# Wikipedia talk:WikiProject Mathematics/Archive 23

This is the archive file "Wikipedia talk:WikiProject Mathematics/Archive 23". It is for March 2007.

## Metric spaces, et al

I'm thinking that we might want to reorganize slightly a set of articles. In particular:

Notice that we have Metric space and Metric (mathematics) both. I think that, if it isn't justified to have both an article for the (quasi)(pseudo)(hemi)(semi)(grape-flavoured)metric as well as the corresponding space, the main article ought to be for the (...)metric rather than the space, as the metric is the more 'basic' object.

It wouldn't really be much work to rewrite the articles to match this, but I'd like opinions on whether it's a good idea before I do such a thing. Also, it seems to me that regardless of whether these are to be moved as I suggested, we need to use consistent terminology throughout this set of articles. I can look into fixing this later today. --Sopoforic 11:51, 25 February 2007 (UTC)

Regularizing the terminology between these articles is a good idea, but I don't see the need to merge the articles on metrics and metric spaces. For important topics like this, there is so much to say that it is easier to split it into two articles, as long as the articles are not covering the same information. In this case, metric covers topics like equivalence of metrics, while metric space includes discussion of the topological properties of the spaces, so there is little redundancy. There is something to be said for articles that are narrow enough that they can be read in one sitting, and there are guidelines on article size that encourage medium-length over long articles.
There are lots of other examples of similar splits. We have Exponentiation/Exponential function, Arithmetical set/Arithmetical hierarchy, etc. CMummert · talk
You misunderstand me. There is currently only one article for each of those (i.e. we have Quasimetric space and not Quasimetric). I think that we should either have two articles (both Quasimetric space and Quasimetric) or that the article should be called by the metric, not by the space (i.e. Quasimetric instead of Quasimetric space). That is to say, I agree with you; do you think we should change the names of the articles? --Sopoforic 14:46, 25 February 2007 (UTC)
I see, I did misunderstand. I don't think the names matter too much, because redirects are cheap. But KSmrq pointed out below that many of the other topological space concepts are in articles with names like regular space, so the current titles for the various types of metric spaces seem to match some informal convention. CMummert · talk 20:52, 25 February 2007 (UTC)
I think both names should exist, one a redirect for the other, and that the primary name should be consistent across these articles (also e.g. injective metric space). But I don't care which convention you use to make them consistent. —David Eppstein 16:46, 25 February 2007 (UTC)
Many notions in topology named "foo" are under "foo space"; for example, "compact space" instead of "compact" (which redirects). Perhaps the idea is that to define compactness we need a space, so the idea does not stand alone. We can — and should — separate "metric" and "metric space". Partly this is because "metric" can stand alone, and partly because the technical definition of a metric used to define a metric space is only one usage. This argument does not apply to the examples that began this discussion, which do not really stand alone nor have significant other uses. --KSmrqT 18:28, 25 February 2007 (UTC)
It's not clear to me how a metric can stand alone (what is the point if it isn't defined on any set? it seems meaningless), but I am far from an expert. I only came across these articles because the topics came up in a book and I thought I'd see what we had. The motivation for my asking this is this: take a look at Pseudometric space. It is mentioned in the lede that this is a set together with a pseudometric, but the rest of the article is spent talking about the pseudometric in particular, and not the space, which made me think that it might be appropriate to rename the articles. But the feeling seems to be that they are fine as they stand, so I'll leave them be. Thanks for your input. --Sopoforic 02:12, 26 February 2007 (UTC)
As content is added to articles, their focus can often change in major ways, making any given title seem odd-fitting. If you expand these articles, say, doubling their size, then a title change may be warrented -- or maybe instead an article should be split in two. For now, the titles fit, they seem consistent, and they leave room to grow. Its an organic process. linas 03:34, 2 March 2007 (UTC)

## LT code

Since Oleg included Category:Coding theory in the list of math articles a few days ago, I've been trying to review all of those new articles, to be sure they make sense. LT code doesn't make much sense to me, the way it's written. I'd appreciate an independent review by somebody here who understands algebraic coding theory.

From reading a little bit about "Luby Transforms" from other sources, it seems the best way to describe them is to think of the encoding and decoding process in terms of the "Exclusive Or" operation. Since the exclusive or of any bit string with itself is identically zero, it's pretty easy to understand how this randomized encoding strategy works. But I sure can't get that out of the existing article, no matter how hard I try.

