although it is helpful to have an article that is little more than a definition or theorem, it is much more helpful to explain in what area of study the definition is used, why it may be useful or plausible, and to show it in action either directly or with links. And since this is an encyclopædia, we also like to cite at least one academic source (something more reliable and permanent than lecture notes or online course material).

Looking at the partial geometry article, I see again the need to use "\operatorname{pg}" instead of "pg", but I also see two other problems. (And, again, I discuss this here for the benefit of everyone, not just one editor and one article.) The first sentence looks like this:

• "An incidence structure S=(P,B,I) is a (finite) partial geometry …"
• "An [[incidence structure]] ''S=(P,B,I)'' is a ([[finite]]) partial geometry …"

The italics are misused; only the variables should be italicized, not the equality and not the parentheses. While we're at it, we'd like the equation to have a little breathing room but not a bad line break. Here's a way to do all that.

• "An incidence structure, S = (P,B,I), is a (finite) partial geometry …"
• "An [[incidence structure]], ''S''&nbsp;= (''P'',''B'',''I''), is a ([[finite]]) partial geometry …"

The wiki markup is a nuisance, and we eagerly look to the day when BlahTeX will rescue us; but, for now, that's it.

The second issue has to do with your HTML/TeX/PNG confusion. The sad fact is that mathematics markup is confusing. Again we look to BlahTeX, which will simplify this as well. Switching your preferences affects you alone; most of your readers will not be using the "PNG always" preference. For example, I don't. Many of us do not like to see big PNG images jutting out in our inline text. We do our best to confine the PNG to displayed equations, and there we always want to see it.

This leads to a highly annoying dual writing technique: hard-to-edit wiki notation for inline, and TeX notation for display. Either way, we're taking a leisurely stroll through a minefield. We have a diversity of philosophies about what we're comfortable with inline, with some people using TeX whenever they need a special character and others (including me — see here) using Unicode; but we have a broad consensus that "built-up" material such as "{a \over b}" is undesirable inline. So this is a second thing you should fix in the partial geometry article.

I find that TeX (or LaTeX) has many subtleties that the average mathematics writer overlooks; the typesetting of operator names is but one of them. For example, not many people know the correct way in TeX to write the colon in f: R² → R. (Use "\colon" instead of ":" to get the right spacing; try it!) However, our current situation is even worse, because Wikipedia depends, not on genuine TeX, but on a lame partial imitation, texvc. Again we look to BlahTeX for eventual relief!

I appreciate that there is a lot to learn about writing mathematics for Wikipedia, and I hope you will not be discouraged. We're here to help, and eventually we'll have new software to help as well. --KSmrq^T 19:22, 28 June 2006 (UTC)

Bots and automatic Unicode conversion

I noticed User:Bluebot is automatically converting HTML entities to Unicode on various articles. See e.g. [27]. Does anyone have an opinion on whether such conversion is desirable in mathematics articles? Would it hinder possible future efforts to automatically switch to MathML? - Gauge 05:55, 28 June 2006 (UTC)

First of all, MathML only affects math written in <math> tags, and unicodifying only takes place outside <math> tags, so it would have no effect of MathML. As far as being desireable, it makes it easier to read the article in edit mode, especially for newbies who are not used to used to HTML entities. —Mets501 (talk) 12:44, 28 June 2006 (UTC)

I know the automatic conversion of Blahtex would only apply to math tags; I was thinking instead of possible future efforts to convert inline HTML being used for math into MathML (using blahtex with math tags), once it is widely supported by browsers (likely several years off, but worth discussing now). What if different bots use different Unicode symbols for the same HTML entities? - Gauge 18:38, 28 June 2006 (UTC)

It makes a little more difficult to edit the article, especially with HTML entities such as & nbsp; , but it's probably a good thing. — Arthur Rubin | (talk) 17:25, 28 June 2006 (UTC)

Converting Unicode to MathML should be just as easy as converting HTML to MathML I think, so &int; --> \int and ∫ --> \int should not be that different. I would be opposed however on such bots (or worse, semiautomatic editors) doing mass unicodification very often, they just obscure watchlists with no good purpose. Oleg Alexandrov (talk) 19:02, 28 June 2006 (UTC)

Somewhere we've had this discussion before. My recollection is that many editors objected to replacing an HTML named entity with Unicode because the HTML name and the TeX name were the same, making consistency easy. That objection does not apply to numerical entities, but those are so unpopular that we rarely see them. MathML can cope with any Unicode (UTF-8) character for a symbol; in fact, it knows special things to do with many more than are supported in TeX. I don't recall exactly how BlahTeX copes, but it either can or will do better than texvc, at least for passing things on to MathML. My personal preference at the moment is to stop the bot, on the grounds of previous rejection and of TeX (not BlahTeX) incompatibility. --KSmrq^T 19:38, 28 June 2006 (UTC)

On a different note, will we deprecate HTML math formulas with the arrival of BlahTeX? —Mets501 (talk) 20:19, 28 June 2006 (UTC)

I think not. Not in the immediate future.

To address KSmrq's question: currently blahtex does not allow non-ASCII characters in math mode material, on the grounds that people would abuse it, and it would lead to the database becoming horribly incompatible with standard tools. People should be using the TeX commands instead. It does allow arbitrary non-ASCII in text mode, which gets passed through to the MathML <mtext> element. I suppose this could lead to the same sort of abuse (like <math>\text{∫}_0^1</math> -- yuck!). It might become desirable to limit the characters that could be used in text mode (e.g. extended latin, and other scripts like japanese, chinese, klingon, etc). Dmharvey 20:49, 28 June 2006 (UTC)

Why wouldn't we deprecate HTML math formulas, though? If we put it in <math> tags, then BlahTeX will render it as HTML, anyway. So there seems to be no reason why we should keep using math formulas written in HTML. In fact, I'm not quite sure why we use inline HTML now for things like variables or "flat" equations that would render (in <math> tags) now as HTML now anyway with texvc. —Mets501 (talk) 01:13, 29 June 2006 (UTC)

The main reason to use HTML now instead of texvc for inline stuff is that the texvc conversion of TeX to HTML on "simple formulas" is so pitiful. Blahtex would generate MathML output for math tags for people who want it, but I think it still falls back to the old texvc HTML conversion for people not using MathML. Also, there are certain things that texvc will tend to encode as PNG rather than HTML (any sort of spacing, for example), so one might be forced to use HTML for the desired result anyway. - Gauge 19:59, 29 June 2006 (UTC)

In response to KSmrq's comment about prior discussions involving unicode in mathematics article, on this page, there have been at least three:

• Unicode in math articles (Sep 24 2005)
• Mathematical characters usage (Oct 18 2005)
• IE compatibility (Mar 28 2006)

Paul August ☎ 21:37, 28 June 2006 (UTC)

Thanks Paul. I found this quote by Dysprosia that I thought was worth repeating here:

The difference is that the Unicode alpha is just another character in the text, like "t", or "q". The HTML entity is the string "&alpha;". All good computer systems should support ASCII, and the HTML entity consists of only ASCII characters, so no matter if you use a computer that supports Unicode or if you don't, the string will be unchanged. However, some browsers that don't support Unicode simply ignore the Unicode characters, so if someone edits with one of those browsers, it will look like all the Unicode characters in the article have suddenly disappeared. If the browser chooses to render "α" with a Unicode character, that's fine, but it doesn't mean that that Unicode character is somehow equivalent to the HTML entity -- they aren't. Hope that explains things a bit better...

I think this is reason enough to discourage proactively converting HTML entities to Unicode. Let the browser decide which symbol to use instead of forcing a particular Unicode symbol. Also, what is the state of screen reader support for Unicode as of about 5 years ago? It seems reasonable to give handicapped users some time to upgrade their software if Unicode is going to be proactively deployed. I don't mind if people use Unicode in articles, but they shouldn't be converting HTML entities to Unicode wholesale without some discussion. - Gauge 22:53, 29 June 2006 (UTC)

\mathscr anyone?

Are people interested in having the \mathscr command available? (Provided by \usepackage{mathrsfs}.) Here's what it looks like:

The top one is \mathscr, the bottom is \mathcal (which is what we have now). I've noticed that \mathscr (or something similar) is quite popular in certain fields. I've noticed it especially in functional analysis.

There wouldn't be any difference in MathML because MathML only defines a single "mathvariant=script".

Opinions welcome. Dmharvey 19:25, 28 June 2006 (UTC)

It's also popular in algebraic geometry, for denoting sheaves and sheaf-y versions of various things like functors. I've once or twice wished I could use it. It's not essential, but I guess I would say that I'm interested in having it. Ryan Reich 21:11, 28 June 2006 (UTC)

Do we get one or the other, or can we have both? Personally, I find \mathcal very useful at times, and wouldn't want to lose it. If we can have \mathscr for those that want it, without losing \mathcal, then that would be great. Madmath789 21:21, 28 June 2006 (UTC)

You get to have both. Unless you're viewing with MathML, in which case they look the same. This would only become a problem in articles that use the same letter in the two fonts to mean different things. It would be possible to disable MathML for \mathscr if that's what people wanted, in which case it would fall back on PNGs. Dmharvey 21:50, 28 June 2006 (UTC)

MathML is only part of the obstruction. Unicode itself has no font variation facility to handle this (that I know of). There is a code point for "B" (U+0042) and "b" (U+0062), and for "Б" (U+0411) and "б" (U+0431), and for "ב" (U+05d1), and for "𝔅 (U1d505) and "𝔟" (U1d51f), and for "𝔹 (U1d539) and "𝕓" (U1d553), and for "ℬ" (U+212c) and "𝒷" (U1d4b7). The idea seems that be that these variations of "B" are in separate alphabets (Latin, Cyrillic, Hebrew, Fraktur, double-struck, and script), not separate fonts. (The difference between uppercase and lowercase is an anomaly, retained for historical reasons even though it's somewhat inconsistent.) So an argument would have to be made to the Unicode committee that there is an essential semantic difference between the calligraphic alphabet and the script alphabet. I'm guessing it would be a hard sell; we all know mathematicians have a boundless appetite for new alphabets and new characters. (We need this alphabet for the space, and that one for the structure over the space, and the other one for the mapping of the structure over the space, and so on.) I think we already have enough distinctions to tough it out if we must! In fact, any author who wants to make a semantic or type distinction between script and calligraphy is already unkind to readers. For those who are still not persuaded, MathML accepts CSS styling, so it's possible to use a Latin code point and ask for a different font-family. --KSmrq^T 01:18, 29 June 2006 (UTC)

All very true. In fact, there are a few more: for example there's also 𝖡 (U1d5a1) which is "MATHEMATICAL SANS-SERIF CAPITAL B" ([28]). Interestingly, the reference glyphs for script letters given on the mathml site ([29]) appear to be the same as the \mathscr above, even though the fonts that I got from the Mozilla site render more like \mathcal. I wonder what the STIX ones will look like. Dmharvey 01:42, 29 June 2006 (UTC)

Is anyone aware of any sources that use both a mathscr-like font and a mathcal-like font, with different semantics? There's a thread on the www-math mailing list discussing this now. If anyone could build a case, we might well get two different font variants in MathML 3.0 (which is on the drawing board). Dmharvey 18:39, 5 July 2006 (UTC)

he he he

You know how we all put something like "\,\!" at the end of <math> blocks to force the output as PNG? Well I was just doing some database work and happened to be trying things out on the hebrew wikipedia, and discovered that they all put "\ " at the beginning of the equation! (e.g. [30]) Or is it the end of the equation? I don't even know... the </math> comes before the <math>... Dmharvey 22:02, 28 June 2006 (UTC)

The LaTeX equation itself runs from left to right. In this equation the "\ " is at the beginning. If we think of the eqn as an atom in a right-to-left context, then to the reader the blank space appears to appear to the left of and therefore after the atom (instead of being part of the atom). --Lambiam^Talk 22:50, 28 June 2006 (UTC)

interesting statistics

More database work.... last time I checked around the beginning of March, the 13 largest wikipedias had 208,000 distinct equations altogether. Now (as of about mid-June) there are about 289,000. That works out at about a 10% growth rate per month. Pretty amazing. Dmharvey 02:06, 29 June 2006 (UTC)

You should write a paper about it. When it gets published, I can write a Wikipedia article about the paper. Ryan Reich 02:53, 29 June 2006 (UTC)

And make sure in the Wikipedia article that you use more formulas :-) —Mets501 (talk) 03:15, 29 June 2006 (UTC)

Help wanted

The "proof that 0.999... equals 1" article is once more under attack — from the inside. And for the n-th time, Melchoir is involved. I'm sick of dealing with him and (now) Supadawg. If anyone is interested, please get involved in whatever way you see fit. As for me, it's come down to a revert war or walking away.

Some of you may be aware I completely stopped editing Wikipedia articles awhile back, except for really minor things like typos. I confined my contributions to talk pages, because I had no more stomach for seeing articles obstinately trashed by editors with inadequate subject knowledge, horrible writing skills, and no social skills. That worked for me, though not so well for the articles I abandoned. In the current instance, I can't see wasting more time debating with someone who pretends a proof using Dedekind cuts and the Archimedean property is original research, and who doesn't see a problem in beginning a sentence with a decimal point, but who knows exactly how the article should be rewritten.

However, if you long for abuse or have a desperate yearning to save the world (or both!), here's your opportunity. You'll need to act quickly, for the Mongol hordes are invading as we speak. They have already insisted that an article devoted to a proof should not be so named, nor should state that in the opening sentence. ("It's unencyclopedic!") Next on their agenda is a complete rewrite. It boggles the mind.

OK, so saving this article probably won't save the world. Still, I'll bet it gets more page views than the snake lemma and the hairy ball theorem put together (no disrespect intended). Please stop by the talk page, or help revert. (This version works for me, tolerably.)

Just for fun:

Question at job interview: "What is one third plus two thirds?"

• Mathematician: "It's one."
• Engineer (using calculator): "It's 0.999… ."
• Accountant (winking slyly): "What do you want it to be?"

Thanks, all. --KSmrq^T 06:42, 29 June 2006 (UTC)

I must say that I find the article unconvincing, also in its earlier incarnations. Surely, it is intended for people who, in a Zeno-like way, feel queasy with the identity. Most of what is in there is completely above their heads. If I was not mathematically educated, and I saw something that needed so many different proofs for its validity to be demonstrated, I would start to doubt the claim made! Can't we just have two proofs:

1. A solid one from first principles, basically saying (sketch): (1) By definition, 0.999... stands for the limit of the sequence 0.9, 0.99, 0.999, ... (2) That limit is, by definition of limit, equal to one when the elements of the sequence |0.9-1|, |0.99-1|, |0.999-1|, ... eventually become less than any positive number ε you care to state. (3) And indeed, it does: if the decimal representation of 1/ε has n digits before the decimal point, then the n+1st and subsequent elements are all less than ε.
2. The informal argument: 10x = 9.999...; subtract x giving 9x = 9.000... and therefore x = 1.000..., remarking that this, in fact, informally presents an actually valid mathematical argument.

More is not always better. --Lambiam^Talk 09:23, 29 June 2006 (UTC)

First of all, thanks for your imput Lambiam, but I'm afraid that's a no (from me at least). It doesn't need so many proofs to prove its validity. The many proofs are to present alternate methods of prooving this "theorem". Any one of those proofs would serve to prove that 0.999…=0.

Second, KSmrq, I think that you're actions were not appropriate above. We don't have a consensus yet either way, and you're already assembling a revert army, or so it seems from your statement above. Also you did not provide a link to the infinite geometric series proof, and only to your version of the article, without the proof. If we do achieve consensus to delete the section, I will let it be deleted (although personally I would rather it stay – perhaps you remember when I added the proof on April 1 of this year, and you swiftly removed it), but until we have that consensus, it will stay in the article. —Mets501 (talk) 13:00, 29 June 2006 (UTC)

Please direct all follow-ups to the article talk page. They will properly be associated with the article history, and won't annoy the vast majority of mathematicians who don't long for abuse. Thanks. --KSmrq^T 15:44, 29 June 2006 (UTC)

I'm happy to join the corps of reverters for that article, but I cannot in good conscience revert to the version you link, which is buried behind over a hundred edits already. The best I can do is add the article to my watchlist and revert future changes. -lethe ^{talk +} 15:37, 29 June 2006 (UTC)

Not a problem. I had a hard time picking through all the debris to find a good target, with all the additions and reversions that have been happening lately, so I went back further to be safe. Thanks for anything you feel comfortable doing to help. --KSmrq^T 15:44, 29 June 2006 (UTC)

Redirect question

Is there a way to have a redirect focus the point on a specific section of the article? Specifically, I have in mind the redirect from Koszul connection to covariant derivative, which reads

# REDIRECT [[covariant derivative#Koszul connection]]

If you follow the link explicitly, by clicking the above link, then the point focuses on the relevant section. But if you follow the link Koszul connection, then you are taken to covariant derivative without the change in focus. Any thoughts or advice? Silly rabbit 17:32, 29 June 2006 (UTC)

See Help:Link#Redirects_with_section_links. I recall reading a different document that explicitly said that they had no intention of ever allowing section links within redirects, but I don't know where that went (the "Help" is not always very much help here; they make it very hard to find the detailed manual and I always forget how). Ryan Reich 18:05, 29 June 2006 (UTC)

Hehehe... I just found some related results, and was about to come here and answer my own question: Meta:Help:Redirect#A redirect to an anchor and bugzilla:218. It's kind of annoying that this seems to be impossible. Any stylistic pointers on how to handle a merger of this sort? Silly rabbit 18:13, 29 June 2006 (UTC)

Redirect to the top of the page. If the article is well-written then the appropriate section header will be in the TOC and clearly visible (i.e. the preamble won't take up much space). If not, well-rewrite it. In any case, if you have a page that used to link to Koszul connection, you could just put a pipe in that link and avoid the redirect entirely. Ryan Reich 18:45, 29 June 2006 (UTC)

Split of List of mathematicians

Sorry if I startled you, the WikiProject, but I boldly separated the List of Mathematicians article into eight smaller articles. Prior to this, the article was giant: it ranked in the Top 50 on Special:Longpages. Seeing as this is problematic, since not all of our users have the patience to load a page that is hundreds of kilobytes in size, I took the liberty to divide it into smaller pieces. I'm sorry if it's unacceptable to the WikiProject, but I was doing what I felt was good for the list. —THIS IS MESSEDOCKER (TALK) 02:50, 30 June 2006 (UTC)

Relax. :) As I told you on your talk page, the big problem is that you did not realize a bot is used to update that page, and it will just happily overwrite your changes, or worse, will get confused by it and then the page will be messed up.

The list of mathematicians is 164 kilobytes. Time to split? Should it be split modeling the list of mathematics articles, that is, separate lists for each letter, or should there be a grouping into bigger lists, say A-C, D-F, etc.? Oleg Alexandrov (talk) 02:55, 30 June 2006 (UTC)

Yes a split seems a good idea. I would go for one list per letter. I can't really see an an advantage of A-C lists etc. I suspect most people who use the list will be looking for a specific person and so it will be easy enough for them to click on a specific letter. Further, the number of mathematicians per letter is already quite long for about half the letters. --Salix alba (talk) 08:41, 1 July 2006 (UTC)

I thought of the same thing. I will work on it when I find time. Oleg Alexandrov (talk) 16:56, 1 July 2006 (UTC)

Done. Oleg Alexandrov (talk) 03:52, 15 July 2006 (UTC)

Geostatistics

This article is extremely POV, particularly considering the open criticism of Geostatistics within the main page. I was hoping that someone with more experience could build some equations and expand on the evolution of geostatistics. Considering how widely geostatistics is used for the natural sciences, environmental planning, climate studies, oceanic studies, military analysis, urban planning, and Geographic Information Systems, this topic warrants some attention from math experts. SCmurky 03:56, 30 June 2006 (UTC)

JanWMerks is at it again. He's been editing geostatistics, semivariance, spatial dependence, variogram, sampling variogram, kriging, junk science, consensus science, Tolstoy syndrome, and Bre-X; I may have missed some. He's been admonished in the past for his crusading; see his talk page and his list of "contributions". It might be nice if more people added these pages to their watch lists to undo his edits. (BTW, SCmurky, why did you delete my previous comment?) Lunch 17:50, 30 June 2006 (UTC)

Maybe it is time to take more serious action Wikipedia:Resolving disputes posibly a request for mediation. --Salix alba (talk) 20:03, 30 June 2006 (UTC)

Jul 2006

Serre conjecture vs Serre's conjecture

Do we need a disambiguation page for these? Dmharvey 21:56, 1 July 2006 (UTC)

It would suffice to put a disambiguation link at the top of Serre conjecture, the Quillen-Suslin theorem being the only likely ambiguity. Having "Serre conjecture" and "Serre's conjecture" mean different things is asking for trouble. --KSmrq^T 22:48, 1 July 2006 (UTC)

Done. Septentrionalis 00:24, 2 July 2006 (UTC)

OK for the present, but Serre has dozens of conjectures, I believe. --Charles Matthews 10:58, 5 July 2006 (UTC)

Rogue wikibots

This unicodification stuff made me realize that as just one editor I have very little control over what people decide to do with their bots on wikipedia. I asked the guy running User:Bluebot politely to stop proactively converting HTML entities to Unicode in math articles (and am waiting for a response), but if he doesn't comply what recourse do I have before all of the articles are converted anyway? Apparently he already refused Dysprosia's request.

It seems to me that bots could do a lot of damage in a very short amount of time (shorter than it would take to get the hosting user banned, for instance), and the damage might also be difficult to fix, probably requiring someone to write up a new bot just to fix the mess that the former bot created. How long will it be until someone truly malicious tries to write a bot that trashes (or worse, subtly introduces sign errors, for instance) in hundreds or thousands of articles? Are there any measures in place to prevent this sort of thing from happening? - Gauge 23:38, 1 July 2006 (UTC)

As a bot owner, whose bot has, on occasions, gone rogue, I can say that it does not take long for somebody to notice something odd and notify the bot owner and/or block the bot. Bots are fifth class citizens (in order: Jimbo/bureaucrats/admins/users/anons/bots), they are shown no mercy. :) Oleg Alexandrov (talk) 00:04, 2 July 2006 (UTC)

If an ordinary user can block a bot, how is this done? When should one do it? JRSpriggs 10:09, 2 July 2006 (UTC)

Blocking a bot, like any user, requires an admin. (There are several in this project: Oleg Alexandrov, Jitse Niesen, Lethe, Charles Matthews, Mindspillage, Fropuff, Michael Hardy, Mikkalai, Toby Bartels, The Anome, Isomorphic, Charles Stewart — did I miss anybody? — and me.) Paul August ☎ 15:58, 2 July 2006 (UTC)

TeX tips

While working through many pages with equations listed as acceptable to texvc but incorrect according to BlahTeX's parsing, the single most common issue seems to be a construction like

<math>x^\sqrt{2}</math>,

which must be changed to

<math>x^{\sqrt{2}}</math>.

This often arises with a subscript like

<math>x_\mbox{kind}</math>,

which must be changed to

<math>x_{\operatorname{kind}}</math>.

The corrected appearance is as follows.

$x^{\sqrt {2}}$

$x_{\operatorname {kind} }$

It would be helpful to keep this in mind when editing: Use the braces. --KSmrq^T 02:16, 5 July 2006 (UTC)

Since TeX rightly rejects x^\sqrt{2}, so texvc should also, hence texvc is being Bad. Dysprosia 02:26, 5 July 2006 (UTC)

I am currently rewriting blahtex in python. Along the way I am reworking the parser. As a result it detects even more TeX incompatibilities than the current blahtex version. Dmharvey 02:38, 5 July 2006 (UTC)

You mean texvc problems? Dysprosia 02:42, 5 July 2006 (UTC)

Yes. I mean that the new version of blahtex will produce error messages for certain inputs that texvc accepts and that the current version of blahtex accepts but for which TeX produces an error. Dmharvey 03:13, 5 July 2006 (UTC)

I'm sure the BlahTeX developers are aware of this, but I want to point it out before people go out and mangle the TeX code in articles. The current BlahTeX sandbox seems to support <math>x_{\mbox{kind}}</math> as well, which has the semantic advantage that the word kind should get set as text. The MathML output seems to put operatorname into <mi> and mbox into <mtext>. I don't know the MathML standard, but I doubt these are guaranteed to be the same font. I think operatorname should be reserved for operators. According to the sandbox, BlahTeX also supports the AMS \text command for putting text into math formulas. CMummert 02:44, 5 July 2006 (UTC)

Here's what I can tell you about blahtex's behaviour. The \mbox command is treated very similarly to \text. Pretty much the only difference is some fiddly stuff to do with text sizes. So in x_{\mbox y}, the "y" is the same size as the "x", but in x_{\text y}, the size of "y" is what you would expect a subscript to be. The arguments of \mbox and \text are both treated as text mode material; so for example whitespace is significant, and you can't use mathematical symbols. (This is also why <mtext> is used.) On the other hand, \operatorname takes a math mode argument; it's supposed to be used for things like \operatorname{sin} when you don't have a shortcut like \sin. Using \operatorname has spacing implications too. Compare the output of \operatorname{lim sup} X, \mbox{lim sup} X and \operatorname{lim\,sup} X. It's still got some bugs, for example \operatorname{sin}\limits_2 doesn't do the right thing, for reasons I don't yet completely understand. Dmharvey 03:13, 5 July 2006 (UTC)

Assuming folks are reading this with the typical PNG output, here's a comparison of subscript options (with a deliberate error message):

input		output
<math>x_{\mbox{Hello world}}</math>		$x_{\mbox{Hello world}}\,\!$
<math>x_{\text{Hello world}}</math>		$x_{\text{Hello world}}\,\!$
<math>x_{\operatorname{Hello world}}</math>		$x_{\operatorname {Helloworld} }\,\!$
<math>x_{\operatorname{Hello\ world}}</math>		$x_{\operatorname {Hello\ world} }\,\!$
<math>x_{\mathrm{Hello\ world}}</math>		$x_{\mathrm {Hello\ world} }\,\!$

It should be obvious why I suggest "\operatorname"! (Or perhaps "\mathrm".)

