# Wikipedia talk:WikiProject Mathematics/Archive 10

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## 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

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. --KSmrqT 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. --KSmrqT 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)

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 $\lim_{x \to 0} {\frac{1}{x sin{1/x}}}$ 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. --KSmrqT 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 Vω+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)
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

Template:Axiom

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. --KSmrqT 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:ab and g:bc, the composition gf:ac exists.

This is merely an example. Styling details can be tweaked per taste. --KSmrqT 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. --KSmrqT 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. --KSmrqT 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 [itex] 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)