I think I understand LT codes well enough to rewrite the article. But I'd appreciate some reassurance from someone who has previous experience with them. Thanks! DavidCBryant 01:02, 26 February 2007 (UTC)

I have no experience with these beyond having seen Luby talk about this stuff once years ago. But I think the relevant source to cite for this, among Luby's many erasure code papers, may be the FOCS 2002 one entitled LT codes. —David Eppstein 01:35, 26 February 2007 (UTC)
Thank you for the citations, David. I also found a few reasonably well-written articles that are freely available on the web, and I've finished rewriting LT code. I think it makes more sense now, but would still welcome a review by anyone who likes coding theory. Interestingly, I ran across an online article from which the original Wikipedia article was probably cribbed. At least the style of description, with bins and balls and edges and graphs, is very similar. DavidCBryant 01:25, 2 March 2007 (UTC)

## Category:Important publication

I nominated Category:Important publication and all its subcategories for deletion at Wikipedia:Categories for discussion/Log/2007 February 28. Comments welcome. Oleg Alexandrov (talk) 03:21, 28 February 2007 (UTC)

There is currenlty a confusing number of top level mathematical book categories with considerable overlap. We have
Personally I think Category:Mathematical publications is a better name for the lop level cat than Category:Mathematical literature as literature generally makes me think of fiction. --Salix alba (talk) 09:56, 1 March 2007 (UTC)

## Maximal independent set

I notice that Independent set is redirected to by Maximum independent set, and has 30-40 references. Since Maximal independent set is somewhat stubby and has only one reference (excluding lists), would it make sense also to merge and redirect this one? If not, I'll add enough of a definition to Independent set to refer back to it. Hv 07:11, 28 February 2007 (UTC)

I think it would make more sense to make maximal clique (currently a redirect to clique problem) and maximal independent set point to the same place, since they are complementary. I think there's enough material in both of them to make a real article rather than having to combine with other clique and independent set topics. For instance: any graph has at most 3n/3 of either type of set (Moon and Moser; see also [1]); algorithms for listing all of them in polynomial time per set (see references in [2]); planar graphs and chordal graphs both have O(n) maximal cliques though that may have many more maximal independent sets (and chordal graphs may have many more non-maximal cliques); the number of maximal independent sets on a path or cycle is counted by the Padovan sequence or Perrin sequence [3]. I don't have time to write all this in appropriate detail for an article tonight, but could probably get to it some time in the next few days if nobody else does. Though, the level of self-cites in what I've listed here may mean that someone with less of a conflict of interest would be more appropriate as an unbiased writer... —David Eppstein 07:56, 28 February 2007 (UTC)
Ok, I've added the definition and backref in independent set. If you are moved to write up the detail, I'd be happy to review it (leave me a message) from the POV of someone almost completely unversed in graph theory, but I guess you'd need another expert in the field to properly judge conflict of interest. Hv 08:24, 28 February 2007 (UTC)
I've now completed a major rewrite of the article, and redirected maximal clique to point to it. I'd appreciate any constructive criticism anyone might have, especially regarding the two self-citations. —David Eppstein 02:15, 2 March 2007 (UTC)

## Overfitting, Data-snooping bias, Data dredging, Testing hypotheses suggested by the data

The following four articles:

overlap and should be merged. Statisticians call it data-snooping bias when it's accidental, data dredging if it's intentional (and data mining, before that term got taken over for something else). Testing hypotheses suggested by the data describes the same thing, and also doesn't seem to be a commonly used phrase. Overfitting is what it's called if an algorithm did it (through overparameterization) rather than a human (through pattern recognition), and indeed what the machine learning community calls it. The machine learning community have studied overfitting ad nauseum since it's the problem with tuning parameters to any supervised learning algorithm. In machine learning you always partition data into a training set and testing set, and even use cross-validation (the data dredging article calls using two sets of data "randomization"; "partitioning" would be a better descriptor).