Also keep in mind that the design of MathML mixes "presentation" and "semantics" in peculiar fashion. The distinction between <mi> and <mo> is named "identifier" versus "operator", but it's hard to know what that really means. --KSmrq^T 04:16, 5 July 2006 (UTC)

Possibly <math>x_{\mathrm{Hello\ world}}</math>, which gives $x_{\mathrm {Hello\ world} }$ would be acceptable too.--LutzL 10:08, 5 July 2006 (UTC) || other possibilities: bold face $x_{\mathbf {Hello\ world} }$, sans serif $x_{\mathsf {Hello\ world}}$, italics $x_{\mathit {Hello\ world}}$--LutzL 06:54, 6 July 2006 (UTC)

Worth noting. I've added it to the table. --KSmrq^T 19:24, 5 July 2006 (UTC)

The problem is that neither \operatorname nor \mathrm is the right font for textual identifiers; it is a shame that texvc only accepts operatorname. It looks like there is nothing that can be done until if and when BlahTeX is implemented. Then <math>x_{\text{Hello world}}</math> will work. CMummert 12:10, 5 July 2006 (UTC)

I'm not sure what you're hoping for as the "right font". Within MathML I believe it could be inherited from the surrounding document, giving a sans-serif font like Arial. Within TeX, that's not going to happen. And even if that's fixed, we already have a mix of fonts for variables, serif within TeX and sans serif in wiki markup.

I remind you that, although it does not choke BlahTeX, usage like

<math>x_{Hello world}</math>, producing $x_{Helloworld}\,\!$

is still rampant. --KSmrq^T 19:24, 5 July 2006 (UTC)

Boy do I hate that, using words and text in variable-mode. I see $Diff(M)$ a lot for diffeomorphism group, $hom(a,b)$ for hom-sets, etc. -lethe ^{talk +} 18:38, 6 July 2006 (UTC)

Mathematics Templates

I'm not that good at creating/organizing templates, but I'd like to throw out the idea that using templates in mathematics-related articles would be quite helpful/unifying. There could be an overall Template:Mathematics which includes every topic from elementary algebra to knot theory; we could also make individual topic-related templates such as Template:Calculus. So far as I can see, there are currently very few mathematics templates, with apparently only one in Category:Mathematics templates and a handful in Category:Mathematics navigational boxes. 66.229.182.113 09:03, 6 July 2006 (UTC)

For my part, I don't like linkfests or find them helpful; we had some a while ago, and deleted them after consideration as random collections of articles. Septentrionalis 18:39, 6 July 2006 (UTC)

The template Template:mathematics-footer may already provide what you're looking for. -lethe ^{talk +} 18:48, 6 July 2006 (UTC)

I agree with Septentrionalis, one should keep templates small and use them very sparingly. Templates can be distracting linkfarms in many cases. Oleg Alexandrov (talk) 18:55, 6 July 2006 (UTC)

I am not sure but I think it may be useful to have infoboxes for theorems, inequalities, conjectures, lemmas, mathematicians. (Igny 21:12, 6 July 2006 (UTC))

I would strongly disagree with any of that. I don't quite understand what you mean by infoboxes, but from what I can tell they will just amount to more clutter. Oleg Alexandrov (talk) 22:08, 6 July 2006 (UTC)

I just would like to say that many people have infoboxes, see Abraham Lincoln, Isaac Newton, Friedrich Nietzsche (note the nice infobox the philosophers have), Blaise Pascal; but not so many mathematicians are with infoboxes, see Friedrich Bessel, Andrey Kolmogorov, Henri Poincare, Fermat etc. (Igny 02:56, 7 July 2006 (UTC))

I see. I thought infoboxes are some kind of glorified templates allowed to be transcluded on hundreds of pages. I agree now that they could be useful, although the danger of creating unnecessary clutter is still there. Oleg Alexandrov (talk) 03:20, 7 July 2006 (UTC)

Additive Group

Can someone look at Additive group and clean it up. It's marked as a disambiguation page. --Usgnus 18:20, 6 July 2006 (UTC)

And so it ought to be: it is a disambiguation page. It links to three different articles which are in three different branches of mathematics, and all of which could be the topic for additive group. If you mean Abelian group, written additively, go there. Septentrionalis 18:37, 6 July 2006 (UTC)

It's marked for disambiguation cleanup. --Usgnus 18:41, 6 July 2006 (UTC)

Oh, so that means it doesn't conform to Wikipedia's disambiguation page norms. Well I'm not sure what those norms are. Perhaps this request should go to Wikipedia talk:WikiProject Disambiguation instead, seems like more their cup of tea. -lethe ^{talk +} 18:46, 6 July 2006 (UTC)

(Edit conflict) Yeah, I'm not sure what the problem is. I don't see a need for an article about additive groups. On the other hand, I might support redirecting additive group to abelian group, so long as the latter article had a segment about underlying additive groups and other additive group functors. -lethe ^{talk +} 18:43, 6 July 2006 (UTC)

I'm asking for help here because the last time I tried to clean up a mathematics-related "disambiguation" page, I was scolded. --Usgnus 18:55, 6 July 2006 (UTC)

Ha! Asking mathematicians to disambiguate is asking the fox to guard the chickens. We even have a little ritual phrase, "by abuse of notation", to cover some — but by no means all — of our wanton ways. Anyway, since you don't want to offend anyone who is passionate about one of the meanings as being "the right one", asking for participation in such edits is wise. --KSmrq^T 20:38, 6 July 2006 (UTC)

The {{disambig-cleanup}} tags are an unnecessary evil, a policing of format by editors who often don't understand the subject matter. The complaint here seems to be that each line of a dab page should link to an article for that meaning, if one exists, and ideally there should be no other links. I have revised the format; I trust that will do. Septentrionalis 20:22, 6 July 2006 (UTC)

Huh? Did you miss to save your edit? It's still in the unwanted many-links-per-line format. --Pjacobi 21:03, 6 July 2006 (UTC)

No, I intentionally left some links, because those terms may not be clear to the dabber. I see the link to addition has been restored, which is probably unnecessary. Septentrionalis 02:19, 7 July 2006 (UTC)

Thanks for your help, Septentrionalis. --Usgnus 21:11, 6 July 2006 (UTC)

I'm confused about these definitions, and currently none of the links point to anything about the first term additive in the definition. So from the article I can know that an additive group can be a group, ring, field, or functor, but nothing about additive apart from its and addititive group if we choose to call it such.

Consider a deliberately perverse example. Take the multiplicative group of non zero integers. Instead of writing × for the symbol write +. Now by the first line this staisfies the definition for an additive group, even though it has a very different structure.

The mathworld article has a stricter definition for the first line, (identity must be called zero and the inverse written as -a) and is much more extensive. I'd suggest making the page a real article rather than a disambig. Either that or just redirect to group. --Salix alba (talk) 19:16, 7 July 2006 (UTC)

Point of detail: in your example, do you mean the integers, or the rationals? (The details of the answer will be different if the group is {-1,1} or the non-zero rationals). But the gist is the same: yes, I'd call that perverse; but I'd also call it an additive group. Septentrionalis 19:28, 7 July 2006 (UTC)

I would support a redirect (but to abelian group, not to group). In fact, it used to be one. Charles Matthews changed it to a disambig. Maybe he can offer some arguments why we need that disambig. As for making it an article in its own right, I don't support that. There's nothing to say about additive groups that isn't actually a statement about abelian groups, right? -lethe ^{talk +} 19:41, 7 July 2006 (UTC)

Probably my fault for scolding User:Usgnus. There have been cases where editors, who are not very good at math, have been marking various pages as needing merges or splits or disambiguation, etc. These show up on cleanup project pages, whereupon other editors, who know nothing at all about math, attempt to do a good deed, and perform the recommended split/merge. And make a mess, because the article should not have been tagged in the first place. I caught one such in progress and pseudoscalar, and posted some nastygrams recommending that this project be contacted first .. which is what Usgnus did. linas 03:43, 9 July 2006 (UTC)

new article: algebraic equation

I'm not sure the definition given is that widespread. Seems a bit too restrictive. Author gives Mathworld as a source. Please comment at Talk:Algebraic_equation. Dmharvey 20:16, 6 July 2006 (UTC)

Nice double arrows

I just figured out how to do nice looking double arrows in texvc exact sequences. Here is a demo:

${\mathcal {F}}(U)\rightarrow \prod _{i}{\mathcal {F}}(U_{i}){{{} \atop \longrightarrow } \atop {\longrightarrow \atop {}}}\prod _{i,j}{\mathcal {F}}(U_{i}\cap U_{j}).$

The point is to put some phantoms above the top arrow and below the bottom arrow which apparently forces the arrows to space more closely together. I also did a native TeX diagram for splitting lemma this way, using names for the arrows. I hope someone finds this useful. - Gauge 00:26, 7 July 2006 (UTC)

Of course what you really want is this... Dmharvey 01:24, 7 July 2006 (UTC)

I noticed that the character ⇉ looks too short and stubby in MathML compared to the png output. It doesn't rescale when I change the text size either. Maybe it's because I'm missing the Symbol font? I still haven't found a reasonable explanation of how to get Symbol to work on my Gentoo box. I successfully installed all of the others required for MathML. Running Firefox 1.5.0.4, of course. - Gauge 04:11, 7 July 2006 (UTC)

It sounds like a font thing, but it might also be a problem with Firefox's scaling code. It knows how to stretch some operators but not all. Dmharvey 22:04, 7 July 2006 (UTC)

Regular number up for deletion

Please comment at Wikipedia:Articles for deletion/Regular number. --Trovatore 16:52, 7 July 2006 (UTC)

That article was deleted, but there is a genuine (and different) concept here; so I wrote a new one. Weissstein got it wrong. If anyone insists on AfD'ing the new article, fine; we can discuss it there. Septentrionalis 21:42, 13 July 2006 (UTC)

I think this one should be fine; I made a mistake in my MathSciNet search the first time and missed a few references to sexagesimal numbers, Babylonians, etc. There appear to be six articles (with only one by Sachs), which while not overwhelming, is probably more than enough, going by the usual standard. There are more or less the same number of hits for other definitions of regular numbers though, in number theory, group theory, etc. So it may be best to create a disambig page for "regular number". --C S (Talk) 23:11, 13 July 2006 (UTC)

The Bernouilli-number definition I would put at regular prime; what are the others? But it may be simpler if we write Regular number (disambiguation) and then decide on what goes where. Septentrionalis 02:26, 14 July 2006 (UTC)

A regular number can refer to the order of a regular element of a finite reflection group; Springer is apparently the name here. Actually, looking up "Springer" and "Regular element" brings up a lot more hits; I imagine regular number is mentioned much more often in the actual articles, rather than in the MathSciNet reviews. Springer's 1974 article "Regular elements of finite reflection groups" already defines regular number in that context. There are also k-regular number fields; here, the usage may be different, but is similar enough to require some disambiguation in my opinion. There's also several other usages that appear in a MathSciNet search for "regular number", but it's hard to tell how common they are (as it shows up only if it's in the title or review). So it looks like there is some work to be done here. --C S (Talk) 16:16, 14 July 2006 (UTC)

Scalars

A proposal to merge Scalar has turned into a protracted discussion of whether or not the term 'scalar' means the same thing in different disciplines. See Talk:Scalar. --Smack (talk) 05:13, 10 July 2006 (UTC)

Gosh Numbers

(copied from Portal talk:Mathematics)

Wikimathematicians, if you are interested, please help determine this afd discussion about Gosh Numbers. Thanks! Bwithh 04:40, 10 July 2006 (UTC)

AFD listings

The following articles have been listed at AFD and not picked up by the current activity 'bot:

• Basic matrix (mathematics) (AfD discussion)

Please contribute to the discussions. Uncle G 23:18, 10 July 2006 (UTC) The following articles have been listed at AFD and not picked up by the current activity 'bot:

• Maths A (AfD discussion) (including Maths B and Maths C)

Please contribute to the discussions. Uncle G 13:17, 18 July 2006 (UTC)

sextic equation

A microstub of dubious utility. AfD? -lethe ^{talk +} 06:19, 12 July 2006 (UTC)

It was already (correctly IMO) changed to a redirect. However, alternatively, we could snatch [31] from PlanetMath if anyone can confirm the veridicity of the information. AdamSmithee 07:53, 12 July 2006 (UTC)

Arthur Rubin for admin

I nominated one of us, Arthur Rubin, for administrator. If you are familiar with Arthur's contributions, and would like to vote, see Wikipedia:Requests for adminship/Arthur Rubin. Oleg Alexandrov (talk) 04:38, 13 July 2006 (UTC)

I definitely will. RfA is the biggest popularity contest these days and it seems that scientists and mathematicians aren't very popular amongst the general public. See Wikipedia:Requests for adminship/Edgar181 to see what I mean - some people who do 2000 small edits and write 1 article get twice as many votes. Blnguyen | rant-line 04:45, 13 July 2006 (UTC)

I disagree about scientists and mathematicians. It seems to me that most of them sail through RfA without hardly a sideways glance. -lethe ^{talk +} 22:44, 18 July 2006 (UTC)

In any event, Arthur Rubin was promoted to administrator a few minutes ago with a 99/2/3 final tally. CMummert 02:40, 20 July 2006 (UTC)

User:Tokker and ...illions of redirects

He's created approximately 200 redirects from names of large numbers to Jonathan Bowers. Any chance a mathematically inclined admit could delete these, or at least automate the RfD script.... — Arthur Rubin | (talk) 05:17, 14 July 2006 (UTC)

It looks to me like the page Jonathan Bowers is a candidate for deletion:

• It has a lot of unsourced material which I doubt is verifiable
• It is a biography of a non-notable person.

Also Bowers style acronym looks like original research. CMummert 12:49, 14 July 2006 (UTC)

Good idea. I've alraedy summarily deleted the names of the large numbers and the notations for creating large numbers from the article, as naming things and re-creating notations are not notable unless the new notation catches on. I'm investigating whether the Polychoron family should be deleted as well, as being a neologism, not used in professional mathematics. (15 of the first 20 examples of the netscape search for "polychora" are Wikipedia, Bowers' site, or MathWorld. The other 5 may be from one of the other members of the Uniform Polychora Project. I've contacted a professional recreational mathematician named in one of the articles for further information.) — Arthur Rubin | (talk) 14:44, 14 July 2006 (UTC)

The word "polychoron" would not appear in classic Coxeter because it is more recent. We use 4-dimensional polytopes often enough that it is helpful to give them their own name. Both Johnson (of Johnson solids) and Olshevsky were students of Coxeter, which lends a certain amount of credibility to what they say. Here's the story of the name, as reported by Olshevsky on his web site:

• POLYCHORON (plural: polychora) is my term for a four-dimensional polytope, analogous to polygon in two dimensions and polyhedron in three. The only other names for such a figure that I had seen in the literature, “polyhedroid” and “hypersolid,” seem uninspired and inappropriate, because they’re too close to terms for three-dimensional polytopes; the ending -oid connotes similarity or resemblance; and the prefix hyper- is badly overused. A four-dimensional polytope resembles a polyhedron no more than a polyhedron resembles a polygon, so it should have a similarly distinctive root following the poly-. The Greek root choros means “room,” “place,” or “space,” describing the three-dimensional polytopes, or cells, that make up the polychoron. In early versions of this website, I called such a figure a polychorema (plural: polychoremata), but Norman W. Johnson persuaded me of the benefits of the shortened form, and I changed this document everywhere accordingly.

Therefore "polychoron" is relatively new, but that doesn't mean it isn't also respectable. Remember that “polytope” itself was a neologism of Alicia Boole Stott before it was popularized by Coxeter. A possible contact to assess academic acceptance of the name might be computational geometry expert David Eppstein, a professor at UC Irvine famous for his Geometry Junkyard pages. Another academic contact might be Brown University professor Tom Banchoff, well known for his interest in things four-dimensional.

My impression is that although neologisms are rampant among enthusiasts, this term has gained traction and has been around long enough that it will probably persist. --KSmrq^T 20:01, 14 July 2006 (UTC)

Our article says that Coxeter uses polytope; unless there is some differentiation for polychoron, there is probably consensus against it. The images and facts should probably be salvaged. Septentrionalis 16:39, 14 July 2006 (UTC)

If polychoron is strictly dimension 4, that is the required difference. Septentrionalis 21:59, 14 July 2006 (UTC)

Even if I were an admin (see the above nomination), I'd need help keeping up with these. Someone is creating separate articles for the sections I deleted from Jonathan Bowers, and creating more pieces. (Is there something I could put in my .js which would, with a single click, add an {{rfd}} to the above redirect, and add it to a list in a user subpage so I could copy the list to WP:RfD. This is would be tiring.) — Arthur Rubin | (talk) 17:02, 14 July 2006 (UTC)

I don't think those redirects are actually that bad. Having them makes it less likely that someone will create stub entries on those numbers. It's kind of like the redirects we have at names of large numbers, which otherwise people would create stub articles on those numbers. Voortle 17:26, 14 July 2006 (UTC)

If those redirects are original research, they should be deleted also. Oleg Alexandrov (talk) 17:31, 14 July 2006 (UTC)

Dear Lord [32]. I suggest a massive speedy delete campain. Any comments on that? Oleg Alexandrov (talk) 17:27, 14 July 2006 (UTC)

Wikipedia:Articles for deletion/Other names of large numbers dealt with this issue, and the decision was to delete back them. Oleg Alexandrov (talk) 17:29, 14 July 2006 (UTC)

Yeah, redirects to other names of large numbers should be deleted, as that page doesn't exist. However, redirects from -illion names are not bad, because they prevent someone from creating stub articles on these numbers. Voortle 17:32, 14 July 2006 (UTC)

Redirects to other names of large numbers should be deleted, as that page shouldn't exist. Redirects to Bowers' names of large numbers are just as bad. — Arthur Rubin | (talk) 17:41, 14 July 2006 (UTC)

I don't think it would be any great loss to delete all of these. Paul August ☎ 17:52, 14 July 2006 (UTC)

Nominate for deletion all Jonathan Bowers related pages?

Is Jonathan Bowers that important a person? To me he appears to be a crank, and not even notable at that. How about nominating for deletion his page and all his other stuff? Oleg Alexandrov (talk) 17:37, 14 July 2006 (UTC)

Anyone got a script? I think we need to delete most of the Polychoron pages, and the other people linked from Uniform Polychora Project. — Arthur Rubin | (talk) 17:41, 14 July 2006 (UTC)

I would agree with deleting the whole lot. I don't believe they enhance wikipedia at all. Madmath789 17:44, 14 July 2006 (UTC)

Note that Oh Crap (talk · contribs · deleted contribs · nuke contribs · logs · filter log · block user · block log) has created a malformed AfD for Jonathan Bowers and L. Craig Schoonmaker. Is there any way to separate them. (The issues are not related.) — Arthur Rubin | (talk) 18:05, 14 July 2006 (UTC)

See Wikipedia:Articles for deletion/Jonathan Bowers. Oleg Alexandrov (talk) 18:07, 14 July 2006 (UTC)

STOP! First off lets look at the members of the Uniform Polychora Project among them was the late Norman Johnson a student of Coxeter, and perhaphs one of the most important recient figures in the field of polyhedra, having created the Johnson solids, and also the nicest way of classifying the uniform polyhedra List of uniform polyhedra by vertex figure (Johnson, N. W. Uniform Polytopes. Cambridge, England: Cambridge University Press, 2000). So Johnson then went onto study the four dimensional polyhedra and enlists the help of various amature mathematicians, Bowers being one of them. Bowers is responsible for discovering most of the uniform 4D polyhedra and as discoverer probably gets the naming rights. Bowers names are probably becoming the defacto standard for 4D uniform polyhedra, considerably more pratically useful than the long names (First due to Coxeter, modified by Wenninger and later by Johnson). So we have a group resposible for discovering most of the uniform 4D polytopes. So its run by amatures who don't bother to publish in maths journals. Well the whole field of polyhedra is very much dominated by the amature, the most read book on the subject is Wenninger polyhedra models and Wenninger is in an order of Monks, not a professional mathematician.

As for the array notation. I'm not sure but I think is is capable of representing larger numbers than the closest contender Conway chained arrow notation. In my book thats worth a page, published or not. This stuff is important as it has close links to transfinite cardinals, helps us get a feel for the true emensity of natural numbers and is also a good way to bring people into apreciating mathematics, a natural extension of the game of naming bigger and bigger numbers we all played as kids.

I'm less bother about the names of large numbers, although the largest finite number so far conceive by man, seems to be of some interest. Here I'd take a pragmatic approach, we will always be getting people adding these very large names. Theres two options, spend our lives reverting Names of large numbers or keep a seperate out of the way page for these numbers to appear.

To sum up Wikipedia isn't great because it's like the Britannica. The Britannica is great at being authoritative, edited, expensive, and monolithic. Wikipedia is great at being free, brawling, universal, and instantaneous. — Cory Doctorow --Salix alba (talk) 18:11, 14 July 2006 (UTC)

I strongly object to wholesale deletion without closer scrutiny. As I noted above, the name "polychoron" was created jointly by Olshevsky and Johnson, both of whom worked and studied with Coxeter, and both of whom were involved in creating the Uniform Polychora Project. Partly we are confronting a problem of volume and organization: there are too many of these beasts! They can hardly all be well-known, it's a pain to enumerate them, it's a pain to name them, names are still in flux, and so on. Frankly, I doubt many people can name the convex regular polytopes in four-dimensional Euclidean space, or even recall how many there are — and these are surely notable. Or how about the Archimedean solids? Our page lists 13 of them, over half with more than two names! Please, ease off on that trigger finger; don't shoot first and ask questions later. I'd suggest that few polychora deserve a page of their own, and that we surely don't want to duplicate the content of the project; but don't throw out the baby with the bathwater. I'd also suggest it would be absurd to delete the page on Norman Johnson. --KSmrq^T 20:29, 14 July 2006 (UTC)

I'm not in a hurry to delete the polychora; I'm still researching. Mr. Bower and his pet names are not notable. Messers. Olsehvsky and Johnson may be more notable. — Arthur Rubin | (talk) 22:19, 14 July 2006 (UTC)

First, Norman Johnson is not late. He is alive and well.

About Jonathan Bowers and polychora, I am familiar with his work and have met him at a conference. I am also acquainted with Olshevsky, and know Wenninger and Johnson fairly well. Jonathan Bowers would be classified as an amateur mathematician, but has an astounding ability to work with four-dimenionsal figures. He can sketch three-dimensional cross-sections of polychora as easily as I might sketch, say, an equilateral triangle.... He is in close contact with Johnson, and Johnson is trying to incorporate Bowers's work into an upcoming book to be published by Cambridge University Press.

User Tom Ruen is also working on the Wikipedia pages on polychora.

This group is at the forefront of work on polychora. The project is to enumerate all uniform polychora in four dimensions. The problem of enumerating the 75 uniform polyhedra in three dimensions was solved only in the 20th century and has an interesting history. I think it is reasonable to assume that any work done in the area (in 4D) will be known to this group.

I only recently read about Bowers's work on naming large numbers. I think that subject should be discussed independently of his work on polychora.

I would argue that Jonathan's work is legitimate, even though he doesn't have appropriate 'credentials.' You might not wish his work in the Wikipedia for other reasons, but it is certainly not spurious. Vince Matsko 21:10, 9 August 2006 (UTC)

The work is legitimate. The classification theory seems notable enough; however his naming conventions (both for large numbers and for polytopes), any of the individual names that have articles, and the term "polychoron" may need to be removed, unless some legitimate geometer publishes those names. — Arthur Rubin | (talk) 00:55, 10 August 2006 (UTC)

Evolution of an article!

I am still fairly new to wikipedia, and I would really appreciate a view from a more experienced wikipedian about the evolution of the article Homogeneity. I have looked at the history of this article over the last year or so, and it seems to have 'evolved' in an extremely strange way. Please take a look at the Revision as of 07:02, 10 February 2006, and compare with the Revision as of 08:34, 10 July 2005. What on earth is going on here??? I am totally baffled by the latest incarnations of this article, but if more experienced editors tell me it is OK, I will accept their wisdom ... Madmath789 22:47, 14 July 2006 (UTC)

It looks like an editor decided that there is basically only one meaning for "homogeneity", i.e. its use in statistics, and then proceeded accordingly. --C S (Talk) 10:50, 15 July 2006 (UTC)

Yes, indeed, but I can't make much sense of the article as it stands, despite being a reasonably competent mathematician with a fair knowledge of probability and statistics! I am also a little suspicious of the possibility of OR here, as much of the editing of Homogeneity and a linked article Reliability (statistics) seems to have been done by David Cruise or by Cruise, and a couple of external links from Reliability (statistics) point to 'visualstatistics.net (e.g. The problem of negative reliabilities ) which seems to be authored by David J. Krus / Cruise scientific. I might be off-beam, but I am very suspicious of these articles. Madmath789 11:37, 15 July 2006 (UTC)

Yes I agree the article does look very out of ballance. Go ahead and bring it back into line. --Salix alba (talk) 11:53, 15 July 2006 (UTC)

Apart from the present article being whacky, I also think that Homogeneity (instead of Homogeneous) should be a disambiguation page, with Homogeneous a plain redirect to Homogeneity, and the statistical concept being handled at Homogeneity (statistics), which now redirects to Homoscedasticity, a different concept in statistics. --Lambiam^Talk 12:34, 15 July 2006 (UTC)

Whacky indeed! I have spent some time trying to decide if this article homogeneity is genuine or totally off-the-wall. Can I make a plea: if anyone here knows more than I do about this sort of statistics, could you please advise as to the validity of this weird-looking stuff? Madmath789 16:56, 16 July 2006 (UTC)

Greek letter proposal

Please see my proposal for Greek letters at Wikipedia talk:WikiProject Mathematics/Conventions CMummert 23:27, 15 July 2006 (UTC)

Computability Articles

JA: User:CMummert is making a mass of what appear to be improper page moves, renames, and reorgs to computability related articles. Could somebody please sort all that out and makes sure it's by the book? Thanks, Jon Awbrey 15:58, 16 July 2006 (UTC)

What I've seen looks legit to me. --CSTAR 16:23, 16 July 2006 (UTC)

I would be glad to explain, if anyone asked me; one the other hand, I am an expert in the area. For a while, there have been two articles: Computable function and Recursive function. These titles are synonyms in the current vernacular, and having them as separate articles is confusing. I have moved Recursive function to Mu-recursive function which is the consensus on what that article is actually about. I made Recursive function into a disambiguation page, which is important because there is a CS meaning for the term that was not reflected on the previous page. Then I chased almost all the things that linked to Recursive function. Many of them actually wanted to link to Recursion or Recursion (computer science); the previous page had no relation to the material in articles that were linking to it! So I fixed many of the links to Recursive function to point to a more helpful location. I also made a start towards fixing Mu-recursive function. CMummert 16:35, 16 July 2006 (UTC)

STIX Fonts update

Many of us have been eagerly awaiting the culmination of the STIX font project. A major milestone was recently announced.

• On 10 July, the STI Pub group received the final delivery of requested glyphs for the STIX Fonts Project. This final set is being reviewed by the STI Pub Technical Review Committee, and packaging instructions for the beta test of the fonts are being prepared. Tables of STIX glyphs will begin to appear on this website within the next few weeks, and the beta font set will begin to be constructed.

So far every deadline has been overly optimistic; still, progress has been real. It appears the race is on, between universal adoption of the STIX mathematics glyphs and Wikipedia adoption of BlahTeX! Regardless of which tortoise crosses the line first, we all win. Huzzah! --KSmrq^T 09:47, 17 July 2006 (UTC)

Fleiss' kappa

I don't know if this is the right place to ask about this, but I've been working on Fleiss' kappa, and I'd like to get someone who actually knows what they are talking about to look over it. I have the paper here, but I worked out what is what by trial-and-error because I am pretty much maths illiterate. I'd appreciate it if anyone could look over it, and add {{accuracy}} or something if I've made a mistake. Thanks - FrancisTyers · 16:01, 17 July 2006 (UTC)

See my comments on the talk page of Fleiss' kappa. VectorPosse 22:44, 17 July 2006 (UTC)

Discussion at Category talk:Mathematics user templates

Hi all,

Just wanted some of the editors opinion on a discussion I started at Category talk:Mathematics user templates. The discussion is about userboxes, a bit technical, but not serious. I don't want to advertize, but the fact is that in most cases, category pages are usually watched by the creators only, and probably even worse in this case, only be the sysop who moved the category. Thanks, — Ambuj Saxena (talk) 17:17, 18 July 2006 (UTC)

Homogeneity

The 'whacky' article Homogeneity is up for deletion - please take a look and comment at Homogeneity. I think it really needs looking at by a statistician. Madmath789 06:33, 20 July 2006 (UTC)

Following some moves by Michael Hardy, the AfD seems to have vanished, and the material I was worried about now lives at homogeneity (statistics) - does anyone see a good reason for not having an AfD discussion about this stuff? Madmath789 15:11, 20 July 2006 (UTC)

I've now listed a new AfD at Wikipedia:Articles for deletion/Homogeneity (statistics) and voted speedy keep on Homogeneity, previous votes have been copied across. --Salix alba (talk) 16:22, 20 July 2006 (UTC)

User:David Cruise

I would like someone with experience look at edits made by User:David Cruise, User:Cruise, and also IP 65.39.86.104 ([33]) to the mathematical articles, in particular, Supermatrix, matrix addition, matrix subtraction, canonical analysis, homogeneity (statistics) (this article is currently listed at AfD and this actually triggered my interest in the user Cruise) and probably many other articles as well. Note references to Krus' publications and links to Cruise Scientific ([34]), also note many links from Cruise Scientific (see for example, [35]) to the Wikipedia articles in question. I would like someone to sort out contributions with scientific value from original research. (Igny 18:21, 21 July 2006 (UTC))

I have only looked at the article on matrix addition, but it certainly has all the earmarks by being hijacked. Alterations include non-standard definitions and notation, as well as self-promoting links. --KSmrq^T 19:41, 21 July 2006 (UTC)

I think I am responsible for bringing this to peoples attention, but I have "trodden carefully" as a comparative newcomer to WP (but a comparative 'old-comer' to maths!). I have been looking at the things mentioned above for a few days, and have to say that I believe that most of the content of the articles Homogeneity (statistics) and Canonical analysis are mathematical gibberish, and the matrix stuff is probably nonsense (I have seen many examples of such over the last 4 decades, but these examples are quite staggering!). I do not wish to appear to be waging a vendetta against any contributor to WP, but I have to say that I cannot find anything worth keeping in the previously mentioned articles, and feel that trying to rewrite them would best be done by deleting everything and starting from scratch. Madmath789 20:54, 21 July 2006 (UTC)

I don't think the material at canonical analysis is nonsense, but it is not clearly explained in a manner that makes it comprehensible to mathematicians in general. Similarly at homegeneity (statistics). Michael Hardy 22:29, 22 July 2006 (UTC)

Our discussions here may become academic, as User:David Cruise seems to be trying to blank contributions he has made - see for example: Canonical analysis. I know I have been a harsh critic of some of his contributions, but I am unsure if this is the right way to proceed. What do others think? Madmath789 16:56, 23 July 2006 (UTC)

Ones contributions are an irrevokable gift (if they are not an infringment of someone else's copyright). So we are free to resurrect them by reverting his deletions. Also we should take care that he does not also delete the contributions of other people. But perhaps any such corrections should be done only after he has been blocked so that he will not commit more such vandalism. JRSpriggs 03:16, 24 July 2006 (UTC)

Blatant spam is of course not needed. But as for 'nonstandard stuff', I don't take stock in nonstandard stuff, because doing stuff in a non-standard way can lead to new ideas. As for matrix addition and matrix subtraction, I reverted one of the articles back to the way it was with his changes, and later removed some spam-like stuff from references and external links. I ask someone who knows more than the textbook definition of matrix addition/subtraction that I do to look over whatever new matrial he put in, save actual methodology that works and is substationally useful. I'm not so sure such a lengthy section is needed on a particular application of matrix subtraction, for example, involving variance. Kevin_b_er 04:45, 24 July 2006 (UTC)

David Cruise's additions to matrix addition and matrix subtraction are probably correct (though they are badly explained, so I can't be sure of that). However, his definitions are not used in the field of matrix theory. They may well be used in statistics or social sciences, but all we have are some papers written by D. Crus in nonmathematical journals. In contrast, the standard definitions are in every linear algebra textbook. I do not think that "doing stuff in a non-standard way can lead to new ideas" is a good reason for including nonstandard definitions in an encyclopaedia. I think that the nonstandard material to these two articles should be removed, or at least greatly reduced, unless somebody tells us that these definitions have found widespread use in some disciplines. -- Jitse Niesen (talk) 05:13, 24 July 2006 (UTC)

I noticed that David Cruise just vandalized two sections of this very talk page. From the history:

11:52, 25 July 2006 Gandalf61 (Talk | contribs) (rv blanking)

11:48, 25 July 2006 David Cruise (Talk | contribs) (entries containing libellous statements)

Fortunately, Gandalf61 reverted the vandalism. I think that the first administrator who reads this should immediately block David. JRSpriggs 06:02, 26 July 2006 (UTC)

I was considering asking an admin to look at this myself, in view of his blanking of parts of this page, and also his removal of the AfD notice (and other stuff) from Homogeneity (statistics). I am aware, though, that he has also made contributions from another account User:Cruise (not active since 17th April) and might use that one while blocked. I will keep an eye on it. Madmath789 08:13, 26 July 2006 (UTC)

I haven't been around much, so I don't know the details, but a single blanking at this page, while unacceptable, is probably not sufficient to block. I've placed a warning on his talk page. If his behavior continues, a block can certainly be considered. By the way, if we do decide to block, using sockpuppets is grounds for blocking the second account, so that's not a problem. -lethe ^{talk +} 08:18, 26 July 2006 (UTC)

As I understand things, he has already been given a one week block by User:IanManka. Madmath789 08:27, 26 July 2006 (UTC)

Terminology clarification and first use references: "Hypercomplex Number"

Hello,

I'm currently trying to clarify the use of the term "hypercomplex number" over the years and to-date. The goal is to update the hypercomplex number article. Since this may result in a rewrite, it would be great if any ideas or comments could be posted in talk:hypercomplex number, so the reasoning behind a potential rewrite would remain with the article.

Thanks, Jens Koeplinger 21:27, 22 July 2006 (UTC)

PS - It may be that the term "hypercomplex number" is to-date a rather freely used term, like "numbers with 2 or more dimensions and at least one non-real axis". If so, I'll scratch together what I can find in some common places (here, mathworld) and rewrite hypercomplex number in a fashion that puts different systems into different categories (like Cayley-Dickson, split-complex, etc). Thanks, Jens Koeplinger 13:28, 24 July 2006 (UTC)

I've just posted a rewrite of the hypercomplex number article. While I tried to carry over all previously existing information and statements into the new version, it now contains much more detail and categorization. I would appreciate any comment or help. Thanks, Jens Koeplinger 22:29, 31 July 2006 (UTC)

Hello; I haven't received much feedback yet about the hypercomplex number rewrite, so I figure it can't be too bad. There are two obvious weeknesses: "The term hypercomplex number has been used over the years rather freely ..." - if anyone knows about references to be added, please do so. I've seen two more book titles mentioned in the internet, but I'm reluctant to referring to books or titles I didn't read. Without references, my statement has no support within the article.

The second weakness is that I'm writing about "Arguably the most common use of the term hypercomplex number [...]" and only provide links to some other numbers. I'm comfortable with this wording, but to the least I'd like to add a section that groups together these 'arguably not so common uses' of the term "hypercomplex number" (surreal, hyperreal, transfinite, superreal nubers, and - as I recently learned - Mark Burgin's hypernumbers which appear not to have an article in Wikipedia yet).

Maybe we could tailor the "hypercomplex number" article into an overview over all number systems that somehow go beyond or extend the reals. This might help to have the current number article focus on commonly used systems (from natural to complex numbers), and clean-up references to other less frequently applied numbers.

But first I'd like to put the "hypercomplex number" article on better feet, and remove the 'stub' notice once done. Any comment is greatly appreaciated. Thanks, Jens Koeplinger 12:40, 8 August 2006 (UTC)

Good articles

While trying to expand the list of important articles in Wikipedia:WikiProject Mathematics/Wikipedia 1.0, I've come across a few articles I feel are close to Wikipedia:Good articles status and nominated them appropriately. of these Euclidean geometry, Georg Cantor and David Hilbert has reached GA status. Pi, Fractal, Gottfried Leibniz, Ronald Fisher have failed. Fractal needs someone to check recent additions made by reviewer, Leibniz needs some work organising the references and Pi and Fisher needs more extensive work. If anyone would like to have a look at these articles it should not take much to gain GA status. --Salix alba (talk) 09:47, 23 July 2006 (UTC)

84.40.138.111 (talk · contribs · deleted contribs · filter log · WHOIS · RDNS · RBLs · http · block user · block log) and -http://www.apronus.com/provenmath/ links

We've got a new IP address adding external links to the above mentioned web site. I'm tempted to revert en mass, but I'd like a second opinion. — Arthur Rubin | (talk) 17:52, 24 July 2006 (UTC)

I had just noticed this too, and I agree the links don't belong here. Dmharvey 18:36, 24 July 2006 (UTC)

Yes, noticed them earlier, and find them hard to read (but they may well be valid) - the notation used on that website is 'tedious' to read - see [36] I agree they don't belong here. Madmath789 21:19, 24 July 2006 (UTC)

If I read this page correctly, they claim to have their own proof of the equivalence of Zorn's Lemma and the Axiom of Choice; I hope I'm being unfair, but... What next, the Pythagorean Theorem? Septentrionalis 23:03, 24 July 2006 (UTC)

Proving induction

Please take a look to the article proof of mathematical induction. As a consequence of a remark of mine [37] an editor made some addition to the hypothesis of the proof to make it work. I would like to understand if this proof is "standard" (it should be other wise would be original research) and what is his original form (in particular which hypothesis should we require). What do you think?--Pokipsy76 15:41, 23 July 2006 (UTC)

The concept of "proving" induction is strange. Typically we use an axiom scheme that explicitly states that induction works. A quick glance at this leaves me feeling that it's a bad article. --KSmrq^T 19:02, 23 July 2006 (UTC)

The concept of proving the principle of mathematical induction is certainly not strange - it is a well-known part of mathematical logic and the development of the number system logically. The article might need a bit of work, but the idea is good. Madmath789 19:15, 23 July 2006 (UTC)

I'm not quite sure what you mean by "proving". For example, here's a quote from Peano axioms:

---

Informally, the Peano axioms may be stated as follows:

• 0 is a natural number.
• Every natural number a has a successor, denoted by Sa or $a'$.
• No natural number has 0 as its successor.
• Distinct natural numbers have distinct successors: a = b if and only if Sa = Sb.
• If a property holds for 0, and holds for the successor of every natural number for which it holds, then the property holds for all natural numbers. This axiom of induction legitimizes the proof method known as mathematical induction (induction over the naturals).

---

I draw your attention to the last item. Essentially it says we "build in" induction; we don't deduce it. Although there are many ways to approach foundations, I don't think we can avoid something along these lines; natural numbers and induction are inseparable. If natural numbers are defined per Peano this whole proof article is silly. If not, the article is confusing; it's not clear where we're beginning, nor exactly what is being accomplished.

If we are going to discuss the article further, we should do so on its talk page. --KSmrq^T 23:19, 23 July 2006 (UTC)

Proving just means deduction from axioms. Clearly, in PA, mathematical induction is an axiom, but in developing maths from ZFC, it is not an axiom, so it needs to be proved from the axioms. Madmath789 06:51, 24 July 2006 (UTC)

I have to agree with both KSmrq and Madmath: The idea of proving the induction principle is not "strange" in itself, and yet the article in question is a bad article (and I have my doubts that any article with that title would be good). Induction is not assumed explicitly in, say, the usual formulations of ZFC, and can be proved once you've defined the naturals. But there's less here than meets the eye; it's a boring technical detail rather than something particularly significant, and having an article about it might give the misimpression that there's something fundamental being done. The existing article is worse than that; it starts with the assumption that the naturals are wellordered. From there the induction principle really is a triviality. --Trovatore 19:56, 23 July 2006 (UTC)

It's not clear to me in which sense can we be supposed to prove induction principle from the well ordering assumption: the well ordering itself is useless unless we have some extra assumption to work with (for example the assumption that x#0→x=y+1)--Pokipsy76 20:04, 23 July 2006 (UTC)

I gave that article a prod. -lethe ^{talk +} 20:37, 23 July 2006 (UTC)

Maybe you could have waited a little bit to let us discuss about it before going to vote.--Pokipsy76 20:55, 23 July 2006 (UTC)

Prodding does not involve a voting process. We have ample time to discuss this. --Lambiam^Talk 00:39, 24 July 2006 (UTC)

Are you sure? Look here.--Pokipsy76 20:59, 24 July 2006 (UTC)

The PROD, which involves no voting and can be halted in an instant, was forced into AfD, which requires voting and admin participation. The official decision was no consensus. My unofficial summary of the comments: the article needs improving, and probably the proof should be merged into the parent article. It would be nice for one of the "keep" voters (Pokipsy76?, Ryan Reich?) to volunteer. --KSmrq^T 00:18, 1 August 2006 (UTC)

Done. I "morally" merged the article; the actual material in it was sort of long-winded. I also put in the stuff on transfinite induction and included a reference to Kolmogorov and Fomin. The original proof article remains, with a {{merging}} tempate added. Ryan Reich 02:23, 1 August 2006 (UTC)

Thanks, that's much better. --KSmrq^T 09:56, 6 August 2006 (UTC)

Good. I've changed the old article to a redirect now. Ryan Reich 15:25, 6 August 2006 (UTC)

Articles listed at Articles for deletion

The following articles have been listed at Articles for deletion but not caught by the 'bot:

• Wilkinson's polynomial (AfD discussion)

Uncle G 11:54, 25 July 2006 (UTC)

it is now. Septentrionalis 21:25, 26 July 2006 (UTC)

The decision on Wilkinson's polynomial was keep, after a number of editors worked on cleaning it up and clarifying its significance. --KSmrq^T 00:15, 31 July 2006 (UTC)

The following articles have been listed at Articles for deletion but not caught by the 'bot:

• Imaginary logarithm (AfD discussion)

Uncle G 17:24, 28 July 2006 (UTC)

The bot runs once a day; it may be preferable either to wait a day and see if it is picked up, or add this to the list by hand. Septentrionalis 22:49, 28 July 2006 (UTC)

The decision on imaginary logarithm was redirect to complex logarithm, agreed unanimously. --KSmrq^T 09:54, 6 August 2006 (UTC)

article variational number theory is back

User_talk:Karl-H has recreated the page. He's also made edits to calculus of variations and number theory among others. Somebody familiar with the subjects and the original RfD might want to take a look. Lunch 19:09, 26 July 2006 (UTC)

Integral equations has been edited too. Lunch 19:14, 26 July 2006 (UTC)

Reverted all of those. — Arthur Rubin | (talk) 21:18, 26 July 2006 (UTC)

Removing the redlinks in the list of mathematicians

Currently the list of mathematicians has a certain number of redlinks. I would argue that that was a good thing when Wikipedia was new and plenty of famous people did not have articles and when there was no bot to maintain that list.

I would think that now we would be better off having the list of mathematicians list articles which actually exist, with redlinks (requests for new articles) going to Wikipedia:Requested articles/Mathematics instead. Removing the redlinks from the list of mathematicians would also make it easier to see what mathematician articles got created/deleted by inspecting the Current activity.

In short, how about removing all the redlinks from the list of mathematicians? Oleg Alexandrov (talk) 20:32, 29 July 2006 (UTC)

I think that's a good idea. Can I also encourage people to add to the requested mathematician list? As a grad student, I'm hesitant to create articles for mathematicians that work at my school. I'd feel more comfortable if they were on the requested list. Thanks. Originalbigj 19:45, 30 July 2006 (UTC)

The bot now removes redlinks from the list of mathematicians (log). Oleg Alexandrov (talk) 23:53, 31 July 2006 (UTC)

It appears that you removed the redlink to Thomas Jech from the list of mathematicians, but did not add it to the list of requested articles on mathematicians. If a redlink is removed from one, I think that it should be added to the other (if not already there). And what if someone destroys the article or moves it to another name? JRSpriggs 03:10, 1 August 2006 (UTC)

Update. I just created a stub for Thomas Jech. I did not see the redlink removal in the log. But I remember creating a redlink for him a month or two back. JRSpriggs 03:27, 1 August 2006 (UTC)

I did not add the redlinks to Wikipedia:Requested articles/Mathematics on purpose, it is not clear if those redlinks are indeed "Wanted" articles.

If an article gets deleted (which only administrators can do) my bot will remove it from the list of mathematicians. If an article gets renamed, the bot will reflect the rename in the list. Oleg Alexandrov (talk) 04:55, 1 August 2006 (UTC)

Oyam's Pyramid

The article Oyam's Pyramid is currently proposed for deletion. It seems to me that it would be likely to be covered by some area of mathematics rather than being a complete hoax, but I've been unable to track down any evidence for its existence with this title. Could somebody take a look and see if a) it's a valid but wrongly-titled article, b)it needs merging or redirecting to some other concept, or c) it's complete garbage. Thanks Yomangani 10:46, 31 July 2006 (UTC)

Since there are no Google hits for any of this (except to Wikipedia), it is definitely made up. In my opinion it doesn't make much practical sense if you actually mean to build a pyramid. (Disclaimer: I have no actual experience in pyramid construction.) Mathematically it seems to be a pointless triviality. --Lambiam^Talk 23:00, 31 July 2006 (UTC)

Piotr Blass

I was wondering what people thought of the article Piotr Blass and the anon User: 69.163.189.9 who has created it and spent some time inserting the name of Piotr Blass into the articles of several distinguished mathematicians, e.g. Hassler Whitney and Heisuke Hironaka. I spy several dubious claims to fame in the Blass article, e.g. inventing the World Wibe Web. There's also a very interesting assertion that he's the student of a number of famous mathematicians (such as the ones I mentioned prior). Blass is apparently enough of a famous mathematician that the statement that Whitney taught "mathematics education" to Blass is an important thing to include into Whitney's article.

Blass' publication list looks fairly average and is bolstered by a number of publications to a journal that he founded and that I've never heard of. To be fair, I noticed that Zariski surface exists and was created by User:r.e.b.; it appears that Blass named Zariski surfaces and has some papers on them in respectable journals. So I wouldn't advocate a deletion of the Blass article. But it seems there's a lot of what might be called "tooting one's own horn" (if the anon is indeed Blass). --C S (Talk) 17:14, 31 July 2006 (UTC)

A quick google reveals Blass was given Grothendieck's prenotes for EGA 5. [38] So he certainly knew some influential people. There also seem to be proof of editorship of journal [39], standing in elections as a write in candidate (lots of links). Slashdot (that most relaible of sorces) mentions hims in conection with some dubious compression algorithm work with ZeoSync [40]. --Salix alba (talk) 19:35, 31 July 2006 (UTC)

And another quick look at Google Schoolar shows 24 publications mentioning his name, including some on Zariski surfaces. Google Print also gives few hits. On the other hand, the article needs copyedit and other claims ('one of the fathers of the Internet) seem more dubious.-- _{Piotr Konieczny aka Prokonsul Piotrus | talk}  02:53, 2 August 2006 (UTC)

I removed links to his name from several well known mathematicians. Math Genealogy lists two advisors: James Milne and Melvin Hochster. Others may have taught him some undergrad classes but anyway this is not notable. Using ip trace I found a clear evidence that he is trying to promote himself and is using WP for political purposes. I actually don't mind (and don't care) whatever is on the page on him but find inappropriate the insertion of his name averywhere. Inventor of WWW is simply laughable (he does give half the credit to Sir. Tim Berners-Lee). Mhym 14:36, 2 August 2006 (UTC)

15 of his 33 publications are in the Ulam Quarterly, which he founded. This journal was founded in 1987; before going defunct in 1997, it published a whopping 10 issues, each of which contains at least one (sometimes two) articles co-authored by Piotr Blass. This journal is, according the journal website, also the first electronic mathematics journal and is apparently the basis for Blass' claim of being inventor of the WWW.

It's not just the WWW claim that is dubious. A number of his achievements listed are suspect. Simply knowing and interacting with famous people is not an achievement. In fact, a number of people do this...that goes hand-in-hand with being famous (a lot of people know and talk to you). Organizing seminars at IAS is not an achievement. Being a member (even visiting), would be.

Blass' claim to fame is doing some of the early work on Zariski surface and naming it. I'm not sure if he's even as notable as Norman Johnson. But like I said, his bio should probably stay, but it needs to be heavily edited by people other than Blass. --C S (Talk) 16:51, 2 August 2006 (UTC)

I got the founding date of 1987 for the journal from the anon/Blass edit, but apparently the first issue came out in 1992 according to the journal website (see contents of first issue) and MathSciNet. I don't suppose this really matters or adds anything except to give a more accurate context for Blass' WWW claim. --C S (Talk) 17:29, 2 August 2006 (UTC)

There is some wonderful dirt on Blass [41]

[42] I don't quite understand it all but it seems to involve a company called CyberNet, 5 Star Trust Bank, kids in abusive treatment center, Diebold. Seems like Blass had evidence of defects in Diabold voting machines, being hacked by kind from Bay Point School correction facility (where he taught), but he withheld information due to ties with an atoney with connections to the republican party (the attony helped Blass get his son out of another correction facility).

So to add to inventing the WWW, we might add Blass was responsible for Bush getting into the whitehouse in 2000. --Salix alba (talk) 18:19, 2 August 2006 (UTC)

AfD it is Wikipedia:Articles for deletion/Piotr Blass. --Salix alba (talk) 19:11, 2 August 2006 (UTC)

Aug 2006

Prerequisites

I was reading an amusing interchange on the talk page for Lie groups just now. (Sorry, I don't know how to link to the specific section in the talk page. Maybe someone can help me with that.) Anyway, a user who clearly didn't understand the complexity of Lie group theory was trying to suggest that the page was worthless. This user suggested that the complexity of the article meant that the uninitiated could not follow it and the initiated didn't need it since they knew it already.

While I vehemently disagree with these sentiments, the discussion did lead me to think that maybe we need some system by which we can communicate prerequisites to those seeking information on a topic for the first time. No textbook would ever discuss Lie groups without either mentioning in the preface the need for a solid background in smooth manifolds, or else providing a reasonably comprehensive introduction to the subject in the book itself. I fully realize that Wikipedia is an encyclopedia and not a textbook. Nevertheless, a newcomer to Lie groups should know first thing that they ought to be comfortable with smooth manifolds (and probably some group theory too) before attempting to read (let alone criticize) an article on Lie groups. (I am thinking about this for all math topics, not just Lie groups, of course.)

What do y'all think? VectorPosse 05:58, 6 August 2006 (UTC)

The link you want is to Talk:Lie group#is this useful?. I am not familiar with templates, but perhaps we need a template for pointing to another article containing the prerequisites for reading the current article. JRSpriggs 06:44, 6 August 2006 (UTC)

I strongly disagree with putting any list of prerequisites on top of articles.

First, if a user never heard of differential geometry before, and complains that Lie group is hard to read, he/she has only himself/herself to blame. Reminds me of somebody who complained that logarithm is a useless article, because that person could not find a motivation for that article to exist.

Second, a well-written article should have a good introduction, and relevant links to other subjects should be embedded in context. That's encyclopedic.

All in all, while I strongly agree that articles should be accessible, boxes of prerequisites are not the solution. Oleg Alexandrov (talk) 07:07, 6 August 2006 (UTC)

An encyclopedia article is not a textbook, nor even a chapter of a textbook. Also, the web of knowledge admits no simple linear ordering. We get complaints about mathematics articles being opaque on a regular basis. The appropriate response depends on the state of the article, and on the topic.

People can arrive at an article in many ways. Perhaps they were searching the web for a word or phrase. Perhaps they were reading another article that thought this would be a useful link, either for background or enrichment. Maybe someone overheard the topic in a conversation and wanted to get a feel for what it's about. Or maybe someone has a text that is less than clear to them and thought Wikipedia could help. (We wish!)

Sound like a challenge? It is. A good mathematics article on a popular topic is especially hard. If that topic includes a modicum of technical difficulty, look out. If lots of people think they know something about it, the editing can get controversial.

Unfortunately, "Lie group" should be a major service article. It needs an introduction that a high school student can handle, but also needs to touch on material that can occupy months of graduate study.

We never want to say "if you haven't studied group theory and differentiable manifolds, go away". And what about matrices, since many of our examples occur as subgroups of GL(n,R)? No, prerequisites are unacceptable.

What might be more helpful is a "related topics" box. We would want to indicate something about the nature of the relationship, and we would need to avoid the temptation to link everything to everything. But I think it could be a major project to begin augmenting our articles in this way, and I'm not sure who would do it. Meanwhile, we do have a "Categories" area at the bottom of the page, which means it is often overlooked. --KSmrq^T 09:48, 6 August 2006 (UTC)

I initiated the discussion without any preconceived notion of what might be a "good" or "bad" way to approach the idea, but now that I've seen some of the discussion, I would tend to agree with Oleg Alexandrov. A well-written introduction can and should refer to the subjects that are required without causing any great disruption to the thousands of pages that already exist. (Having said that, many such pages probably do need better introductions. The more abstruse pages seem very far removed from their basic categories.)

I do not think that prerequisites suggest "go away". If presented correctly, they should come across as helpful. Those who are curious about an advanced topic will try to read the article anyway (and this is a good thing), but at least they are informed as to why the article is confusing to them and where they can go for more basic information. I think there are unintimidating ways of writing an introduction that communicate the essence of a topic, but at the same time point the reader toward articles which may be more appropriate for their level. I would guess that this is an ideal that we can all get behind. VectorPosse 21:30, 6 August 2006 (UTC)

This might be a good time to mention that we do have a Manual of Style specifically for mathematics, and that the first piece of advice offered is:

"Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds."

In my experience, the advice is accurate, but no substitute for experience! Anyway, perhaps that article will help. --KSmrq^T 23:27, 6 August 2006 (UTC)

Proposed merge: "Bicomplex number" into "Tessarine"

Hello. I recently came across the article bicomplex number, which appear isomorphic to tessarines. The latter appear the first use of this arithmetic, and all properties listed in "bicomplex number" are already contained in "tessarine". Another complication is that when Hamilton's quaternions were still new, some also referred to them as "bicomplex number" (but I have not seen this term used for quaternions in articles in the past 100 years). See also talk:bicomplex number.

As a suggestion, we could have bicomplex number redirect to tessarine, and add the isomorphism (with the one reference) there. The tessarine article itself needs some minor work, e.g. to list its algebraic properties first and then refer to isomorphic numbers (I acknowledge having contributed to this disorder while working on rewriting hypercomplex number; sorry for that, I simply haven't gotten to clean up "tessarine" yet).

Any comment, concern, or help is appreciated. Thanks, Jens Koeplinger 13:17, 8 August 2006 (UTC)

After finding at least four different uses of the term "bicomplex number" within just a few hours, we may be looking at (yet another) term that appears to have been used freely in mathematics, where each use was apparently clear within the context of the particular program where it was used. Similar to the use of "hypercomplex number". Well that's just great. I hope for the future that the internet, and in particular establishments like Wikipedia and full-text search, will give authors better tools to research existing terminology when scoping out naming for something they deem "new". Therefore, maybe we should rather make the "bicomplex number" article in a way that disambiguates all these uses. A simple disambiguation may not be enough, because one may want to write a few sentences for each section. Oh well. Thanks for any comment or additional information (see also talk:bicomplex number. Jens Koeplinger 17:18, 8 August 2006 (UTC)

Looks like the current version of the bicomplex number article stub refers to a special type of the multicomplex number program, and appears to be widely used. Therefore, I've added a new multicomplex number stub, with some barebone description, and updated some references and isomorphisms. So the bicomplex number article is really for keepers, but we must also provide reference to the other uses. One use (synonym to quaternions) is outdated and can be referenced as such, another use is actually from a compound term "variational bicomplex" and we can provide a link to this different area (which doesn't exist yet in Wikipedia). I'll follow-up on the one remaining use (appears to be initiated by Aristophanes Dimakis and Folkert Müller-Hoissen about 6 years ago), as name for an algebra program. - - - Thanks for your patience in reading my monologues here; though I'd always be glad for *any* kind of feedback. Thanks, Jens Koeplinger 01:42, 9 August 2006 (UTC)

I noticed that the article Hypernumber (redirected from Conic quaternion) states the following: "Conic quaternions are isomorphic to tessarines". I have to confess ignorance as to the proper terminology in this area, but this should be taken into account if true, or corrected if wrong. --Lambiam^Talk 01:53, 9 August 2006 (UTC)

Agreed, just updated, thanks for letting me know. For reference on the term "conic quaternion" see e.g. the preprint http://www.kevincarmody.com/math/sedenions1.pdf . Thanks, Jens Koeplinger

Hypernumbers crackpottery

From the immediately preceding discussion I stumbled upon the article on hypernumbers which is, at best, incomprehensible (to me being a mathematician) and probably plain crackpottery. Nowhere does the article state what hypernumbers actually are (presumably certain finite-dimensional algebras over the real numbers, but what properties are sought of them is left entirely unstated), nor is the linked site http://www.kevincarmody.com/math/hypernumbers.html any clearer. (On the other hand, it does contain such ridiculous statements as "New kinds of number [sic] will likewise give rise to new areas of science." or "This enables great advances in consciousness and matter." (page 15 of http://www.kevincarmody.com/math/hypernumberreference.pdf — which claims to be a reference but still does not explain what hypernumbers are).)

The only reference we are given are the papers of a certain Charles A. Musès, all published in Appl. Math. Comput., so I looked them up in MathSciNet and the reviews are eloquent enough (indeed, most reviewers flatly decline to comment, or seem to have found them hilariously funny); in fact, such sentences from the articles are quoted as: "How can any mathematician doubt where the source of new creativity in mathematics lies? […] We suggest that hypernumbers in our unrestricted sense are the key to a coming and deeper nuclear mathematics; that their explanation and delineation will mark as great a step as did the implications of nuclear structure in modern physics." (this is from "Hypernumbers II. Further concepts and computational applications", Appl. Math. Comput. 4 (1978), 45–66). Obviously C. Musès found the editors or referees of Appl. Math. Comput. sympathetic to his kind of crackpottery.

It would be nice to have the Wikipedia article deleted, but as it is nearly impossible to suppress an article, I guess we should just put up a banner of some kind. Ideally, the article would be reduced to a sentence such as: "Hypernumbers are a 16-dimensional non-associative algebra over the real numbers (or certain subalgebras thereof) which was studied by Charles A. Musès who believed in their application to physics, biology and engineering." Perhaps with a description of the generators and relations of the algebra, if anybody can make sense out of them.

(I don't have time to fight this battle or to argue with crackpots, so I'm just writing to make sure other participants are aware of this.) --Gro-Tsen 11:25, 9 August 2006 (UTC)

Your last sentence is remarkable. I thought I had filtered the properties of certain hypernumber types from all of the rest Musès wrote. The filter I applied was that at least two people had published about it (C. Musès and K. Carmody), and that I could understand and confirm it from defining relations. I find Mr. Carmody's works on hypernumber arithmetic clear, sound, and well written. I find the focus on multiplicative modulus of a number interesting, do believe they qualify as their own number system, and do not believe that deletion of the article is an improvement. How do we deal with a situation where the person who discovered something gives ridiculous and even derogatory statements, throws out statements and "proofs" that don't work? I do not find Musès' articles funny, I am actually frequently offended by them. To my knowledge, though, it was him who found the real powers and logarithm of $\varepsilon$ (the non-real root of +1 that is also part of split-complex algebra), and it was K. Carmody who found sedenions with a multiplicative modulus. As far as I can see, what's currently on the Wikipedia page "works" ... What do we do? Thanks, Jens Koeplinger 15:25, 9 August 2006 (UTC)

I think for a start, we should define hypernumbers. I don't understand after reading the article what they are, and I followed the link to Carmody's page, and I can't tell from what he has there what they are either. Everything that is written seems to assume that the reader is familiar with the definition. Take the subsection Hypernumber#Epsilon numbers, from which no one could deduce what an epsilon number is, what epsilon itself is, and what it means for them to be the third level in the program. Not to mention that the seemingly fundamedntal idea of "power orbit" is referenced everywhere but never described (I suppose it means "all powers of a number", but the terminology is new to me, and confusing). I have to say that everything in the article strikes me as typical of what crackpot ideas I've seen: a confusing and grandiose compilation of claimed results without clear definitions, consistent notation, or verifiable statements. Of course, that's the way the articles on Carmody's page are written too, so it's not necessarily your fault...but if there doesn't exist a coherent account of this stuff I would say it's the work of a crackpot. However, if it's been published it may be "notable", so at the very least it would then be our duty to figure out what "it" is in the first place. Ryan Reich 20:46, 9 August 2006 (UTC)

Sounds great to me. I recognize that the article is not well structured and lacks clarity, and it would be wonderful if it could be improved. What about adding an "algebra stub" notice on the article, to highlight that the article cannot remain in its current form? Thank you very much for pointing out several weaknesses. While we may have trouble finding a definition of hypernumbers in general (Musès did not provide one ...), we can put the numbers that are currently stated on the page on defining relations. We could say "Musès conceived hypernumbers as [...thisandthat...] Select examples are [...]" and so on. As for the definitions that are missing, epsilon is a non-real base number with $\varepsilon {}^{2}=1$ and is identical to j from split-complex algebra. The "power orbit" of a number b is $b^{\alpha }$ with $\alpha$ real. Maybe it would make sense to have two sections in the article, the first section focusing on the hypernumber types containing reals, imaginaries, and $\varepsilon$ bases, and then a section that gives a briefer overview over the three other types currently listed. Well, let me put the stub notice out there for now, hopefully we'll get more responses (possibly on talk:hypernumber?). Thanks a lot, Jens Koeplinger 01:18, 10 August 2006 (UTC)

Already the article on split-complex numbers seems of dubious interest to me: most unfortunately it does not mention the (obvious) fact that, by the Chinese remainder theorem, "split-complex numbers" / "epsilon numbers" can be identified with pairs of real numbers with termwise addition and multiplication (I mean, not only are they a two-dimensional algebra over the reals, but actually they are the direct product of two copies of the real numbers), which makes them sort of boring (why bother about the product of two copies of the reals, not arbitrary tuples?); the identification takes the pair $(a,b)$ to ${\frac {a+b}{2}}+{\frac {a-b}{2}}\varepsilon$ (the number $\varepsilon$ is called $j$ in the article on split-complex numbers; and it's a trivial exercise to see that this is indeed an isomorphism). (Also, incidentally, the article is wrong in stating that split-complex numbers have nilpotents: they don't, they have divisors of zero but no nilpotents.) I'm stating all this to refute the idea that the number $\varepsilon$ is an interesting object. As to it's "power orbit", i.e., a one-parameter subgroup, once we have identified split-complex numbers with pairs of real numbers as I explained, and the number $\varepsilon$ with the pair $(1,-1)$, it is clear that one-parameter subgroups all lie in one connected component (both coordinates positive) of the multiplicative group of invertible split-complex numbers, and $\varepsilon$ is not there, so it does not have a "power orbit" (no more than -1 has in the real numbers). Similarly, trying to add both $i$ with $i^{2}=-1$ and $\varepsilon$ with $\varepsilon ^{2}=1$ just gives you pairs of complex numbers, again not very interesting. This is all basic algebra and applications of the Chinese remainder theorem. --Gro-Tsen 10:15, 10 August 2006 (UTC)

I can only agree that many articles need improvement (but I am glad that you did respond). If you repost your last message in talk:split-complex number I'd be glad to respond (it's getting very specific now). Or, to save you time, I'd also be glad to cite your last post there ... This will be funny, I'm looking forward for the reactions.

As for the hypernumbers page, I do thank anyone for the attention, and I'm glad to "let go" and answer question on the talk page, from what I can answer. I'm a physicist, with interest on physics on numbers that are not typically used, and I noticed gaps, missing information, and missing links (isomorphisms) in Wikipedia. So I've added some as good as I can, though I'm not native to the field (mathematics). Any review or improvement is, as always, welcome. Thanks again, Jens Koeplinger 12:08, 10 August 2006 (UTC)

Feel free to repost my comment elsewhere if you think it wise. Personally I won't follow the "split-complex numbers" page because I don't think it's interesting in any way (but it's not really crackpot stuff either: it's just entirely boring) and I don't have time to improve it. I just find it laughable if it turns out that nobody noticed that these "split-complex numbers" are just isomorphic to pairs of real numbers (something which should be obvious from the start to anyone with a minimal background in algebra, e.g., having read Lang's book). Btw, "tessarines" / "bicomplex numbers" are similarly isomorphic to pairs of complex numbers. Any (commutative and associative) étale algebra over the real numbers is a product of copies of the real numbers and the complex numbers, anyway. --Gro-Tsen 12:38, 10 August 2006 (UTC)

I looked at this Kevin Carmody's website, the main reference of the hypernumbers page, and I'd like to point out that he's an unmitigated crackpot. Even if this topic were at all standard, we probably shouldn't be using his website as a reference. I will say that it can be very difficult to tell crackpot math from real math, especially if the crackpot in question studied mathematics in earnest before losing their grip, and especially they attract followers. I think this is the situation we have going here. It just has that certain feel - think of John Nash in "A Beautiful Mind" with the newspaper and magazine clippings. Originalbigj 16:55, 10 August 2006 (UTC)

Please see talk:hypernumber for the list of sources from which I directly drew from, and the reasoning behind it. Thanks, Jens Koeplinger 18:03, 10 August 2006 (UTC)

I would like to point out that "epsilon number" already has an established meaning. An epsilon number is an ordinal $\epsilon _{\alpha }\!$ such that $\epsilon _{\alpha }=\omega ^{\epsilon _{\alpha }}\!$. JRSpriggs 02:58, 11 August 2006 (UTC)

This is one of several meanings of ε, ranging from conic sections to calculus. If Carmody and Musès have come up with another one, so be it. Nor are they entirely original; the use of ε for a non-trivial unit is fairly common in the study of rings - outshone, I think, only by ω. Septentrionalis 13:57, 11 August 2006 (UTC)

Adminship requested

I have requested adminship, largely to deal with the backlogs of move and discussion pages. Since Oleg endorses, I think I can mention it here. See Wikipedia:Requests_for_adminship/Pmanderson. Septentrionalis 20:50, 12 August 2006 (UTC)

Am I the main math admin lobby or what? :) Good luck! Oleg Alexandrov (talk) 20:55, 12 August 2006 (UTC)

Ovoids in polar spaces

Hello,

as you can see I am on the list of participants of the Math Project. I'm still not experienced in creating my own articles.

Any quick look at Ovoid (polar space) would be appreciated, also because of the fact that English is not my native language (I do my best though).

And one fundamental question : what to do with these ovoids, they are often only treated in the case of finite polar spaces, while in fact there isn't exactly anything wrong with the definition for infinite polar spaces.

Thanks a lot,

Evilbu 22:32, 12 August 2006 (UTC)

What's lacking most are the references. --Lambiam^Talk 02:24, 13 August 2006 (UTC)

You could probably say the same about polar space though at least there's a wiki-link to Tits there. Lunch 02:45, 13 August 2006 (UTC)

Okay, I get the message. There should be references. I am willing to accept any suggestion. The problem is that incidence geometry is not well represented on the net, most of the sources would be (online) courses from my own university. It would help me a great deal if I could know which users are into geometry as well. Evilbu 12:24, 13 August 2006 (UTC)

Use Google scholar as a starting point, and the library resources of your university to find good references, usually either a textbook, or the original articles introducing the concepts. Another acceptable source is the Encyclopaedia of Mathematics. Make sure the article agrees with the reference. --Lambiam^Talk 18:25, 13 August 2006 (UTC)

Our university does have a library... But on a side note : the first professor's article on that Google scholar link, is my own professor, who taught me the definition of polar space... Evilbu 19:05, 13 August 2006 (UTC)

Verifying a reference

An anonymous contributor has edited A. Cohn's irreducibility criterion to claim that the criterion has been proved to hold for the case n=2, whereas the relevant PlanetMath page says that this is a conjecture. The contributor provided the following link to a dvi file as a reference. I cannot read the dvi file, but I think it contains an article by number theorist Ram Murty published in Amer. Math. Monthly, Vol. 109 (2002), no. 5, 452-458. Perhaps someone with a dvi reader, or with access to the journal itself, can verify that this paper does indeed provide a proof for the case n=2 ? Gandalf61 10:25, 14 August 2006 (UTC)

It gives a new proof for the n>2 case, then a long discussion and another lemma claimed to give the n=2 case as well. JPD (talk) 11:20, 14 August 2006 (UTC)

JPD - thank you for the prompt response. Gandalf61 15:54, 14 August 2006 (UTC)

Well, it seems the Planet Math page is very outdated, giving as the only reference Polya and Szego vol 2, which is actually a very old book: the 1998 version is just a reprint of the 1976 English edition which was translated and revised by someone other than the original authors. Furthermore the 1976 German edition (according to Math Reviews reviewer) differs very little from the original 1925 edition. In any case, the Murty paper mentioned above gives as the first reference a 1981 paper which proves Cohn's theorem for any base (Brillhart, John; Filaseta, Michael; Odlyzko, Andrew On an irreducibility theorem of A. Cohn. Canad. J. Math. 33 (1981), no. 5, 1055--1059.) The review for it on MathSciNet notes that the original Cohn theorem was mentioned in Polya and Szego. So it seems this conjecture has been known to be closed for quite a while. --C S (Talk) 02:07, 15 August 2006 (UTC)

I updated the article A. Cohn's irreducibility criterion to reflect Brillhart et al's priority for the n=2 case. In a future edit I hope to change the letters used for certain subscripts to agree with the Ram Murty paper, because using 'n' it is easy to confuse the base used with the degree of the polynomial. The other improvement that might be suggested is to change the title to 'Cohn's Irreducibility Criterion', because Wikipedia's search function is too feeble to return this article in the first screen when you type in 'A. Cohn'. EdJohnston 22:04, 18 August 2006 (UTC)

Antiderivative

I wonder if there are any comments on this edit (please write them at talk:derivative). Thanks. Oleg Alexandrov (talk) 16:16, 14 August 2006 (UTC)

Did you mean to say write comments at Talk:Antiderivative? I don't see much need for discussion; the matter was already considered and decided long ago, at the top of the talk page. Are you suggesting it should be reconsidered? (Follow-ups to talk.) --KSmrq^T 03:37, 15 August 2006 (UTC)

Mathematics needed

Please help with adding the various mathematical analyses of the game Fetch (game) to the article. (See the references and further reading given in the article.) Uncle G 10:56, 15 August 2006 (UTC)

The process by which a dog tries to catch a ball may be similar to the way that a fielder in baseball tries to catch a ball which has been hit in his general direction. I know that that has been analyzed mathematically, but I do not remember the details. JRSpriggs 05:10, 16 August 2006 (UTC)

Abel Prize more prestigious than Wolf Prize in Mathematics?

That is what one anon has insisted, but I believe this is unsubstantiated and actually OR. See Talk:Wolf_Prize for my lengthy comment with diffs. Perhaps a personal remark here is in order. When the anon replaced the mention of the Wolf in the intro to Serre's article (saying Wolf is not more prestigious than Abel), I was willing to let it go as I thought at least that the Abel would be more familiar to the lay reader (due to the extensive media coverage); however, a later edit revealed that this person regards the Abel as more prestigious than the Wolf and that would be appear the basis for the first edit. I would appreciate if people could take a look, particularly mathematicians who have been been in the mathematical community for a longer time than me who can gauge this issue with their more extensive experience. I think this is kind of an interesting math cultural issue. --C S (Talk) 11:33, 15 August 2006 (UTC)

I take the Wolf Prize to be, de facto, the top lifetime achievement award. That being said, we can't possibly talk about prestige in the abstract (would have to be via quotes). I suggest just removing all loose talk. Charles Matthews 12:19, 15 August 2006 (UTC)

Ditto. Prestige is in the eye of the beholder. Speaking of which, please report all rumors on the talk page of Grigori Perelman! ---CH 07:17, 16 August 2006 (UTC)

That's also how I would rank them, but looking at the winners they seem to be the best of the best for both, so now I wonder, what would actually make one more prestigious than the other? For the Fields Medal, could it play a role that it is only awarded once every four years? And of course you can't be an old geezer, so it does not honour a lifetime of servitude service to mathematics, but specific memorable achievements.

Problem editor

All mathematics editors should be alert to the ongoing behavior of Bo Jacoby (talk). In article after article Bo has tried to use invented (original research) notation. Then Bo lures others into endless discussions on the talk pages, where a host of editors again and again waste their time saying the same thing: "Don't do it." Examples include

• Talk:Function (mathematics)
• Talk:Root of unity
• Talk:Discrete Fourier transform
• Talk:Exponentiation
• Wikipedia:Articles for deletion/Ordinal fraction

A related wrong-headed persistence has been seen at Talk:Wilkinson's polynomial. I do not know the cause nor the intent of this behavior, but we need to find some effective way to deal with it. Patient responses on article talk pages have not been effective. Please be vigilant to catch more abuses, and please do not let Bo turn article talk pages into his own chat room. --KSmrq^T 14:23, 16 August 2006 (UTC)

I would add to that talk:polynomial and talk:formal power series. I believe we are dealing with a person without formal math education, and it takes a long time (and many editors sometimes) to convince him that he is wrong. Oleg Alexandrov (talk) 16:25, 16 August 2006 (UTC)

Aha, I would also add Talk:Lebesgue integration. That explains a lot.--CSTAR 16:53, 16 August 2006 (UTC)

And Talk:Binomial transform. Bo's behaviour, while annoying and disruptive, is minor in comparison to some of the mono-maniacal and outrageous behaviour I've seen recently seen (e.g. my talk page, ughhh). linas 03:49, 17 August 2006 (UTC)

Wikipedia:Lamest where it applies. Charles Matthews 21:12, 17 August 2006 (UTC)

Could someone check out inferential statistics? This is an article that seems to have been largely written by Bo. Statistics is not my field, but some of the technical terms defined in the article, like "deduction distribution function" and "induction distribution function", don't seem to appear anywhere else on the web (at least, not with the same meaning). A closer look by a statistician might be warranted. Another article largely written by him, in which he cites his own publications, is Durand-Kerner method. Again, I have not checked this and make no claim as to whether it is good or bad, but it might be worth a closer look given Bo's past behavior. —Steven G. Johnson 15:45, 21 August 2006 (UTC)

Durand-Kerner is ok, he earlier claimed to be the inventor of the method, since he did not find related information, but changed or allowed to change to the more usual name. The method is, as it seems, not widely known, but (personal communication by prof. Yakoubsohn at Toulose) common knowledge in the root finding community.--LutzL 17:04, 21 August 2006 (UTC)

There's still the vanity link/redirect at Jacoby's method. Lunch 20:38, 23 August 2006 (UTC)

Also, in the article to which this redirect points, Durand-Kerner method, there are two references to Bo Jacoby added by Bo Jacoby. Being relatively new to all of this, I'm not sure if this counts as WP:NOR or not. VectorPosse 22:44, 23 August 2006 (UTC)

See also Talk:Fourier transform. —Steven G. Johnson 16:29, 21 August 2006 (UTC)

Meaning of QED

Should QED be:

1. a page about the phrase quod erat demonstrandum, with a dablink to QED (disambiguation),
2. a page about quantum electrodynamics, with a dablink to QED (disambiguation), or
3. a disambiguation page, with links to both the above and to lesser uses.

My opinion is clearly (3), but come share yours at talk:QED (disambiguation). --Trovatore 20:40, 17 August 2006 (UTC)

You have shown via your question that the term is ambiguous; therefore, it should be a disambiguation page. QED Ryan Reich 20:50, 17 August 2006 (UTC)

The discussion is taking place at talk:QED (disambiguation), not here; this is just a notice. --Trovatore 20:52, 17 August 2006 (UTC)

At least admit that it was good for a chuckle. Ryan Reich 20:57, 17 August 2006 (UTC)

You could have that on your tombstone. Charles Matthews 21:14, 17 August 2006 (UTC)

I'll take mushroom, black olive, and anchovies. --Trovatore 22:53, 17 August 2006 (UTC)

I've had pizza that chewed like marble myself...Septentrionalis 01:53, 19 August 2006 (UTC)

Oppose anchovies. --C S (Talk) 04:56, 19 August 2006 (UTC)

• Per the ethics of terminology, QED as quod erat demonstrandum has priority by several thousand years over all the New QEDs On The Block. Jon Awbrey 05:26, 19 August 2006 (UTC)
  • Well, my feeling is that, if we were to take the intrinsic importance of the subject into account, it would have to swing massively the other direction: quantum electrodynamics is one of the most fundamental attempts to describe nature yet devised by the mind of man, whereas quod erat demonstrandum is just a phrase, a piece of historio-linguistic trivia. (Obviously this is quite distinct from any consideration of the importance of the idea of proof, or even of individual proofs at the end of which Q.E.D. has appeared; those are separate discussions altogether, and the Q.E.D. article isn't about them.) Perhaps more to the point, just from a practical point of view, it's an observed fact that lots of people link to QED from physics articles, which has bad consequences if it's a redirect to the Latin phrase.
  • Still, if you want to "vote", this isn't the place to do it; I've given a pointer above to the actual debate. --Trovatore 05:46, 19 August 2006 (UTC)
    • Trovatore, Quantum Electrodynamics is a temporary theory. It is a set of rules, and the theory is not entirely well-defined mathematically. On the other hand proofs are very important, not only in mathematics, but also in theoretical physics.Hillgentleman 03:22, 7 September 2006 (UTC)
      • Luckily, there was no need to judge the relative importance of quantum electrodynamics and proof. Proof is an extremely important topic; quod erat demonstrandum is not. --Trovatore 03:32, 7 September 2006 (UTC)

JA: The just notable difference tends to be relative and shifty from year to year. That's why we have rules like prior use. Of course, this is WP, and the rule is to find the "most illiterate use" and go with that, so why am I not already sleeping, he asks himself. Jon Awbrey 05:52, 19 August 2006 (UTC)

ICM Madrid

Starts 22 August, I believe. It would be good if we geared up for the Fields Medal awards. By which I mean: get ready with a story to offer the Main Page here; have articles ready on Terence Tao and Grigori Perelman who are the hot tips; be prepared to do something quick and dirty for anyone else on the list. Compared to 2002, the world's press are likely to turn to enWP for enlightenment, as soon as the news hits the wires. Charles Matthews 21:18, 17 August 2006 (UTC)

Uh, so who else is on the list? --C S (Talk) 05:51, 19 August 2006 (UTC)

So, as part of that, anyone ready with good pictures for Kakeya problem page? Charles Matthews 21:21, 17 August 2006 (UTC)

Update: plenty of excitement as Perelman was a no-show; need work on Andrei Okounkov (I've just mailed Princeton to see if they have a photo), Wendelin Werner. Matter arising from the latter: self-avoiding random walk is surely worth an article. Charles Matthews 12:15, 22 August 2006 (UTC)

A Google Image search turns up photos for everyone, rights status unknown. --KSmrq^T 12:34, 22 August 2006 (UTC)

Perhaps self-avoiding random walk could start as a section of Random walk before being spun off on its own. Michael Kinyon 15:48, 22 August 2006 (UTC)

There is a raw definition somewhere there, true. Quick-and-dirty is to redirect and forget ... given a Fields has been awarded, there might be rather more to it. Also, an article on Charles Loewner would be good (there is a MacTutor article); I just had time to start some of Werner's lecture notes which do hark back to Loewner's work of the 1920s. Charles Matthews 16:10, 22 August 2006 (UTC)

Wikiversity Mathematics School open

I cordially invite the partisipants of this project to the newly founded wikiversity school of Mathematics. We are still working out the policies, but any help is appreciated. --Rayc 23:55, 17 August 2006 (UTC)

Eigenvalue, eigenvector and eigenspace

Eigenvalue, eigenvector and eigenspace is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 22:04, 18 August 2006 (UTC)

A novice editor has created an article for the Jacobi eigenvalue algorithm; a few fixes there could be a big help as well. --KSmrq^T 12:14, 19 August 2006 (UTC)

It seems like there is a need for some people to do some copyedditing on the article. These been a lot of suggestions on fixes to the article needed to get it to FA status but no one is acting on them. Volunteers welcome! --Salix alba (talk) 07:28, 14 September 2006 (UTC)

Talk:Pi#Move Pi to π, the official discussion!

This move idea has come up again. Please discuss. (I made the point that software limitations mean that the actual move, if this passes, will be to Π.) Septentrionalis 01:59, 19 August 2006 (UTC)

Kerala school?

I copied this message from Portal talk:Mathematics. -- Jitse Niesen (talk) 14:34, 19 August 2006 (UTC)

What do you guys think about the Kerala School article and the possible transmission of mathematics from Kerala to Europe? Should the theory get a mention on our articles about calculus, newton, wallis etc? Frankly, I'm a bit alarmed about the points brought up here. Borisblue 07:51, 19 August 2006 (UTC)

I came here to post a message on Madhava, and saw this... Actually, I remember reading somewhere that several conferences have been convened worldwide to discuss the possible transmission. But none of them, AFAIK, have been able to come to a conclusion. However, the theory has never been discounted, because the people who back it, have a very strong point. IMO, (and this is not because I'm from Kerala), this should be mentioned as a theory that is prevalent. All my attempts at introducing it in some articles failed, (primarily because I happen to be from Kerala). It certainly would be nice if someone would be willing to take initiative in this regard (after a discussion, of course).-- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:44, 23 August 2006 (UTC)

An RFC will be nice. However, I have a lot of difficulty finding academic papers that discuss and critique this issue (can't find any record of conferences either?), I think because this theory is so new. Hence, it will be difficult to satisfy verifiability in a lot of the claims, at least untill a few more historians come up with some peer-reviewed papers. Science and math issues require very reputable sources. Borisblue 04:51, 24 August 2006 (UTC)

Unicode article names

User:CyberSkull moved T1 space to T₁ space, that's on the heels of a move of Mu operator to Μ operator. I believe that these are cheap Unicode tricks and not a solution to the fact that Wikipedia can't represent faithfully some mathematical notation.

T1 space should ideally be "T₁ space". Since that's impossible, I think T1 space is a better name than the T₁ space gimmick. Comments? Oleg Alexandrov (talk) 21:18, 19 August 2006 (UTC)

Unless Unicode tricks can solve all our problems along these lines, I would agree that we would be better sticking with things like T1 space. I think it would be better to be consistent and avoid gimmicks - and hope that some future version of the software will give a more sensible solution. Madmath789 21:32, 19 August 2006 (UTC)

My thanks to Oleg for fixing Mu operator and Mu-recursive function which had been moved inappropriately by User:CyberSkull. I agree that titles of articles and categories should not contain characters other than printable ascii characters. It is hard enough dealing with unusual characters in the text of an article. Having such characters in a title is much worse. One might look in the wrong place in the category listing (as I did for the two I mentioned above). Or one might fail to find them with a search or even be able to enter the correct title into the search box. Or the title might not display correctly depending on one's fonts. JRSpriggs 08:48, 20 August 2006 (UTC)

Fields template

If Grigori Perelman has declined his Fields Medal, how should Template:Fields medalists read? Charles Matthews 15:42, 22 August 2006 (UTC)

How about "Perelman (declined)"? Yes, I realize that if he has declined, then technically he is not a medalist, but there should be some indication that the award was offered to him. Michael Kinyon 15:46, 22 August 2006 (UTC)

According to the New York Times, Sir John M. Ball, president of the International Mathematical Union, said, "He has a say whether he accepts it, but we have awarded it." So maybe Perelman is technically a medalist. Having said that, I believe that Michael's suggestion is adequate. VectorPosse 20:50, 22 August 2006 (UTC)

Now of some urgency, since Template:In the news has the Fields as leading item. Charles Matthews 16:16, 22 August 2006 (UTC)

Since the fact the Perelman declined will be discovered at his article, perhaps it's enough to do nothing special. Or at least postpone a more clever solution. The exact details still seem mysterious, so letting the article explain seems wise. If "(declined)" is included, be sure to use &nbsp; between it and his name to prevent an awkward break in the future. (Actually, the current breaks are none too appealing.) --KSmrq^T 18:38, 22 August 2006 (UTC)

It seems that he has indeed specifically declined to accept the Fields Medal. I agree with "Perelman (declined)" in the template. ---CH 23:39, 22 August 2006 (UTC)

There's a New Yorker article on Perelman that got slashdotted: rather interesting read, gives insight into why the prize was declined. http://www.newyorker.com/fact/content/articles/060828fa_fact2

BTW: Manifold Destiny (article) --Pjacobi 20:20, 28 August 2006 (UTC)

Grigori Perelman

I've extensively rewritten this twice in the past week to incorporate latest news and clean up "edit creep" (well intentioned edits by inexperience writers--- or thoughtless ones--- which disrupt the flow of ideas, exhibit poor diction, and generally tend to eventually render an article unreadable.) There has been some apparent trolling by editors who want to discuss the Israeli-Palestine conflict, so watch out. Sheesh! ---CH 23:38, 22 August 2006 (UTC)

Madhava of Sangamagrama

Hello! This article is about Madhava, a mathematician who lived during the middle ages. Despite being one of the greatest mathematicians (he is, in fact considered as the founder of mathematical analysis), most of his work has been discredited. The talk page of the article has a large number of unanswered questions. It would be nice if someone well versed in mathematics take a look at them. I am not submitting the article for collaboration, because it fails the nomination criteria. However, it would be wonderful if people would come forward to cleanup all the confusion and chaos on this article. Thanks! -- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:34, 23 August 2006 (UTC)

Articles listed at Articles for deletion

• Simplex algorithm method (AfD discussion)

The 'bot hasn't picked this one up, it appears. Uncle G 11:43, 24 August 2006 (UTC)

Request from Non-math Person

I feel certain that this comes up a lot, but as a relatively well-educated and well-read individual who has only a general interest in mathematics, I am consistently stumped by even the simplest of mathematics entries on wikipedia. Granted, some math issues, conjectures, and theories are plain ol' difficult, but it seems like Mathematics entries on wikipedia are by far the least accessible entries (for the average reader who comes to an encyclopedia for general information). The Clay Institute's descriptions of the Millennium Prize problems [43], for example, do a much better job of describing and analogizing the problems for us lay-folk. With so much to work on, this may not be a valid top priority for the Project, but as an outsider I would greatly appreciate if it became a focus. Thanks! aww 18:34, 25 August 2006 (UTC)

Well, it's a known issue. For us here, I suppose, the point of view might be that the mathematics is only about 1% of enWP; but its place in sustaining the reputation and credibility of the project is much greater than that would suggest. We have certainly emphasised getting 'professional' mathematics here. An analogy would be with medicine: no one would want the clinical medicine articles to be accessible only to doctors, but on the other hand if a doctor can say "that's just wrong", that is also not good.

Let's look at the Clay description of one of the problems in detail.

Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like

x² + y² = z²

Not true. In the eighteenth century this kind of number theory, namely Diophantine equations, was consider a backwater. That attitude prevailed for a long time.

Euclid gave the complete solution for that equation, but for more complicated equations this becomes extremely difficult.

See Pythagorean triples.

Indeed, in 1970 Yu. V. Matiyasevich showed that Hilbert's tenth problem is unsolvable, i.e., there is no general method for determining when such equations have a solution in whole numbers.

True.

But in special cases one can hope to say something. When the solutions are the points of an abelian variety, the Birch and Swinnerton-Dyer conjecture asserts that the size of the group of rational points is related to the behavior of an associated zeta function ζ(s) near the point s=1.

Actually, writing 'abelian variety' rather than elliptic curve is reprehensible here: far too general. If I tried to write down the equations defining an abelian variety, you wouldn't thank me. It would be much better to say cubic curve, in fact. This slurs over the fact that if such a curve has a singular point, we don't call it an 'elliptic curve'; but that case is already done by the Euclid method, anyway.

In particular this amazing conjecture asserts that if ζ(1) is equal to 0, then there are an infinite number of rational points (solutions), and conversely, if ζ(1) is not equal to 0, then there is only a finite number of such points.

We don't use words like 'amazing', naturally. This is OK, and could usefully go in an article here. (Then for experts we have to remark something on the analytic continuation question, supporting the idea that the zeta function is even defined at the actual point.)

Right then, this was an exercise. I would criticise the exposition for not using the proper term (Diophantine equations). Anyone browsing our Category:Diophantine equations should at least be able to pick up what the subject is about.

Charles Matthews 19:09, 25 August 2006 (UTC)

So this Clay write-up was perhaps good in explaining things to the interested layperson, and lousy for professional mathematicians. We have many articles that are lousy in explaining things to the interested layperson, and perhaps good for professionals. We also have some articles that are lousy for both. Why be so defensive about it? Can't we just admit that we'd like to have more articles that do a good job for both? Unfortunately, we don't have that many editors who combine the required background with the necessary writing skills and also have unlimited time to devote to the project. --Lambiam^Talk 01:34, 26 August 2006 (UTC)

I thought the middle way was found a long time ago. Articles should have a good and easy to read introduction. Moving down an article, things will become more complex, and for good reason.

I don't think Charles was trying to be defensive (he's rather good at writing expositionary articles, without formulas pile-ons :) We have some good articles, and some bad articles. And math articles could be harder to read than say biology articles because we use much more symbolism and abstract concepts, and that for good reason. Oleg Alexandrov (talk) 05:45, 26 August 2006 (UTC)

Well, I was certainly enjoying myself looking at other expositions for change, rather than patching up our own. And I hope I made a point about what the mathematics articles here are good for, at least: we do have a very thorough coverage (23 Hilbert problems you can look up here, not just one). There are plenty of popular mathematical books around that will give you a 'feel' for Fermat's Last Theorem, Riemann Hypothesis, Monster group. What you can find here is one step up from that: the level was defined as undergraduate student, back a couple of years ago. Anyway, let's do it again, for the Hodge conjecture (defined as On a complex algebraic variety, every homology class that could reasonably contain a subvariety does contain a subvariety here). The Clay gves us this:

In the twentieth century mathematicians discovered powerful ways to investigate the shapes of complicated objects. The basic idea is to ask to what extent we can approximate the shape of a given object by gluing together simple geometric building blocks of increasing dimension. This technique turned out to be so useful that it got generalized in many different ways, eventually leading to powerful tools that enabled mathematicians to make great progress in cataloging the variety of objects they encountered in their investigations. Unfortunately, the geometric origins of the procedure became obscured in this generalization. In some sense it was necessary to add pieces that did not have any geometric interpretation. The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.

So they try not even to mention the words manifold and topology. Pieces that did not have any geometric interpretation. Yes and no: de Rham cohomology is fairly geometric. The statement leaves out the technical points that the varieties are over the complex numbers (OK, that's the default), and are non-singular (which one can't really get away with).

Someone writing in the style of the first three sentences here would get them edited to more precision of statement pretty fast. The idea buried in the fourth unfortunately we do not cover well (homology classes represented by actual subspaces - I think there are results by major topologists not here). Saying 'nice' is a lapse into the way mathematicians communicate to each other.

We are really stuck with a world where on Monday we may be having to try to write up what Andrei Okounkov did to deserve a Fields Medal (breaking news) and the next day supposedly trying to find new paraphrases for things like algebraic variety or manifold. I'd like to point out that we also get criticism from the other direction (see for example Talk:Abelian variety for an extreme example).

Charles Matthews 10:02, 26 August 2006 (UTC)

I can certainly see how that would be. It's the problems of wikipedia combined with a less accessible sets of subjects. I have to say, it dawned on my from your examples that the best way to explain a complex problem to a lay person is with analogy and abstraction, which in certain mathematics articles could just as easily translate into "inaccurate" or "wrong." Nonetheless, I would encourage pushing some of the intros even farther, even if they include such vague statements as "while not exactly (thing), it is similar to (thing)." Then again, I'm a lawyer, and this is how we talk about everything, so there you go. Thanks for the good work, and I'll keep reading and trying to learn. aww 13:40, 26 August 2006 (UTC)

To do a good job on a sophisticated mathematics article, an editor must have detailed technical knowledge, the ability to know what's essential versus peripheral, great empathy for the untrained reader (to see through their eyes), a solid command of the English language, exceptional skill in writing, and world-class patience and diplomatic skills.

A one-paragraph introduction may be the shortest part of the article, but is almost always the most difficult to write. The Millennium Prize Problems are singled out because they are connected to a great deal of interesting mathematics, and because they are very difficult to solve. How do you take a problem that the best mathematicians in the world do not yet understand adequately and present it in a few short, accurate, engaging sentences to the general public?

You may be surprised at the extraordinary stuggle behind a basic mathematics article, such as manifold.

Ironically, mathematics today is so broad and so deep that a specialist in one branch may know almost nothing about an advanced topic in another specialty. Therefore we appreciate a good introduction just for ourselves!

Finally, while some in the world are hungry to learn more mathematics and science, others are actively hostile, or indifferent. One consequence is that we continue to struggle to convince the WikiMedia developers to better support our notational needs. Another is that we see lazy outside editors take a quick glance at an article and slap a fixit tag on it, without even doing us the courtesy of leaving a note on the talk page to describe what they see as the problem. Or we see editors reword things they do not understand, which someone must then notice and fix.

And yet, we persist. We mathematicians have a love of beauty and pattern, which draws us in and sometimes leads us to want to share the joy. And to solve difficult problems, we have learned to persist in the face of constant frustration and defeat. Perhaps if it was easier to write a good Wikipedia article, we'd be less interested! ;-) --KSmrq^T 21:26, 26 August 2006 (UTC)

However, we also have introduction to quantum mechanics and introduction to special relativity and why 11 dimensions because there is simply so much to say about these topics at the introductory level, that a single article cannot do justice to both the introductory and the technical aspects of the subject. linas 22:22, 26 August 2006 (UTC)

Department of Injustice

For years I have regarded it as a running joke that named theorems, if they are really important, are almost never named for the "right" person. In funnier, it often turns out that the "wrong" person actually cited the earlier contribution, but nobody listened (or cared)! One can often see that even if famous person F tries to credit obscure person O, the result still usually becomes known for F. Anyway, I invite you to contribute your own examples in List of misnamed theorems, but please be very careful since the syntax is easily munged. If you can't figure out how to do it from the examples in the current version, put your entry in the talk page (with a complete citation if at all possible) and I will move the information to the article. ---CH 05:15, 26 August 2006 (UTC)

Um, isn't this a little bit OR-ish? Granted that lists in general are sometimes given a little rhythm on that point, still this seems especially close to the line, to me. --Trovatore 16:29, 26 August 2006 (UTC)

Surely the many items that cite secondary sources are okay? Melchoir 16:56, 26 August 2006 (UTC)

Its not just theorems. Farey numbers were first noted by Haros in 1802. Care to change the name to Misnamed topics in mathematics?

Its not just theorems and topics: Pell's equation was so named because Lord Brouncker solved it! - How about Misnamed equations? Madmath789 22:35, 26 August 2006 (UTC)

How about misnamed things? Fredrik Johansson 22:39, 26 August 2006 (UTC)

...List of misnomers in mathematics? Melchoir 23:35, 26 August 2006 (UTC)

I'm a little leery of the whole idea. The underlying premise seems to be that something is "misnamed" if named after someone other than the first person to come across it. That is not clear to me. Remember the "Columbus principle": It's not who discovers it first, but who discovers it last; that is, the person who makes the concept permanently available. Not everyone agrees with that idea, which is fine; it's not my purpose to promote it here. I'm just saying that a list that assumes the opposite, for its very existence, strikes me as POV. --Trovatore 17:53, 28 August 2006 (UTC)

Well, maybe there is a way of turning this into more of a history-of-mathematics type article? The few cases that I read about are just that: I read about them because someone else thought it was interesting enough to do some historical research and write about it. Once it is realized that some idea is improperly named, why would people continue to use the improper name? Habit .. laziness . ignorance .. lack of interest. I see no POV problem. FWIW, I recently did a little reading on the principle of least action, the correct attribution of which was littered with denouncemnts and accusations, mediated by councils, and even a kingly decree! At least we don't call it "sos-n-so's principle of least action", but I imagine there are more stories like this. linas 20:15, 28 August 2006 (UTC)

Hm? The POV problem is precisely the claim that such-and-such a name is "improper". --Trovatore 20:19, 28 August 2006 (UTC)

One problem is that many times it is not clear cut who was the "first" to discover something. Usually the modern reformulation is quite different than the original, and then it becomes a long debate whether so-and-so really discovered such-and-such or only a nonimportant special case or whether a later person really added anything essential, etc. Some people go with the "attribute to anyone in the neighborhood" philosophy, e.g. "so-and-so essentially had the idea but didn't know the formalism of the later such-and-such theory" whereas some go with the "attribute to the first person to make that exact statement" philosophy. So there are other reasons besides laziness, ignorance, etc., that somebody may choose to use a particular terminology.

Depending on your particular philosophy, you could argue almost all theorems named after persons are "misnamed". So the list could get quite long and useless. I think, as pointed out by Trovatore, that there are inherent POV issues in this list idea, only some of which have been pointed out. An additional source of concern is that the most reliable sources, say by math historians, will not attempt to assign credit but merely describe what contributions were made. So there's an opportunity here for editors to fall into the OR trap by saying "So-and-so wrote in his book that earlier Bunyakovski did such-and-such. So the theorem is misnamed". --C S (Talk) 22:04, 28 August 2006 (UTC)

Yes I agree with Trov and Chan here. Paul August ☎ 22:10, 28 August 2006 (UTC)

A momentous question

OK, here's a poser for you all, and I'm sure you won't want to eat or sleep until it's settled. If you start a sentence with the phrase von Neumann–Bernays–Gödel set theory, should the "v" be capitalized? I say yes, because you would capitalize it if you start a sentence with "von Neumann", and therefore the article does not need the {{lowercase}} template. Arthur thinks otherwise. Please focus your full intellectual powers on this question, as I know you wouldn't want to make a mistake here. --Trovatore 16:16, 26 August 2006 (UTC)

To up the ante, I don't see anyone crying havoc over Von Neumann architecture, Von Neumann probe, Von Neumann algebra, Von Neumann conjecture, or Von Neumann regular ring. And I've always thought that template was silly anyway. Melchoir 16:55, 26 August 2006 (UTC)

To add to the confusion, the "abbreviation" vNBG (at least, as used in my parents' work on logic and set theory) clearly cannot be uppercased at the beginning of a sentence. I'm now uncertain whether the entire expression, if spelled out, should be lowercased at the beginning of a sentence. I don't have time to research it for another few days, although I made the assertion in the appropriate article. — Arthur Rubin | (talk) 17:32, 26 August 2006 (UTC)

Response to Melchior's comment. It appears that, about 48 hours ago, someone went through and removed the lowercase template from all those pages. That person agrees with Trovatore that von Neumann is capitalized at the beginning of a sentence; I do not know whether this is correct, but it is surely a matter of editorial style, not grammar. In some style guides it depends on the original language (Dutch, German, etc) that the von comes from. The style I am used to would never capitalize von Neumann, even at the beginning of a sentence, and so I think the lowercase template is appropriate. Wikipedia is free to have its own style; my guess is that it is already documented somewhere, although a quick glance at WP:NAME didn't show anything. CMummert 17:34, 26 August 2006 (UTC)

Ah; I looked at the talk pages of those articles, but not their edit histories. I am not familiar with the usual treatment of "von Neumann" at the beginning of a sentence, so I'll back out of that particular issue. Melchoir 20:03, 26 August 2006 (UTC)

(responding to Melchor -- edit conflict) Well, I don't think it's silly on the articles where it really belongs, such as e (mathematical constant). We don't want our students deciding that it's sometimes OK to write it E, say if it's the first letter in an equation. And I'm fine with it, also, at eBay or bell hooks, though I don't think it's as important in those cases. But it should really be expunged from all the articles that start with "de" or "von" or "bin" or "ter"; those article titles are, in my view, correctly uppercased. Anyway, this is getting a little non-mathematical; if you want to get in on the whole earthshaking discussion, please see template talk:lowercase#Inappropriate use of this template (even that discussion should maybe go better at the MoS discussion page). --Trovatore 17:42, 26 August 2006 (UTC)

There's a conflating issue with e, though: in good writing one shouldn't be starting a sentence with it at all. Anyway, while it's a worthwhile goal to avoid misleading readers, usually the first, bolded usage of an article's title is where its correct usage is displayed-- and presumably, where the form will have a greater impact on the reader. In fact, if there's a conflict between the displayed title and the first usage, that alone draws the reader's attention, and that the actual usage is the one to imitate seems implicit. We don't have to beat the reader over the head with it. Maybe I should visit that talk page... Melchoir 20:11, 26 August 2006 (UTC)

(replying to the original question) I would capitalize "von Neumann" if it appears at the start of a sentence. That's at least the rule in German, Dutch and French, and it seems strange that English would deviate from it (though of course spelling is not always logical). -- Jitse Niesen (talk) 02:27, 27 August 2006 (UTC)

John von Neumann was so well known that he was often simply called "John von". So clearly the solution is to go thru all articles whose names begin with "von Neumann" or "Von Neumann" and replace those with "John von". Since this should clearly be capitalized, the ambiguity would be avoided. ;-) JRSpriggs 08:38, 27 August 2006 (UTC)

Navigational templates

I know I'm not a regular to this WP, but I'd like to throw out a suggestion: If the table on Portal:Mathematics/MathematicsTopics could be broken up into templates (as well as one large template of all of them), the templates could be placed on the respective articles to the great improvement of mathematics articles. 24.126.199.129 20:17, 26 August 2006 (UTC)

The majority of folks here despise the use of navigation templates, and delete them summarily. For good reason. linas 22:34, 26 August 2006 (UTC)

For those of us who don't see offhand what's wrong (or what's right) with navigational templates, could someone post a link to an earlier discussion where consensus was reached? The "good reason" linas cites are not evident to me. Michael Kinyon 00:42, 27 August 2006 (UTC)

There are long discussions that took place multiple times in the archives. Mostly, the problems were that the navboxes tended to get very large, chew up a lot of screen real-estate, and contain rather bizarre groupings of topics -- typically, obscure topics lumped in with major fields of study, thus giving undue weight to the obscure topic while effectively hiding the wealth of the major areas. Frequently, the navboxes would be skewed towards a college freshman's view of the world -- 23 ways of solving a differential equation and nothing else matters. If an article is well-written and properly linked, you don't need nav-boxes; you need an attention span that is longer than 15 seconds, which is something most of the editors here posses, but most proponents of nav boxes do not. Basically, you ain't gonna learn no math by surfing, and there's not point in encouraging surfing. linas 04:16, 27 August 2006 (UTC)

Ah. I didn't realize that earlier efforts were bloated and skewed toward the elementary and obscure. Looking at the existing mathematics nav-boxes, I see what you mean. The nav-box for convex, regular 4D polytopes seems fine, but someone stuck E7½ in the exceptional Lie groups nav-box. That was obviously inappropriate. The problem is clear: since the nav-boxes can be edited by anyone, of course they would bloat. Michael Kinyon 13:43, 27 August 2006 (UTC)

I am new to this discussion. I actually came here to propose such an idea! lol... I tend to like how the German wiki does it. For example, look at de:Gruppentheorie, "Group theory" (you may not speak German, but you can probably guess what most of the terms in the nav box mean.) It has three boxes, designating what field of math we are in, what is more general than a group, and what is more specific. It makes browsing around more enjoyable. Even if we dont have a sidebox, a box at the bottom of the articles could be nice. Am I redundant to some earlier conversation? - grubber 02:08, 23 September 2006 (UTC)

I tentively support an idea like de:Gruppentheorie. Personally I find the mathematics articles hard to navigate, and we do get ocasional comments from our readers who get lost engaging in a definition chase. Inline links present the reader with an unstructured web, whease a suitable nav box scheme would provide a more structured tree navigation scheme. Further the inline links can make navigation harder, you need to scan the text to find the appropriate links, these links may not always appear in standard places like the lead and see also sections making navigation even harder. A well thought through nav box system could make it easier for readers to find their way around the vast number of mathematics articles. --Salix alba (talk) 08:15, 23 September 2006 (UTC)

Infoboxes

Also: what is the consensus in WP Mathematics on infoboxes? Michael Kinyon 00:45, 27 August 2006 (UTC)

Dunno. Seem pretty enough in those places where they make sense. linas 04:16, 27 August 2006 (UTC)

Announce: Mathematics subject classification template

I created Template:MSC for use on category pages, for those who are into classifying things. I also did a brutal and summary redirect of Mathematics Subject Classification; specialists are encourages to write a blurb on those topics that don't have a blurb.

Speaking of templates, I'd like to remind everyone again about Template:Springer for links to articles in the Springer-Verlag online encyclopaedia of mathematics. — Preceding unsigned comment added by Linas (talk • contribs)

I undid the redirect as it doesn't make sense. The page on the AMS' Mathematics Subject Classification shouldn't redirect to a page that attempts to list and describe areas of mathematics (using the MSC as a "starting point"). The MSC is an interesting and encyclopedic subject in itself; its article should not only explain the classification scheme, but its differences (from the 2000 and 1991 versions), how it was created, who uses it, etc. --C S (Talk) 23:11, 26 August 2006 (UTC)

OK, well, its just was a nasty and brutal little article that threatens to try to duplicate the conetent of areas of mathematics, and I saw no point in encouraging duplication. linas 04:20, 27 August 2006 (UTC)

A little bit of politics

I'm going to ask here for help from native speakers (German particularly needed) in translation my Candidate statement for the Board Elections starting next week.

Putting together two comments above (User:KSmrq on the need for mathematical software support, and my own on the credibility the mathematics coverage disproportionately brings), having a mathematician on the Board might seem a positive step, to some here anyway.

Charles Matthews 14:23, 27 August 2006 (UTC)

Please place a notice here to assist those (like me) who would like to participate in the voting when it begins. I expect Wikipedia mathematicians will be especially interested in learning about a candidate who is a known mathematics editor. --KSmrq^T 20:33, 27 August 2006 (UTC)

meta:Elections for the Board of Trustees of the Wikimedia Foundation, 2006/En. But I spy a link at the top of this and most other pages. Charles Matthews 21:14, 27 August 2006 (UTC)

Update: I've had some very useful translation assistance, and am working on Italian right now. Spanish, Polish, Russian? Voting opens shortly. Charles Matthews 21:25, 30 August 2006 (UTC)

Soap bubble

Soap bubble is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 17:21, 27 August 2006 (UTC)

Citation templates

Hi all, please use these wherever possible. In particular, when citing an on-line article, please note that very few Wikipedia readers have an academic appointment and are using their office computer to access a journal's website, whereas anyone can download an arXiv eprint for free, so

1. in the case of published papers which are on-line, please use a link to the arXiv abstract page (not everyone prefers to download a pdf!; postscript is much faster for those with a postscript printer!) rather than a link to the journal website,
2. in the case of eprints, please use the arXiv citation template.

Here is the tutorial (created for the defuct WikiProject GTR, hence the gtr-related examples):

• Book:

*{{cite book | author=Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald | title=Gravitation | location=San Francisco | publisher= W. H. Freeman | year=1973 | id=ISBN 0-7167-0344-0}}

• Article in a research journal:

*{{cite journal | author=Kerr, R. P. | title=Gravitational field of a spinning mass as an example of algebraically special metrics | journal=Phys. Rev. Lett. | year=1963 | volume=11 | pages=237}}

• Article in a research journal which was previously an arXiv eprint (check the arXiv abstract page to see if any publication details are noted):

*{{cite journal | author=Bicak, Jiri | title=Selected exact solutions of Einstein's field equations: their role in general relativity and astrophysics | journal=Lect. Notes Phys. | year=2000 | volume=540 | pages=1-126}} [http://www.arxiv.org/abs/gr-qc/0004016 gr-qc/0004016 eprint version]

• arXiv eprint (not yet published):

*{{cite arXiv | author=Roberts, M. D. | title=Spacetime Exterior to a Star: Against Asymptotic Flatness | year = 1998 | version=May 16, 2002 | eprint=qr-qc/9811093}}

• Article in a book:

*{{cite conference | author=Ehlers, Jürgen; & Kundt, Wolfgang | title=Exact solutions of the gravitational field equations | booktitle=Gravitation: an Introduction to Current Research | year=1962 | pages=49–101}} See ''section 2-5.''

• Biography in the MacTutor archive:

{{MacTutor Biography |id=Friedmann|title=Aleksandr Aleksandrovich Friedmann}}

• Article at the Living Reviews website:

*{{cite web | author=Gönner, Hubert F. M. | title=On the History of Unified Field Theories | work=Living Reviews in Relativity | url=http://relativity.livingreviews.org/open?pubNo=lrr-2004-2 | accessdate=2005-08-10 }}

These have the following effects:

• Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.{{cite book}}: CS1 maint: multiple names: authors list (link)
• Kerr, R. P. (1963). "Gravitational field of a spinning mass as an example of algebraically special metrics". Phys. Rev. Lett. 11: 237.
• Bicak, Jiri (2000). "Selected exact solutions of Einstein's field equations: their role in general relativity and astrophysics". Lect. Notes Phys. 540: 1–126. gr-qc/0004016 eprint version
• Roberts, M. D. (1998). "Spacetime Exterior to a Star: Against Asymptotic Flatness". arXiv:qr-qc/9811093. {{cite arXiv}}: Unknown parameter |version= ignored (help)
• Ehlers, Jürgen; & Kundt, Wolfgang (1962). "Exact solutions of the gravitational field equations". Gravitation: an Introduction to Current Research. pp. 49–101. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help)CS1 maint: multiple names: authors list (link) See section 2-5.
• O'Connor, John J.; Robertson, Edmund F., "Aleksandr Aleksandrovich Friedmann", MacTutor History of Mathematics Archive, University of St Andrews
• Gönner, Hubert F. M. "On the History of Unified Field Theories". Living Reviews in Relativity. Retrieved 2005-08-10.

Maybe some kind project member can move this tutorial to the appropriate project page? And what about a page called something like "introduction for project newbies" which helps newcomers to editing math-related articles find valuable resources like List of mathematical topics (I like the old name better) and this tutorial? TIA! ---CH 19:17, 28 August 2006 (UTC)

Five points:

1. These templates are more flexible than shown; more info is available at WP:CITET.
2. When giving page ranges, please use an en dash (&ndash;) rather than a hypen-minus: "49–101", not "49-101".
3. When giving ISBN data, please be forward-looking and convert to ISBN-13 (with online converter): "ISBN 978-0-7167-0344-0", not "ISBN 0-7167-0344-0". (And, please, do provide a valid ISBN.)
4. When citing a journal, please provide ISSN data using the {{ISSN}} template: ISSN 0031-9007.
5. Many online journal publications have a doi link; please use it if available.

A great deal of work has gone into writing these elaborate templates, and for good reason. They can really help the citation process. --KSmrq^T 23:00, 28 August 2006 (UTC)

Thanks for bringing these to my attention. Why should I use them "wherever possible"? What is the "good reason"? Thanks. -- Dominus 10:08, 31 August 2006 (UTC)

Official Wikipedia policy has not yet determined a standard set of templates, nor dictated their use. A journal or print encyclopedia or other formal publication does have standards. For readers, consistency makes references easier to search and easier to understand. For editors, use of templates makes a consistent preferred style easier to achieve.

Fill in the blanks, and the rest happens automatically. Should the author be listed "John Doe" or "Doe, John"? What gets italicized, quoted, bolded? What punctuation goes where? Where does the date go? All these questions and more are avoided, because the template knows what to do. Experienced authors of technical material have long relied on BibTeX databases and automatic formatting. We do not have a Wikipedia-wide database, but we can at least take advantage of templates.

Consider a novice editor who would like to cite Coxeter's classic Introduction to Geometry. Here's the template:

{{cite book | last = Coxeter | first = H. S. M. | authorlink = Harold Scott MacDonald Coxeter | title = Introduction to Geometry | edition = 2/e | publisher = Wiley | date = 1989 | pages = 366–368 | id = ISBN 978-0-471-50458-0 }}

and here's the result:

Coxeter, H. S. M. (1989). Introduction to Geometry (2/e ed.). Wiley. pp. 366–368. ISBN 978-0-471-50458-0.

A novice might not italicize the title, without the prompting of a template might not include an ISBN, and so on. Journal citations are a still greater challenge. Yet merely populating the slots of a template:

{{cite journal | last = Lawvere | first = F. William | authorlink = William Lawvere | title = Taking categories seriously | journal = Revista Colombiana de Matemáticas | volume = XX | pages = 147–178 | publisher = Sociedad Colombiana de Matemáticas – Universidad Nacional de Colombia (Bogotá) | date = 1986 | url = http://www.tac.mta.ca/tac/reprints/articles/8/tr8.dvi | format = [[DVI (file format)|]] | ISSN = 0034-7426}}

produces this lovely citation:

Lawvere, F. William (1986). "Taking categories seriously" (DVI). Revista Colombiana de Matemáticas. XX. Sociedad Colombiana de Matemáticas – Universidad Nacional de Colombia (Bogotá): 147–178. ISSN 0034-7426.

Finally, use of such templates across Wikipedia makes a global change in convention, perhaps for another medium (or a non-English wikipedia), a minor change to implement. For example, we could switch to omitting quotation marks, or to using the typographically preferred curly quotation marks. --KSmrq^T 21:08, 31 August 2006 (UTC)

Have the recommendations, examples and points to remember in this section been posted somewhere more permanent and publicly visible?  — merge 13:46, 31 August 2006 (UTC)

The math-specific template examples could be put in a subpage, which could be added to the list of math Project Pages at WP:WPM. EdJohnston 02:12, 1 September 2006 (UTC)

But wait! The WikiProject Mathematics page says there is already a math-specific manual of style: Wikipedia:Manual of Style (mathematics) . How about putting the new template advice in there? For extra visibility, also add the manual of style to the list of math Project Subpages? EdJohnston

One question re arXiv version versus versions published in journals. I would suspect that these will not be exactly the same as the journal version is likely to have gone through a review process before publication. Whats the best way to handle this? --Salix alba (talk) 18:47, 31 August 2006 (UTC)

Sep 2006

13-digit ISBNs

Above KSmrq, suggests the use of 13-digit ISBNs. However, since many (most?) sites (e.g. Amazon) can not handle 13-digit ISBNs, using them will make many of the "Find this book" links fail when clicking on the ISBN links. For example clicking on: ISBN 0-7167-0344-0, then clicking on "Find this book" link for the Amazon.com entry under the section "Individual online booksellers" finds this page, while doing the same thing for ISBN 978-0-7167-0344-0, gives this result So we might want to hold off for now on using 13-digit ISBNs. In the future I'm sure some enterprising bot will come along and convert all our ISBNs for us anyway ;-) — Paul August ☎ 16:03, 1 September 2006 (UTC)

The future arrives four months from today. Rich Farmbrough has a bot [User talk:Rich Farmbrough/Archive/2006Sep#The bot and ISBN-13 contemplating] an automatic change-over. In the linked discussion I mention a few other issues as well. I'm wondering if it would be too cumbersome to provide both ISBN forms (especially for print). Perhaps the MediaWiki ISBN magic could handle it for online use, like the handling of date formats; but, as always, implementation is not in our hands.

Meanwhile, my feeling is that the ISBN-13 form is future-proof and international, and allows the intended book to be found, even if it doesn't find all the sellers the ISBN-10 form matches. Every ISBN has annoying limitations. A paperback and a hardback have different numbers, as do versions of classics provided by different publishers; and each edition has its own number, which is at times good and at other times an obstacle.

Regardless of which ISBN you prefer, please do take a moment to provide one (and, ideally, check its validity).

Another way to assist readers in finding books is to check against online versions. Some texts can be found at Project Gutenberg, but mathematics is a minority there. Fortunately, we have alternatives.

• Cornell Historical Math Monographs
• U. Michigan Historical Math Collection
• The Electronic Library of Mathematics
• AMS Mathematics Books Online
• Euclid's Elements with Java
• The Perseus Digital Library
• NUMDAM Digitization of ancient mathematics documents
• UPenn Online Books
• George Cain's list
• Alexandre Stefanov's list
• Reprints in Theory and Applications of Categories
• Project Euclid journals online

These sites also include links to others. --KSmrq^T 18:19, 1 September 2006 (UTC)

Good articles

I've been going through the list of mathematics Good articles and I'm not sure that some of them really meet the grade. Riemann hypothesis is what I would consider to be the standard for a good article. My main concern is that the articles are either lacking in any history of the topic failing criteria (3a). Also it would be good to see some illustrations (6).

• Fair division - clearly failed, just too brief. Now delisted.
• Measure (mathematics) - lacks history. Could easily be expanded. Listing on Wikipedia:Good articles/Review
• Homotopy groups of spheres - lack history, could do with some more illustrations. Recently successfully went through review. Comment on talk page.
• Fractal - is a failed GA, though considerably better than the above.
• Renormalization - listed as a maths article but really physics, should there be an article on the mathematical use of the term?
• Ordinal number - I think fails criteia 1.(a) it has compelling prose, and is readily comprehensible to non-specialist readers, this article is heavily linked from the various number pages and other general articles, eg. floor numbering or Roman numerals. For readers clicking on a link from those pages the articles pretty incomprehensiable. Hence I'm listing it on Wikipedia:Good articles/Review. --Salix alba (talk) 11:48, 3 September 2006 (UTC)

Moreover, I think there is some need to discuss what makes a mathematics good article so we can establish a standard. Maths articles seem to be a bit of a special case as they are often highly technical, so they are likely to have problems with GA criteria 1a: it has compelling prose, and is readily comprehensible to non-specialist readers. We also seem to run into problems with 2b the citation of its sources is essential, and the use of inline citations is desirable, although not mandatory. Often inline citations are not really appropriate as the topic as a whole will be covered in cited textbooks.

Generally our number of GA's is very low with only 15 articles. Are there any other articles out there which people think are especially good? --Salix alba (talk) 10:37, 3 September 2006 (UTC)

I think the article on knot theory is a good target to turn into a GA, and eventually maybe even an FA. It doesn't try to do too much, and what is there currently should be fairly easy to brush up. I note that the section on Conway notation and planar graph notation is incomplete, but shouldn't take too much time to complete. There are several obvious ways to add good illustrations (and illustrative examples) to the article. --C S (Talk) 11:10, 3 September 2006 (UTC)

There's also quite a bit of bickering going on at Grigori Perelman, but it seems to me that this article has recently undergone a great deal of attention and editing and if all disputes can be resolved, I expect it could become a GA. Perhaps even Poincaré conjecture...but that will require a lot more work, and I've dropped the ball on that for which I apologize. But eventually I'll have a decent writeup of Perelman's proof ("alpha" version is at User:C S/todo/PC proof) and we can rewrite the article around that or whatever. --C S (Talk) 11:21, 3 September 2006 (UTC)

Yes I agree that knot theory could be a good target. Are people happy to defend the article, if so I think it should be nominated.

Grigori Perelman and Poincaré conjecture are probably too volitile at the moment GA 5 It is stable, i.e. it does not change significantly from day to day and is not the subject of ongoing edit wars. , that said it might be a good time to list if there are active contributors.

I'd quite like to create a B+ rating, for articles which are nearly but not quite at the standard of GA, we do have a good number of articles listed on Mathematics 1.0 which would fit this category, for example Pi which is good but has been delisted from GA. --Salix alba (talk) 12:05, 3 September 2006 (UTC)

Rename "Ordinal number"? God forbid!

User:Salix alba wants to rename (move) Ordinal number which is (in my opinion) one of the most important articles in the general area of Set theory. There are more than FIVE HUNDRED articles which link to it by its current name. Now, admittedly the majority of them would just as well be linked to the article which he proposes to put in its place -- an article on "first, second, third, fourth, fifth, etc.", but there is still a large fraction of them which are important mathematics articles. Please resist this disruptive change by talking at Talk:Ordinal number and elsewhere. Notice that there is already a link at the beginning of "Ordinal number" to the section Names of numbers in English#Ordinal numbers which covers the material in which he is interested. JRSpriggs 02:53, 4 September 2006 (UTC)

I agree, of course: "ordinal number" is correct. You can point him to this book, for example:

Halmos, Paul (1974). Naive Set Theory. Springer. ISBN 0-387-900092-6. (reprint of 1960 classic)

Chapter 19 is entitled "ordinal numbers".---CH 21:17, 6 September 2006 (UTC)

McNugget number is up for AFD

I've listed McNugget number for AFD. This is the second nom (first was by somebody else in October). AFD discussion page People may be interested in looking over the first discussion, which ended as "no consensus". --C S (Talk) 01:03, 5 September 2006 (UTC)

Multidimensional Gaussian integrals

User:EulerGamma recently removed a section about multidimensional generalizations from the Gaussian integral article for being "complicated" and lacking sources. The topic is real, but the lack of sources for the details is a valid complaint. Unfortunately, the original author seems to have been inactive for several months. I'm sure some people here are knowledgeable enough to check the content (I'm not); please have a look if you do. Fredrik Johansson 20:40, 6 September 2006 (UTC)

Leonhard Euler is up for FAC

Please see this page for the discussion. Borisblue 00:39, 7 September 2006 (UTC)

Mathematical Wikiers in Chinese

Dmharvy, here is your link. zh:Wikipedia talk:数学兴趣小组维基人列表----Hillgentleman 03:41, 7 September 2006 (UTC)

User:WATARU

New user WATARU appears to me to be almost certainly User:WAREL. However he hasn't yet done any of the things that got him banned before. Let's keep an eye out, but not provoke. "Don't start none, won't be none", as Huey P Freeman would say. --Trovatore 20:30, 9 September 2006 (UTC)

see [44]. --Trovatore 18:33, 11 September 2006 (UTC)

Now he's changed the Japanese link at division ring to something else. I don't read Japanese, so I don't know if it's appropriate or not, but given his history I'm not inclined to trust him. He may well be planning some shenanigans at ja.wiki and making edits here to prepare for them. (It goes without saying that he has long since used up his assumption of good faith.) Would someone with some competence in Japanese please look at this? --Trovatore 21:02, 12 September 2006 (UTC)

And he is insisting on using the Big Omega function on square number, where it is pointless showing off. (See diffs: [45][46].) Given the number of complaints we get for being technical where we have to be, there is no excuse for this in an article that proves that the squares of odd numbers are odd. Septentrionalis 19:48, 13 September 2006 (UTC)

Articles tagged as too technical

For a list see Wikipedia:WikiProject_Mathematics/Current_activity/Lists#Articles_that_are_too_technical. I've noticed, as I'm sure others have, that sometimes well-meaning editors just go through mathematical articles tagging them as "too technical". For example simple module has been tagged; however, I don't really see why it was tagged other than it looks like "gobbly-gook" to someone who doesn't know what a ring or module is. I can't see how this article can really be improved in a significant way to be accessible to someone without such a background. Perhaps an example built from the ground up would help...but that would seem to be the equivalent of writing a wikibook on abstract algebra. In any case, I believe this article (and some others) have been tagged wrongly.

The unfortunate thing about all this is that it makes it hard to find the actual overly-technical articles that can be made much more accessible. As a first step to making articles more accessible, therefore, I suggest that some people take some time and untag as many articles as they can -- those that are very advanced topics or seem to have been made as accessible as possible. --C S (Talk) 02:30, 11 September 2006 (UTC)

I added a sentence about graphical projection to Projection (linear algebra) and removed the tags. There wasn't anything in the talk page about why the tags were added. User:ST47 who added the "technical" tag was bot assisted. User:Srleffler added the original tag didn't leave any explanation. It seems Srleffler's attention was drawn to the article through graphical projection; they also left the same tag on projection (relational algebra) which Jon Awbrey summarily removed. Guess it's just another example of what you're talking about. (I know it's just one article. Sorry.) Lunch 23:15, 12 September 2006 (UTC)

got a bunch more. btw, it seems the current activity list hasn't been updated in a couple of weeks. did the bot run out of gas? Lunch 04:58, 24 September 2006 (UTC)

page move?

the article on Robert Berger, the mathematician, was linked to by several film-related articles mentioning the writer robert berger. i changed those to refer to Robert Berger (writer). might it be a good idea to move Robert Berger to Robert Berger (mathematician) and put a redirect in its place? how does one go about doing this? tia. Lunch 03:38, 11 September 2006 (UTC)

The easiest is to use the "move" tab at the top of the article to move Robert Berger to Robert Berger (mathematician). This will automagically leave a redirect in its place. --Lambiam^Talk 05:31, 11 September 2006 (UTC)

But looking at this stubby article, I think there is not enough info to merit having a separate article here, as was noted by others on its talk page. --Lambiam^Talk 06:16, 11 September 2006 (UTC)

Two points here: (1) Are you sure that these are two different people? Sometimes one person does work in two completely unrelated fields. For example, Dorthy Lamour (hope I remembered the right actress) Hedy Lamarr was both a film actress and the inventor of a method of encryption. (2) There is no point in moving the page unless you replace the redirect with a disambiguation page listing various people named "Robert Berger" and giving links to their pages. JRSpriggs 07:05, 11 September 2006 (UTC)

Try Hedy Lamarr for the inventive star. --Lambiam^Talk 10:09, 11 September 2006 (UTC)

My thanks to Lambiam for the correction. JRSpriggs 05:26, 12 September 2006 (UTC)

According to his entry at the IMDB, the writer Robert Berger was credited as "Robert H. Berger M.D." for being a consultant for the movie Final Analysis. As that movie is about a psychiatrist, that Robert Berger is very likely too a shrink. Citations of (Berger, Robert. "The undecidability of the domino problem". Memoirs of the American Mathematical Society, 66, (1966), 1–72) all appear not to give a middle initial. --Lambiam^Talk 10:35, 11 September 2006 (UTC)

This Robert Berger seems not to have an entry in the Library of Congress, but he IS in the Harvard library catalog! He is given as Berger, Robert (born 1938), author of the AMS memoir on domino undecidability. They don't know his middle initial. I also looked up the memoir itself, and it includes no middle name, middle initial, thesis advisor, and no acknowledgments that I could find. There were four references, including one to a paper of Hao Wang. WP's entry for Wang says he was at Harvard from 1961 to 1967, so it's reasonable he could have been Berger's advisor. AMS MathSciNet does not seem to have any papers by this Robert Berger besides the domino memoir. EdJohnston 19:36, 11 September 2006 (UTC)

the harvard library catalog lists several holdings under the title "the undecibility of the domino problem." one of them is the AMS publication. another one of them is a copy of his dissertation. the title page there probably has his advisor's name. i'll be visiting there at the beginning of november; if i get a chance, i'll look it up. (i'm also morbidly curious to see ted kaczynski's dissertation, too, so i might actually take the time. :) UMI has him listed at harvard in 1965, too, but they don't have a copy of his dissertation (not even the abstract).

what originally brought me to the article was just a haphazard meandering. i saw the article on the list of "too technical" articles and was curious why it was there. when i looked at the list of "what links here," i noticed the three (four?) links to the movie writer/producer. although a quick check through IMDB now makes me think there are at least three robert bergers of note: the mathematician; Robert H. Berger, M.D., the writer/consultant for "final analysis"; and robert berger, the producer. this last fellow was making films as far back as 1962 so unless the mathematician robert berger was also a rookie film-maker during his harvard days, they're not the same person. (and incidentally, robert berger has produced almost three dozen movies; maybe there should be an article on him.) that doesn't rule out that the mathematician went out and got an M.D. and got into the film business, but i'd hazard a guess that didn't happen.

anywho, all this attention seems way out of proportion, but i'm glad to see some other amateur sleuths out there too.  :) i s'pose my two bits is that i go back an un-wiki-link robert berger, the writer/consultant of final analysis; make a stub on robert berger, the producer; and move robert berger, the mathematician. whaddya all think? too much?

thanks. Lunch 20:21, 11 September 2006 (UTC)

(oops, kaczynski did his PhD at michigan. he was an undergrad at harvard. oh well, maybe some other time.) Lunch 17:27, 22 September 2006 (UTC)

OK with me. The Harvard library catalog shows many, many Robert Bergers. But this man is the most famous of the mathematical Robert Bergers. Google Scholar still shows 216 citations to the domino paper, so he is notable. EdJohnston 22:55, 11 September 2006 (UTC)

The plan sounds fine. Just be careful of the other mathematician named Robert W. Berger who wrote quite a few papers, mostly in German. His genealogy can be found here. I don't know how notable he was/is.

By the way, this book review (a postscript file) asserts that the Robert Berger we have been discussing was indeed Hao Wang's student. Michael Kinyon 23:10, 11 September 2006 (UTC)

thanks. (i think the link is [47] for the postscript or [48] for the pdf, but i think the pdf got chopped off.) to address lambiam's early point, should the robert berger article mention all three since separate articles would be too short? i started a stub for Robert Berger (producer); potentially it could be much longer (he was rather prolific), but isn't long now. i dunno how long the article on robert berger the aperiodic tiler could be, or how long the article on robert w. berger could be. Lunch 00:12, 12 September 2006 (UTC)

WP:BLP violation at Louis de Branges de Bourcia

I've changed to a far better version while trying to incorporate some of the recent factual additions. But the previous version definitely had way too much speculation, ramblings, and just poor sourcing. Given the number of people (although maybe some of the IPs are really the same person), who have edited it into this state, I think it's wise if people keep an eye on this page. --C S (Talk) 06:04, 11 September 2006 (UTC)

Some of the details are from Sabbagh's book, but I have not seen it recently enough to edit. Septentrionalis 20:32, 11 September 2006 (UTC)

What does it mean?

I find that many math articles give definitions in a way that is 100% accurate but only 10% useful. (This is true of math writing beyond Wikipedia.) For example, until recently the definition of symmetric matrix simply stated that $A_{ij}=A_{ji}$. That's all well and good—it correctly defines the term—but it does not answer the question "what does it mean for a matrix to be symmetric?". As best I can tell, the answer is "it means the eigenvectors are orthogonal", which I added. After all, this is what mathematicians think when they think "symmetric".

I propose a concerted effort to get answers of this form into the definitions of math terms—answers that allow readers to think like a mathematician rather than stare at syntax. Perhaps a template Template:what_does_it_mean? —Ben FrantzDale 23:35, 11 September 2006 (UTC)

As for the statement you added, it wasn't quite correct, so I fixed it in the article. (It turns out to be exactly the symmetric matrices that have orthonormal bases of eigenvectors which makes your addition even more appropriate to this particular article.)

As for your suggestion, I agree with you in principle but not in practice. A mathematical definition is just that--a definition. While it may be equivalent to any number of conditions, some of which are intuitively more appealing than others, the definition is usually the more straightforward one. In this case "symmetric" means literally that the matrix entries exhibit some kind of symmetry, in this case with respect to the matrix transpose. That's why we have a whole article to follow; the article should explain "what does it mean". A good article probably does not need any additional template if it's doing its job correctly.

Having said this, thanks for your contribution and suggestion. We do need to make sure that the math articles fully explain the "why". VectorPosse 00:26, 12 September 2006 (UTC)

what do you mean by "mean"? ;) that there is a complete set of orthonormal eigenvectors of a symmetric matrix (along with real eigenvalues) is usually called a theorem, and the symmetry of matrix entries is usually called the definition. of course, it is equivalent to do the reverse. (and there are several other definitions that result in equivalence.)

but the symmetry of matrix entries is by far the simplest definition, and the eigenvector/value property is listed shortly thereafter in the article (and this is good practice). also, the symmetry of matrix entries does have significance: if two vectors are related by multiplication by a symmetric matrix, then changes in entry i wiggle entry j as much as entry j wiggles entry i. symmetry is also preserved under a congruence transform (as like with change of coordinates applied to a quadratic form - not to be confused with a similarity transform, a change of coords for a linear system). physicists love these sorts of things. (as do mathematicians, engineers, and a whole party of people. :) but i'd stick this in a list of properties...

i guess my point is that people usually go with the simplest possible definition and stick equivalent definitions under "properties" or "lemmas/theorems". Lunch 00:43, 12 September 2006 (UTC) (oops. edit conflict.)

maybe i'd add that "simplest" doesn't always mean "most intuitive" or "most informative about why this is useful/interesting/wheretheheckdidTHIScomefrom". you're right in thinking that an article on such a subject deserves a bit of history/motivation in the leading paragraph(s). or maybe i'm not thinking what you're thinking. Lunch 00:54, 12 September 2006 (UTC)

Lunch, I think we are on the same page when you say “‘simplest’ doesn't always mean ‘most intuative’...". In the case of this example I'd argue that the obvious definition of symmetry, while important, is essentially intuition-free and so not very helpful for newbies. That's why I like the format "X is defined as y but really a mathematician is thinking z." Overall I'd like to see a move towards systematically answering “wheretheheckdidTHIScomefrom”. —Ben FrantzDale 02:40, 12 September 2006 (UTC)

you mean you didn't like my wiggling components analysis?  ;) not to beat a dead horse, but as a mathematician who spends a lot of time doing linear algebra, i do think in components often enough. imho, the component-wise definition of a symmetric matrix is a good one and does have intuitive appeal. (i'd also add that linear algebra is almost always first introduced to students from a components point of view -- and with good reason.) Lunch 19:47, 12 September 2006 (UTC)

VectorPosse, as for the template idea, to clarify I was thinking a cleanup-style template not an infobox—something to tag an article with when it feels like it's skirting the "mathematician's intuition" definition. —Ben FrantzDale 02:40, 12 September 2006 (UTC)

Oh, I see what you mean now. Well, I'm not sure that changes my opinion much. I'm rather new here myself so I don't know much about templates; nevertheless, I suspect there's already a common template to indicate that an article needs more explanation or clarification. I'll leave that to more experienced editors to decide. I still agree, of course, that any "mathematical intuition" should be explained in the article (but not in the definition). VectorPosse 04:44, 12 September 2006 (UTC)

I'm not sure this is really necessary. Mathematical objects can have many properties, and one of them is not necessarily more important than others. We have a whole article to explain these properties and what is useful/interesting about them, and the intro should summarise the article. JPD (talk) 08:08, 12 September 2006 (UTC)

I agree that what does it mean? is really context-dependent. We would probably not say that Rⁿ means "cofunctor of an abelian variety". A symmetric matrix may appear in several contexts without reference to spectral properties. pom 15:06, 12 September 2006 (UTC)

A distance matrix is symmetric. This is an easily understood elementary property. Few mathematicians will think: "Oh, I know what that means. It has an orthonormal basis of eigenvectors!'  --Lambiam^Talk 15:11, 12 September 2006 (UTC)

Good point, and good example. I assume the eigenvector symmetry property isn't interesting in that case because the matrix isn't used as a transformation. For a distance matrix, it seams that symmetry is a trivial and not-too-interesting fact. The distance matrix page could do with some "what does it mean" love itself, actually; it says what one is and the fields in which they are used but not how they are used.—Ben FrantzDale 18:09, 12 September 2006 (UTC)

Symmetry isn't trivial or uninteresting in this case: it's one of the three key axioms defining a metric. —David Eppstein 21:28, 12 September 2006 (UTC)

I've been bold and added a Mathematical intuition project sub-page to try to address this issue. —Ben FrantzDale 18:14, 12 September 2006 (UTC)

Please help with extension (mathematics)

I created extension (mathematics) as a new disambiguation page with more than 30 entries. I think it ought to get organized into sections and subsections. Could Wikipedia's many mathematicians please help? Michael Hardy 21:31, 12 September 2006 (UTC)

I put them into some vague sections, people should feel free to subdivide further. Of course, most of these are algebra. -- Deville (Talk) 22:02, 12 September 2006 (UTC)

Does anyone else think it's a little weird that Extension problem is strictly about group extensions, while the stub Group extension mentions fields and other algebraic structures? Michael Kinyon 18:25, 15 September 2006 (UTC)

Yeah, I thought it was weird, so I changed Group extension to mention only groups and added a link at the bottom to Ring extension. This is a stub that could be greatly expanded. The article Extension problem actually has a lot of the material I would put in Group extension if it were up to me. Ah, if I only had the time... VectorPosse 19:03, 15 September 2006 (UTC)

What problems would result from just switching the names around? Michael Kinyon 20:07, 15 September 2006 (UTC)

I like it! If we did that, we would need to restore the few words I removed (probably with some editing), but I think this is a great idea. The page Extension problem ought to be a small-ish, more general page about any kind of extension problem. Then its links direct readers to the particulars of specific kinds of extensions. There is something in the page's discussion about calling it Extension (algebra) (which currently redirects to Group extension) and I think that would be necessary for this solution. Otherwise, one would have to include material on extension problems in all fields and that would be the same list that started this thread to begin with. VectorPosse 23:23, 15 September 2006 (UTC)

It seems fine to me. I am going on a Wikibreak for a bit more than a week starting tonight, and you have thought in more detail about what would be needed than I have. So my "vote" is: go for it! Anyone else have any thoughts about this? Michael Kinyon 03:47, 16 September 2006 (UTC)

Discussion at Euclidean space

There is a discussion occurring at Euclidean space concerning how best to write the introduction to be more accessible (see: Talk:Euclidean space#Obnoxious article and following). Interested parties may wish to join the discussion. Paul August ☎ 23:23, 12 September 2006 (UTC)

Peer review: Boy's surface

Boy's surface (talk) is up for peer review. Please offer any insights (there, not here).—msh210℠ 21:36, 13 September 2006 (UTC)

Martingale paradox

Martingale paradox has been put up for deletion: Wikipedia: Articles for deletion/Martingale paradox. The author has spent a lot of effort on Usenet at promoting this material, e.g. [49] (see User:AntiochCollege for suspiciously similar material). --C S (Talk) 00:21, 15 September 2006 (UTC)

What happened ?

I created a page for Pierre Rosenstiehl yesterday. It just disappeared today (even the traces of the changes I made). I am sure to have saved it after editing and the page is still in my watchlist... If it has been deleted, it would have been fair to post some message on my talk page. Otherwise, what did happen? pom 10:26, 15 September 2006 (UTC)

Here's the entry from the deletion log:

• 02:10, 2006 September 15 Jeffrey O. Gustafson (Talk | contribs) deleted "Pierre Rosenstiehl" (A7)

Go complain. --KSmrq^T 12:13, 15 September 2006 (UTC)

I put a message on Gustafson's Talk page asking him to consider restoring it and, if he still thinks Rosenstiehl is non-notable, putting the article up for AfD so that the rest of us can have some input. Michael Kinyon 12:42, 15 September 2006 (UTC)

Speedy deletion under A7: unremarkable people or groups/vanity pages. An article about a real person, group of people, band, or club that does not assert the importance or significance of its subject. If the assertion is disputed or controversial, it should be taken to AfD instead. I think that was wrongly applied. Charles Matthews 13:31, 15 September 2006 (UTC)

I think the "proper" method would be to take it to DRV. Or you could just recreate it with a {{hangon}} tag. But asking the deleting admin for reconsideration is always in order.

The page came back and I put a {{hangon}} tag. Actually, I am not sure it should be kept as I am not aware of the threshold considered by Wikipedia for notability. Whatever decision is taken does not care too much. However, deletion / restoration without a slightest explanation from an admin is an attitude which does not encourage editing at all. pom 16:05, 15 September 2006 (UTC)

Notability is well known to be a difficult concept to apply in practice. A better question: who would consult Wikipedia as a reference about a given person (excluding family, friends, colleagues)? For a member of Oulipo, it is easy to see that many people might look here. It is an argument you could all there-are-no-minor-poets: of course almost all poets are 'minor', as almost all mathematicians fail to be 'major'. But if someone likes a poem and has only a name, then, yes, they might use a reference work to discover more. Charles Matthews 21:44, 15 September 2006 (UTC)

Ok, but from a practical point a view, what should I do if I want to start to write pages on living combinatorists? Should I consider there is limit on the number of bigraphies and that I should prioritize the additions. If so, what would be the order of magnitude of this limit? pom 22:34, 15 September 2006 (UTC)

Mr. Gustafson pulled the trigger on the article (and perhaps should have known better), but an anonymous user User:151.200.246.168 was the one who tagged the article for speedy deletion in the first place. In the span of just over two hours, they tagged 18 articles for speedy deletion. It wasn't quite vandalism; many of the articles were marginal at best, but didn't quite seem like candidates for speedy deletion either. Weird. Lunch 17:18, 15 September 2006 (UTC)

Weird, indeed. In good faith, perhaps it is just someone who doesn't understand the speedy deletion criteria. In any case, I think this WikiProject can congratulate itself on how this was handled. (But will our backs hurt from patting them so hard?) Michael Kinyon 18:15, 15 September 2006 (UTC)

Etymology

Some unusual updates have been made to the etymology at pentagon (disambiguation), heptagon and polygon. I'm no expert, but I never heard that these terms had a Sanskrit origin before, so I am rather doubtful about the accuracy of these updates. Any comments ? Gandalf61 10:31, 15 September 2006 (UTC)

Here are some etymologies from the OED:

pentagon In A, ad. L. pentagon-us, a. Gr. pentagwn-oj pentagonal, five-cornered, f. penta- penta- + -gwn-oj from stem of gwnia angle. In B, ad. L. pentagon-um, Gr. pentagwnon, the neuter adj. used as sb. Cf. Fr. pentagone sb. (13th c. in Littré), whence the Eng; form in -gone.

penta- penta, before a vowel pent-, a. Gr. penta-, combining form of pente five, occurring in many words in Greek as a variant of the earlier pente-, and forming the initial element in various modern technical words adopted from Greek, or formed from Greek elements or on Greek analogies.

I'm not convinced that those articles need any etymologies, much less ones that seem to have little support in standard references. It may be possible that the words came to Greek from Sanskrit, but without any documentation I think it is better to just remove the anonymous edits instead of correcting or expanding them. CMummert 10:49, 15 September 2006 (UTC)

The Greek did not "come from" Sanskrit any more than the Sanskrit came from Greek. I've removed these changes. --Lambiam^Talk 17:19, 15 September 2006 (UTC)

I asked on wikitionary and got

Er – no, it's wrong. All these related ‘shape’ nouns are from Greek. The Greek suffix was -γωνος, literally ‘angled’, and in this case combined with πεντα-, from πέντε ‘five’. The Sanskrit forms are cognate (i.e. both Sanskrit and Greek are descendants of Proto-Indo-European *penkʷe ‘five’), but Sanskrit is not the immediate source of the English word. Very few words in English come from Sanskrit. -- Widsith

So now we know. --Salix alba (talk) 17:44, 15 September 2006 (UTC)

There was a habit of calling Proto-Indo-European "Sanskrit" a century ago, before the decipherment of Hittite and the present understanding of IE vowels. It should be suppressed where found. Septentrionalis 18:48, 15 September 2006 (UTC)

Polar coordinate system

Hi everyone! An article that I've been working on quite a bit, Polar coordinate system, has just become a good article. We've requested a peer review to find out how it can be improved to featured article status, and it's great so far. Any other comments would be appreciated. Thanks. —Mets501 (talk) 14:20, 16 September 2006 (UTC)

Subcategory for geometric graph theory?

I've been working on a few pages lately that have the flavor of geometric graph theory — that is, about graphs that are either embedded in a geometric space themselves, or that arise from configurations in a geometric space. I'm wondering whether it would be appropriate to make a new category for them, as a subcategory of both geometry and graph theory.

• Existing pages that could add or change to include this as a category: Fáry's theorem, Unit disk graph, Crossing number (graph theory), Interval graph, Graph drawing, Visibility graph, Visibility graph analysis, Euclidean minimum spanning tree, Scheinerman's conjecture
• Redlinks: Intersection graph, Gabriel graph, Nearest neighbor graph, Unit distance graph
• Potential additional topics: Boxicity, Sphericity (of an intersection graph, would need a different name than the unrelated existing Sphericity page), Steinitz's theorem

Evidence that organizing things this way is not just my own hobby horse: Pach's edited collection Towards a Theory of Geometric Graphs (to which I contributed a paper on geometric thickness, a subject that would fit here as well but one that I think someone else should add if it deserves adding).

Anyway, this seems a widespread enough change that I felt I should open up the question for debate here rather than just going ahead and doing it. So, does anyone have an opinion on this possible reorganization? —David Eppstein 21:30, 17 September 2006 (UTC)

Category:Geometric graph theory sounds good to me. --Salix alba (talk) 21:14, 17 September 2006 (UTC)

I don't know if it will be so easy to make the distinction between Geometric Graph Theory and Topological Graph Theory. For instance: the usual crossing number is of topological nature, while the rectilinear crossing number is of geometric nature. Don't you think it could be better to (at least temporarily) merge the two in a Topological and Geometric Graph Theory subcategory? Of course, there are purely topological or geometric results (rotation system / Erdős–Szekeres theorem) but most have several aspects. Graph drawings may rely on spectral analysis or poset related properties (like track drawing). The classification of theoretical results may also be problematic (e.g.: Schnyder's theorem is about planarity, poset dimension, decompositions into particular forests, and induce a straight line drawing on a linear grid). All of this does not mean I am against subcategories, but rather that I am afraid by the number of topics which will cross the boundaries of categories. pom 21:59, 17 September 2006 (UTC)

To me the distinction seems clear enough: topological graph theory concerns graphs embedded on 2-manifolds such as the Euclidean plane, with vertices as points and edges as curves, while geometric graph theory either considers similar type embeddings with edges as straight line segments or other restricted geometric curves (polygonal paths with few bends, or circular arcs, though I doubt there is much already in WP that mentions these), or graphs coming from other geometric constructions (intersection graphs, visibility graphs, arrangements, etc). But of course there is overlap between the two; fortunately WP allows entries to have multiple categories. Perhaps I shouldn't have included Crossing number (graph theory) above since it's about the topological version of the problem; it's a long article so it might make sense to have a separate article on Rectilinear crossing number or Geometric crossing number (two different names for the same thing). Fáry's theorem seems like a good example of an article that overlaps both categories since it states that a topological graph has a stricter geometric representation; Scheinerman's conjecture is also of that type. —David Eppstein 03:20, 18 September 2006 (UTC)

You are fully right. pom 05:41, 18 September 2006 (UTC)

Can we put the Leonhard Euler FAC nomination on the project page?

Leonhard Euler is nominated for Featured Article status. I know that the nominator of the article has already posted this 10 days ago on this talk page but I think it would also be worth putting the info more prominently on the welcome page of the project. There's not that much work left to do on it to push it up to the desired quality and it's clearly a goal that should be among the project's priorities. Pascal.Tesson 23:44, 17 September 2006 (UTC)

In related news I've put Ackermann function on FA review. I think it lacks in laymans explination and is not up to current FA standards. --Salix alba (talk) 00:03, 18 September 2006 (UTC)

Speaking of which the primitive recursive article is also in a very sad state. But I digress. Pascal.Tesson 06:17, 18 September 2006 (UTC)

the apes are in question

I just contributed here calculating something. It would be nice if someone could verify what i wrote, because it seems the article contains a mistake. Nerdi 17:50, 18 September 2006 (UTC)

Exponents of mathematics, please help with this

I was going to move the link to the musical ensemble The Exponents from list of exponential topics to exponent (disambiguation) and add this (using the "dablink" template, since the various "otheruses" and "alternateuses" templates are an odious and execrable abomination abhored by all good people):

For other senses of the word "exponent", see exponent (disambiguation).

But the latter page does not exist. This caused me to notice that the list of exponential topics is quite incomplete as a list of Wikipedia articles already existing that belong there. Here's what needs to be done:

• Enter "exponent" in the search bar and click "search", not "go".
• Add to the list of exponential topics the mathematics articles that belong there.
• Add to a new exponent (disambiguation) page the many "exponent" topics on non-mathematics topics, and also add the list of exponential topics to that page after a few of the most prominent mathematical senses of the word, with a note saying the list is fairly long.

I'll be back later to participate in this, but maybe not till tomorrow. Michael Hardy 21:20, 18 September 2006 (UTC)

Ackermann function

Ackermann function is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 15:46, 19 September 2006 (UTC)

256^(4.7*10^9) on prod

It's not in any math categories, so it won't show up on current activity; listing here. --Trovatore 21:15, 19 September 2006 (UTC)

and current activity hasn't updated for a week; is something wrong? Septentrionalis 23:25, 19 September 2006 (UTC)

Tagging talk pages and assessing articles

Wikipedia Assessments within AWB. Click on the image to see it in better resolution

Hi. If you still have work to do tagging talk pages and assessing articles, my AWB plugin might be of interest to you.

The plugin has two main modes of operation:

• Tagging talk pages, great for high-speed tagging
• Assessments mode, for reviewing articles (pictured)

As of the current version, WikiProjects with simple "generic" templates are supported by the plugin without the need for any special programatic support by me. I've had a look at your project's template and you seem to qualify.

For more information see:

• About the plugin
• About support for "generic" WikiProject templates
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• About AWB (AutoWikiBrowser)

Hope that helps. If you have any questions or find any bugs please let me know on the plugin's talk page. --Kingboyk 14:01, 20 September 2006 (UTC)

Manifold Destiny (article)

It has been suggested to me that this page, dealing with a controversial New Yorker dirt-digging story about Perelman, needs semi-protection. I can't quite see that it fits the guidelines at Wikipedia:Semi-protection policy, although there have been some anons making edits there that could get WP into legal trouble. In any case this page is potentially something very troublesome. Charles Matthews 21:28, 21 September 2006 (UTC)

I think you've been mislead by Lubos Motl's comment on your talk page [50]. Look through the history of the article. In particular, look at all the anon edits. I don't see what is trouble some about them; the worst I can see is a new user (not anon) that added an unsourced statement that Tian had never spoken to the New Yorker, but it was later removed by an anon.

One anon even reverted this incredibly biased addition by Motl [51] (there is one anon edit before this revert that added a pov check tag, probably because of Motl's previous edit). This was subsequently reverted by Motl, who does not seems to understand that saying that an article has an "unflattering potrayal" of someone does not imply to anyone that it is true (his edit summary reads: "anonymous edits reverted. The article really can't talk about "unflattering image" of a person because this indicates that the article is true, and Wikipedia would have to become a subject of lawsuit)"). Perhaps realizing that his previous edits were straightforward violations of NPOV, he then made the following "softening" edit: [52], which had the advantage of adding that "many" thought the "biased article" was filled with lies and conspiracies. Anyway, this is clearly this a violation of NPOV, so I reverted it; however, to address the complaint I did add some more info and used the words "paint an unflattering potrayal" to emphasize that this is a potrayal by a specific publication and Wikipedia is not in fact endorsing this is true.

I think given that this article exists, the edits that have been made by new or anonymous users thus far, are in fact of decent quality, certainly better than some by registered users! So I don't see any valid reason someone could want the page semi-protected.

Whether this page should exist is another issue. I didn't used to think so, but given the media coverage, it seems to me that this article is sufficiently notable. Some may not like what is going on, or that dirty underwear is being aired, but this kind of thing is par for the course on many topics. The mathematical community does not have any special protection on Wikipedia against this kind of stuff and shouldn't. Sure, the article could be potentially troublesome, but that is true of many controversial articles. We should deal with it like any other. Keep an eye on it and make sure people don't turn it into a version of their blog. --C S (Talk) 10:56, 22 September 2006 (UTC)

Thanks for filling me in. As I said, after I had been asked my conclusion was not to semi-protect. As you say, watching should be enough for the present. Charles Matthews 11:08, 22 September 2006 (UTC)

Order 3 groups are cyclic proof

Order 3 groups are cyclic proof is up for deletion. Chime in at the appropriate spot. Michael Kinyon 00:28, 23 September 2006 (UTC)

Gleason's theorem

This page was tagged as needing attention. It was a stub which simply stated the theorem in question. I have expanded it quite a bit, and removed the tag; I hope that my edits were sufficient to do so! My expansion has centred mainly on the application of the theorem, in quantum mechanics and the philosophy thereof. On the talk page, someone suggested sketching an outline of the proof of the theorem, which could be a worthwhile addition at some stage, but since most references to the theorem are centred on its uses and implications, this is probably not necessary at the moment (the proof is also hideously long and complicated, and not easy to summarise for an encyclopaedia article). Anyway, I wanted to find out the following. Now that the tag is gone, does your magical bot remove the page from the "needing attention" lists your project maintains? Or should I do that manually? I didn't want to just go ahead and do it, in case it interferes with the bot somehow...do let me know! Byrgenwulf 18:06, 23 September 2006 (UTC)

thanks! the article certainly no longer is a stub (and the "expert needed" tag was probably misplaced). and don't worry, the 'bot will eventually pick up on the tags. Lunch 05:12, 24 September 2006 (UTC)

Maybe this should be raised on the article's talk page, but I don't get the bit about P(y) being 1 for every lattice point y. Is 0 not also a lattice point? Doesn't this require y to be the sum of n (instead of any r) orthogonal atoms? And if true, isn't "the probability is fixed" a weak way of saying: the event is almost sure? --Lambiam^Talk 07:36, 24 September 2006 (UTC)

That's a typo...the "=1" shouldn't have been there (it's gone now). So: any y can be expressed as the union of some (not necessarily n) number of orthogonal atoms x_i. The probability P(y) is the sum of the probabilities P(x_i) (all r of them). "The probability is fixed" simply means "uniquely determined" in this context. Byrgenwulf 10:19, 24 September 2006 (UTC)

Regarding the bot, there is some problem with the computer on which it runs. I'm on the other side of the planet and can't reach the computer remotely. I should be able to bring it up next week after I return to my office. Sorry about the problems (but it is nice to see that people are noticing). -- Jitse Niesen (talk) 14:45, 27 September 2006 (UTC)

Ear curve

Ear curve is up for deletion. Opine at its AfD page. Michael Kinyon 11:22, 24 September 2006 (UTC)

number needs attention

The section on real numbers is quite weak and maybe even misleading. Michael Hardy 02:15, 25 September 2006 (UTC)

I do agree that it is weak. Did you have something particular in mind when you say it's misleading? VectorPosse 02:39, 25 September 2006 (UTC)

I don't know what Michael Hardy had in mind; but the real numbers section conveys the impression that some of them (e.g., 0.1010010001...) are not constants. That is definitely misleading. JoergenB 13:31, 25 September 2006 (UTC)

While we're at it, the "Infinitary extensions" subsection is very misleading, and the "Transcendental numbers and reals" subsection is worth a look (the first paragraph does not deal with transcendental numbers at all). -- Meni Rosenfeld (talk) 10:49, 25 September 2006 (UTC)

It was less misleading after my edit, just before I posted this comment. It was written so as to make it appear that a real number is by definition a decimal expansion. I suppose in some ways that's no worse than saying a real number is a Dedekind cut, or that it is an equivalence class of Cauchy sequences, or any of various other members of that same isomorphism class, but the prevalence of popular errors about the definition of rational and irrational numbers (thinking that those concepts are defined in terms of decimal expansions) makes me cringe at that way of introducing the idea. Michael Hardy 19:47, 25 September 2006 (UTC)

Two remarks:

• the "needs attention" note is still in. It would help if you could copy-and-paste your detailed explanation to the talk page, so people can have a shot at fixing it.
• defining real numbers as (equivalence classes) of decimal expansions, and rational numbers by properties of such expansions, is correct, if awkward.
• I'm not aware of a definition of real numbers that's better than the one via decimal representations, but still has some connection with non-mathematical culture, and can easily be grasped by non-mathematicians. Dedekind cuts and Cauchy sequences, I'm afraid, are right out for that.

RandomP 20:03, 25 September 2006 (UTC)

Saying real numbers correspond to points on a continuous line certainly can be grasped by non-mathematicians. Michael Hardy 20:06, 26 September 2006 (UTC)

For most people, formally defining any kind of number is a strange ritual. Does a definition of positive integers in terms of sets or successors connect with non-mathematical culture? Mathematics itself was very slow to make numbers formal objects. But in terms of historical development, there is evidence that the Dedekind cut idea is the earliest of the four major approaches. (These are: cuts, decimals, sequences, field axioms.) Cuts are also technically simple, while decimals are a beast. However, the number article should mostly leave the formalities to specialized articles, and concentrate on the big picture, which is that real numbers — however defined — "complete" (fill in the gaps of) the line (rationals). Concretely, what's the diagonal of a unit square? What's the area of a unit circle? --KSmrq^T 14:54, 26 September 2006 (UTC)

This may be OR, but I've found that a good way to explain real numbers is by a sequence of shrinking intervals – possibly of zero width, although that's not essential – [L_i, R_i] with L_i ≤ L_i+1 and R_i ≥ R_i+1, and R_i − L_i → 0. The claim is that this determines a unique real number x that is contained in all intervals: L_i ≤ x ≤ R_i. It is easy (for us) to see that this induces a Cauchy sequence as well as a Dedekind cut. There is no need to require the L_i and R_i to be rationals when explaining the idea. The point is, rather, to formalize the notion that "there are no gaps", a closure property. I've found that for psychological reasons I can't explain the notion of an interval shrinking "in the limit" to zero is easier to grasp than limit in general, even for a monotonic sequence. --Lambiam^Talk 22:13, 26 September 2006 (UTC)

You and your students might appreciate Archimedes' proof that the area of a circle is the same as that of a right triangle with base equal to the circumference and height equal to the radius, found in "Measurement of a circle". (See Heath's translation, ISBN 978-0-486-42084-4.)

We want to be careful about the distinction between conveying intuition, which "number" should do, and establishing a workable definition, which "real number" should do. Working from the definition alone we need to be able to do arithmetic, comparisons, and proofs. That's one reason why Dedekind cuts are more appealing than decimal expansions for formal work. Compare with the modern definition of "compact space" in topology, where the "finite subcover" idea is less intuitive but more effective than "closed and bounded".

Back to your original point: Mental models are important for teaching; they are also important for functioning in the real world, a theme that artificial intelligence research has explored under the names "naive physics" or "qualitative reasoning". (See Smith and AAAI for sample reading.) --KSmrq^T 15:56, 27 September 2006 (UTC)

In which subject areas is the term basis function used?

There seems to be disagreement over whether the term basis function is used in functional analysis. I don't know enough about the subject to have an opinion. Could someone comment at Talk:Basis function? --Jtir 13:04, 25 September 2006 (UTC)

There is a problem with the weakness of the article. There must be several areas, eg wavelets, where this is a relevant concept. Charles Matthews 13:12, 25 September 2006 (UTC)

Correct. I looked at the what links here list and found wavelets, plus articles in chemistry, physics, engineering, and business that link to Basis function (I've put a culled, classified, and alphabetized list of linked articles at Talk:Basis_function). A wikipedia search finds many other examples of the term being used. It is starting to seem to me that making the article a dab would be preferable to trying explain all possible uses of the term. I don't have enough WP experience, though, to know what the implications are. --Jtir 21:26, 25 September 2006 (UTC)

A dab page makes mainly sense if we have separate articles on different meanings of the words "basis function". In mathematical use, isn't there a common meaning: an element of some basis of a vector space whose elements are functions? The main problem of the article may be that it starts with the words "In functional analysis" instead of "In mathematics". --Lambiam^Talk 22:38, 25 September 2006 (UTC)

an intro sentence might be, "In mathematics -- particularly analysis -- a basis function is an element of the basis for a function space. The use of the term is analogous to basis vector for a vector space." (NB: some of those words are dab pages so the links are Analysis (mathematics) and Basis (linear algebra).) Lunch 00:56, 26 September 2006 (UTC)

With this formulation, couldn't all the technical content of the article be removed? Basically the article is saying that basis function is a synonym for basis vector in some usages. If so, the article could become a redirect to basis (?) which could parenthetically note the same thing. --Jtir 16:10, 26 September 2006 (UTC)

I don't think a simple redirect to Basis is a good idea. When dealing with bases in function spaces, a Hamel basis (which is what that page focuses on) is usually not the tool of choice. Instead one typically deals with a Schauder basis or, in the more specific Hilbert space setting, an orthonormal basis. Sometimes the word is stretched a bit, such as in the context of Riesz basis (which I think is really just a frame). Michael Kinyon 16:20, 26 September 2006 (UTC)

(I'm gonna CC the conversation here to the basis function talk page. There's some good stuff here that hasn't been mentioned there, and vice versa (along with some repeats). Come on over and join in!) Lunch 19:04, 26 September 2006 (UTC)

Should "Recursively presented group" redirect to "Presentation of a group"

Both finite and recursively presented groups are defined on the page "Presentation of a group". At present "Finitely presented group" redirects to "Presentation of a group" but "Recursively presented group" is just a fairly minimal stub. It would make more sense to me if it too redirected to "Presentation of a group". Bernard Hurley 20:38, 25 September 2006 (UTC)

Yes, it would. I think I created the article, and wasn't aware of that (probably because I thinko'd and created it under the wrong title - sorry, I was just upset we didn't have those articles when rereading Rotman).

RandomP 20:53, 25 September 2006 (UTC)

Well, merge and redirect. Charles Matthews 09:36, 26 September 2006 (UTC)

'Determinants' is a featured article on the French Wikipedia

Are we allowed to steal from the other language Wikipedias? See [53] for a rather nifty treatment of Determinants. It's 111K (vs the 55K of our own English article) and has some nice color illustrations. The language used is not 100% familiar to someone whose linear algebra is several years in the past, but maybe this is the latest thing.

Here are the opening sentences:

"First introduced in algebra to determine the number of solutions of a system of linear equations, the determinant reveals itself as a very powerful tool in numerous domains (study of endomorphisms, search for eigenvalues, differential calculus). It is in this manner that we define the determinant of a system of equations, the determinant of an endomorphism or the determinant of a system of vectors.

"For many operations, the determinant can be defined by a collection of properties (axioms) that we summarize by the term "alternating n-linear form". This definition allows us to make a complete theoretical study and to enlarge further its field of application. But the determinant may also be conceived as a generalization to n-dimensional space of the notion of oriented surfaces and volume. This aspect, often neglected, is a practical and illuminating approach to the properties of the determinant." EdJohnston 23:59, 25 September 2006 (UTC)

I believe that the other language wikipedias use the same license which we have here. So you can use their content freely provide that you give them credit for it and offer it to others under the same condition. In other words, go ahead and copy any of their text and translate it into English. But make sure that you attribute it to them in your edit summary -- specify that it was the French wikipedia and name the article, so that anyone can look in their revision history to see who put the material into it in the first place. JRSpriggs 05:50, 26 September 2006 (UTC)

Yes, you can translate and use here freely. Charles Matthews 09:38, 26 September 2006 (UTC)

Actually, translation is not just permitted (and as far as I can see often not accompanied by credits), but encouraged. Read e.g. Wikipedia:Translations into English. JoergenB 10:13, 26 September 2006 (UTC)

You ought to give credit, though. Anything else is risky under the GFDL. Remember that the original authors still hold copyright, even though they've licensed it to you. If you don't comply with the terms of the license (which requires attribution) you could be infringing. --Trovatore 06:43, 27 September 2006 (UTC)

Well, this sounds reasonable; and 'there are some nice templates', which make it very easy to inform the reader of sources from sister Wikipedia, and which you may place under the heading references. It might be a good idea to use them whenever material is translated, which is seemingly not done now. Not only the determinants article lack such information. JoergenB 13:51, 29 September 2006 (UTC)

Regretfully, I'll have to qualify the statement there are some nice templates. After having been around at the template pages a little, getting more and more confused, but finally finding some adequate explanation, I'l have to rephrase it there are two nice templates (namely Template:German and Template:Polnish). I accidently started by looking at a list of recently translated articles from German to English, and then assumed that I knew the pattern... However, there may be other such templates without proper categorisation (and of course they should not be too hard to create, I suppose, if we want to encourage translators to give more credit).

That discussion perhaps should move to another page, though. JoergenB 16:43, 29 September 2006 (UTC)

Something has gone wrong with LaTeX interpreter

Being realtively new to wikipedia I'm not sure where to post this so it's going here. Something has gone wrog with the LaTeX interpreter on wikipedia so that maths pages are full of lots of raw LaTeX. Bernard Hurley 23:27, 26 September 2006 (UTC)

It seems that the server of formula PNGs (http://upload.wikimedia.org/) is unreachable. As a consequence, PNG formulas only appear in their HTML version. pom 23:52, 26 September 2006 (UTC)

Some images also seem to be broken. I suspect this is a tempory problem which will be fixed in a few hours. Its happened before. --Salix alba (talk) 00:29, 27 September 2006 (UTC)

Have you tried control-shift-R? For several days now, I have occassionally been seeing the formulas unconverted. But they always become correct after control-shift-R. JRSpriggs 06:13, 27 September 2006 (UTC)

That is curious because the LaTeX interpreter is on the server. I can't test this because the problem seems to have gone away, but thanks for the suggestion. Bernard Hurley 08:29, 27 September 2006 (UTC)

If you visted the page while the PNGs are not accesible, the HTML version could be stored in the cache and so appear even after the problem is gone. Purging the cache when everything is working again would fix this problem. JPD (talk) 10:31, 27 September 2006 (UTC)

Spurious dashes

Hmm. Gleason's theorem, at least, still has issues with spurious dashes, though. Does this happen to anyone else? RandomP 02:11, 27 September 2006 (UTC)

Yes, I noticed it an hour or so ago in Character theory. Michael Kinyon 06:37, 27 September 2006 (UTC)

This is a bug in the LaTeX interpreter on wikipedia. The LaTeX interpreter seems to add a dash to the end of formulas containing certain letters and ending in certain other characters. So in the following paragraph "B(m,n)" gets an extra dash:

Let $n,m\in \mathbb {Z}$ where $m$ is odd, $n>10^{78}$ and $m>1$, and let $B(m,n)$ be the free m-generator Burnside group, then every non-cyclic subgroup of $B(m,n)$ is SQ-universal in the class of groups of exponent $n$.

If I change it to "B(x,y)" it is OK:

Let $x,y\in \mathbb {Z}$ where $x$ is odd, $y>10^{78}$ and $x>1$, and let $B(x,y)$ be the free m-generator Burnside group, then every non-cyclic subgroup of $B(x,y)$ is SQ-universal in the class of groups of exponent $y$.

A fix seems to be to add a LaTeX space at the end of the formula but in this case the formula gets displayed with a larger font! So using "B(m,n)\ " we get:

Let $n,m\in \mathbb {Z}$ where $m$ is odd, $n>10^{78}$ and $m>1$, and let $B(m,n)\$ be the free m-generator Burnside group, then every non-cyclic subgroup of $B(m,n)\$ is SQ-universal in the class of groups of exponent $n$.

Incidentally you can get the larger font by including a LaTeX space so:

• "a" gets interpreted as $a$
• "a\ " gets interpreted as $a\$

Bernard Hurley 08:23, 27 September 2006 (UTC)

And a thinner space by using \,: "[<math>a\ </math>]" gives "[$a\$]", while "[<math>a\,</math>]" gives "[$a\,$]". --Lambiam^Talk 10:27, 27 September 2006 (UTC)

There is a bugzilla bug on this. Vote for it to encourage a quick fix. I'd recommend against short term fixes in articles. --Salix alba (talk) 08:27, 27 September 2006 (UTC)

Guys it's totally about the caching. When wikipedia sees an equation it's seen before it re-uses the old image. Sometimes they change the image renderer so you get a version from an old renderer. e.g.: $B(m,n)$ $B(x,y)$ $B(asixhux,sdkcjnjzz)$. So it seems $B(m,n)$ is from the old renderer. $B(mmmnn,nnn)$ Here's another example: $\oint$. Oh look it's broken. That one's cached. But with the new renderer: $Babcasisxajnsx\oint$. I think that last one got fixed when they switched over to dvipng. When you do experiements like this you should always insert random text to trick the caching. 'course I could be wrong about all this, it's just a theory. Dmharvey 12:45, 27 September 2006 (UTC)

That seems to make sense. It would be nice if there were some mechanism to force the re-caching of a formula, but I suppose that could be open to abuse, it would also break any pages that rely on an incorrect old rendition. Bernard Hurley 13:02, 27 September 2006 (UTC)

I did a checkout on phase3 (is this the correct tree?) and was able to reproduce the bug with a fresh mw installation. I found a problem in render.ml, and after fixing it, the problem went away (it was necessary to clear the math table, of course). However, this can't explain why the bug does nolonger occur for new formulas. For details, see bugzilla.--gwaihir 16:25, 27 September 2006 (UTC)

Good stuff. Have you tried running with the preference set to MathML if possible. This has the effect of rendering simple maths as html and for these I'm getting the same problem without a image being used anywhere, so <math>B(m, n)</math> produces the html <span class="texhtml"><i>B</i>(<i>m</i>,<i>n</i>)-</span>. --Salix alba (talk) 17:48, 27 September 2006 (UTC)

Ah the cache issue explaines the difference of apprearance, in some equations

$a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{2}x^{2}+a_{1}x+a_{0}$.

$((\ldots (a_{n}x+a_{n-1})x+...+a_{2})x+a_{1})x+a_{0}\,$.

to me the first looks good, but the letters in the second seem rather blury. I guess the first is cached using an old renderer, but the second is generated using a new renderer. --Salix alba (talk) 08:43, 29 September 2006 (UTC)

Good articles and inline cites

On Wikipedia talk:Good article candidates they have been reworking the criteria, which now currently require the use of inline cites. This resulted in all 11 of our mathematic GA receiving a message warning that the articles may be up for review. Lots of other articles also received the same messages and the physists especially have visiforously protested against the change. Theres now an atempt to reach a consensus on the issue. This particularly affect maths articles as we tend not to use inline cites for the main mathematical content, in Wikipedia:Featured article review/Eigenvalue, eigenvector and eigenspace use of manitory inline cites was contested.

People might like the add their views at on the issue at Wikipedia talk:Good article candidates. --Salix alba (talk) 18:03, 27 September 2006 (UTC)

There is also discussion on Wikipedia talk:Citing sources. This is very relevant as the proposed GA standards would make it difficult for math articles to receive GA status. And there is also discussion on Wikipedia talk:WikiProject Physics. CMummert 03:23, 28 September 2006 (UTC)

Category:Math wars

I nominated this for deletion. The discussion is at Wikipedia:Categories for deletion#Category:Math wars. Comments are welcome. Oleg Alexandrov (talk) 01:51, 28 September 2006 (UTC)

Intro line to analysis

In Areas of mathematics, I think it is misleading to say that analysis is primarily related to rates of change. Many aspects to the theory do not arise in this way. I think it would be better to say that analysis is the study of inequalities, because this is the theme that runs through every branch, at least it seems to me. To quote Krantz (from a book review of 'A Companion to Analysis: A Second First and First Second Course in Analysis') "Analysis is dirty, rotten, hard work. It is estimates and more estimates. And what are those estimates good for? Additional estimates, of course. We do hard estimates of integrals in order to obtain estimates for operators. We obtain estimates for operators in order to say something about estimates for solutions of partial differential equations. And so it goes." Any comments? I tried to change it initially myself, but instantly got reverted. :) I should have started here I suppose, thanks to Oleg for pointing this out to me. Thenub314 03:29, 28 September 2006 (UTC)

Whatever it is, it should match the Mathematical analysis article. (I personally have no really clear "intrinsic" concept of analysis - I know what would be considered analysis amongst the things I know, but if confronted with some mathematics that was totally unknown to me, I might be in doubt as to whether to consider it analysis.

Right now, the areas of mathematics article claims

"Analysis is primarily concerned with change. Rates of change, accumulated change, multiple things changing relative to (or independently of) one another, etc."

which appears to me to be based on real analysis in one variable. Mathematical analysis has:

"Analysis is a branch of mathematics that depends upon the concepts of limits and convergence."

which is what I would consider more appropriate for describing topology. Of course, one approach would be to define analysis historically, as that branch of mathematics that begins with the study of "nice" real functions, integration, and differentiation.

RandomP 03:58, 28 September 2006 (UTC)

Jordan would have probably have considered the "Analysis is... limits and convergence" definition to be correct, but at that time topology did not exist as a separate area of study. It's a matter of historical perspective. The contents of undergraduate analysis courses seem to have been fixed for about the last 50 years, but apart from that it would seem quite difficult to define.

Bernard Hurley 09:31, 28 September 2006 (UTC)

Part of the problem is that "analysis" is actually at least two fields: functional analysis and something which I might term "higher calculus". The former does often concern itself with limits and convergence, but in function spaces rather than spaces like $\mathbb {R} ^{n}$. The latter considers individual functions on $\mathbb {R} ^{n}$ using calculus-like ideas such as the derivative (of course, in many variables). Then there is the mysterious realm of PDE's, which bleeds into differential geometry, while perhaps the entire field is haunted by the ghost of operator theory. Perhaps the best one-sentence summary is that "Analysis is the field of mathematics which studies functions or spaces of functions using techniques related to the notion of limits and convergence." If I wanted another sentence, I would write, "Although all of its techniques, such as differentiation, integration, Fourier analysis, and so on, have seen vast generalizations (for example, p-adic analysis, generalized measure theory, and harmonic analysis on an arbitrary locally compact topological abelian group), it is over the connected, locally compact, and complete metric spaces $\mathbb {R} ,\mathbb {C}$ that they wield the greatest power and demand the most extensive use." This sentence disposes of the vast confusion that arises when you try to generalize about "analysis", since it is now so big. On the other hand, I'm not an analyist, and it seems that by doing this I might be doing the moral equivalent of saying "Algebraic geometry, although generalized to work over arbitrary commutative rings and to answer questions of number theory and even algebra itself, is essentially the study of complex algebraic varieties." Ryan Reich 13:33, 28 September 2006 (UTC)

Funny that this came up; a few days ago, a professor of mine remarked "It's not an exaggeration to say that analysis is the study of estimates". I think there might be some merit to incorporating that word in the definition. Fredrik Johansson 13:36, 28 September 2006 (UTC)

History of Analysis article

I am not a historian, so I probably should not really comment, but is the history section under Mathematical Analysis article seems a bit too good to be true. I did some reading up on the MacTutor math history site. It doesn't seem to indicate that calculus was known in india in the 12th-14th century. Is this really true? In terms of verifiability all I found in any of the articles was a link to some physics prof's web site. Does anyone know more? Thenub314 00:30, 30 September 2006 (UTC)

Citation issues

Lately, there have been many discussions of how to cite science and math articles at WP:GA and WP:CITE. In particular, there are editors out there in Wikipedia-land which would like to see every line in Wikipedia-articles cited. That would include, for example, line-by-line citations for mathematical proofs which I think would be ridiculous. There is currently a proposal at WP:CITE to include an important modification to the guidelines that would state that elementary facts should not/may not be cited. I tried to qualify this with a statement of what things I think (and maybe others think) should be cited in science and math articles and what things should not (and why). Please read, comment, and modify this work here. --ScienceApologist 05:53, 29 September 2006 (UTC)

There is little point giving citations for 'well-known' facts, anyway. Putting a huge effort into that is not going to solve the issue of references for genuinely recherché facts, which are those for which it is valuable to give pointers. Charles Matthews 07:00, 29 September 2006 (UTC)

I would go further. Peppering an article with extra citations is harmful, not helpful, for readers.

Extremists at Wikipedia insist otherwise.

One distorting force is the use of inline citations to address the reliability of our articles, which I believe is a fundamental mistake. Editorial debates belong on a talk page, not an article page. A reader should be able to have confidence that the Wikipedia quality control process has done its job, so that they can safely focus on absorbing content from the article.

Excess citations make it impossible to assess salience. If we cite both for "1+1=2" and "the Riemann hypothesis is true", a reader has no indication that the former is trival and uncontroversial while the latter would be a major claim. Nor will many editors wish to verify dozens and dozens of such citations, so garbage can easily creep in.

If only common sense were more common … --KSmrq^T 17:49, 29 September 2006 (UTC)

agree with above, c.f. 0.999, where every trivial thing, it seems, is cited. Mct mht 00:45, 30 September 2006 (UTC)

I encourage people with views like those above to follow and contribute to the discussions at WP:CITE and WP:GA. Discussing this here won't help to convince the editors who recently revised the GA guidelines. "Consensus" was reached on the changes because nobody from the sciences was contributing to those discussions. CMummert 17:57, 29 September 2006 (UTC)

GA status for Addition?

To my eyes Addition seems to be a good quality article. It might be an idea to put it forward to Wikipedia:Good article candidates, if anyone willing to defend it. BTW it is well cited with both inline and overal cites. --Salix alba (talk) 16:30, 30 September 2006 (UTC)

Citation guidelines proposal

I know you've been having similar concerns about citations and Good Articles here as we have over at Wikipedia:WikiProject Physics. I have a proposal to deal with this debacle. Let's establish, by consensus within the project, a set of guidelines for referencing physics and mathematics articles in Wikipedia. Then, at least, we will have a set of clear guidelines and an established consensus to refer to if we start having problems with WP:GA and WP:FA. I think if we write a reasonable set of guidelines, which respect WP:V and WP:CITE, we'll get little argument from the vast majority of the people over there.

I have already written a proposal, available here: Wikipedia:WikiProject Physics/Citation guidelines proposal. It definitely has a whiff of the first draft about it (some sentences seem pretty tortured), but I'm confident we can bang it into something that is clear and concise. I've tried to write the guidelines in such a way that they don't apply just to physics, although the examples are (by necessity) taken from articles I'm familiar with. I'm hoping that we can get the editors from both WikiProjects (physics and mathematics) to form some kind of a consensus for referencing our articles, which would give it increased legitimacy: we could incorporate the guidelines into both our projects.

To keep the discussion (semi-)unified, please comment at Wikipedia talk:WikiProject Physics or Wikipedia talk:WikiProject Physics/Citation guidelines proposal. –Joke 16:59, 30 September 2006 (UTC)

I urge the participants here to go over the proposal and help reach concensus. I expect it will carry more weight if it is a joint proposal of two active WikiProjects.  --Lambiam^Talk 23:16, 30 September 2006 (UTC)

History of mathematical notation - peer review

History of mathematical notation is seeking peer review. --Salix alba (talk) 19:02, 30 September 2006 (UTC)

Oct 2006

Wikipedia talk:WikiProject Mathematics/Archive 18

Nov 2006

Wikipedia talk:WikiProject Mathematics/Archive 19

Dec 2006

Wikipedia talk:WikiProject Mathematics/Archive 20