I can see keeping overfitting separate since it's an extreme version of data-snooping bias, but the other three are definitely mergeable. Thoughts? Quarl (talk) 2007-02-28 08:49Z

I tend to agree with mergeing, but keeping overfitting seperate as it is a well used term. Statistical bias is currently a redirect to Bias (statistics) which is a short disambig. Maybe these articles would be better treated as a longer article on Statistical bias? --Salix alba (talk) 08:21, 1 March 2007 (UTC)
I think the three articles ought to be merged, probably under the "data dredging" title, with the others as redirects. I'm not so sure about lumping them in with "statistical bias", since that term is often used to refer to systematic sources of error, or bad data collection techniques, in my experience.
I think a classic example of "overfitting" is in the field of econometrics. I remember looking at some big econometric models, with maybe 350 variables input, and 600 "predicted", and maybe 940 different linear equations tying all these things together. The "technique" was to collect all the data (including "predictions") for past periods of time, and then to run this monster regression to minimize the squared error over all the data by treating the coefficients in the linear system as variables! I'd criticize this "model" as having very little predictive power, and no grounding in laws of cause and effect, but the guys who were building it said "We don't have to convince you – we just have to convince the NSF!" Now they're probably predicting next year's GDP, or the federal budget deficit, and I'm writing articles for Wikipedia.  ;^> DavidCBryant 01:07, 2 March 2007 (UTC)

## Cross-project help, Vandalism Studies

Hello everyone. I was wondering if I couldn't ask for a little assistance from you fine people over here to look over our data at Wikipedia:WikiProject_Vandalism_studies/Study1. While the math isn't hard obviously, something might catch your skilled eyes that we'd miss. Also, if you have any suggestions of other things we should do with the numbers (been a while since college adv stats) we'd love to hear it on the talk page. Thanks you guys. JoeSmack Talk 17:57, 28 February 2007 (UTC)

I think that most vandalism is concentrated on high profile articles, e.g. articles about people or things in the news or articles which might be referenced in home-work assignments. I notice that Jerk, Kinetic energy, Newton's laws of motion (when it is not semi-protected), Black hole (when not semi-protected), Natural number, and Job search engine are among those which are frequently vandalized. Perhaps you need a method which emphasizes such articles. But that depends on the purpose of your survey on which I am not clear. The type of statistics needed depends on what you are trying to do.
Also, I noticed that when you computed the average time to reversion at the end, you added 14 numbers together and then divided by 30 which seems odd. JRSpriggs 10:21, 1 March 2007 (UTC)
That (14:30) looked strange to me too, JR. But it's just an artifact of the way they're doing arithmetic -- the fourteen items are subtotals, and there really are 30 instances (possibly 31? one item may have been misclassified) of vandalism in their data. Details are on this talk page. DavidCBryant 12:05, 1 March 2007 (UTC)

## Monkeying around at FA

The effort to remove Infinite monkey theorem from FA has resumed at Wikipedia:Featured article review/Infinite monkey theorem, despite an admission that the original nomination is not based on an FA criterion and near-cons4ensus that the citation complaints are groundless. I think we have three courses:

• To defeat this nomination,
• To rewrite WP:WIAFA, as WP:WIAGA has been rewritten, or
• To figure out what can replace FA.

This is not, of course, an exclusive or. Septentrionalis PMAnderson 04:30, 1 March 2007 (UTC)

I recommend doing some research and improving the article based on concerns from the review process. I came up with all this without setting foot in a library or even using my journal access, and this is the first time I've taken any interest in the article. Incorporating those and similar references will make the article far better and more FA-compliant at the same time. As a bonus, writing takes less energy than arguing. Melchoir 07:03, 1 March 2007 (UTC)
My personal opinion is that there is no benefit to me or WP that justifies that time it takes to nurse articles through the FA process and keep them at FA status if they are accepted. Other editors are free to do so if they find it more valuable. The FA standards are not particularly flawed, but the review process is not collegial nor enjoyable, and the standards and their interpretation are subject to change at a moment's notice.
Salix Alba commented (this page, 09:46, 5 February 2007, above) that it might be a good idea to make an A-class rating system for the math project to recognize the best articles that we have. This would fall under the third bullet above, although it would supplement rather than replace FA. I find the idea very appealing. CMummert · talk 13:13, 1 March 2007 (UTC)
Yes, I'd also like to give something like that a try. Apparently, some of the larger WikiProjects have their own procedures for assessment and peer review. See Wikipedia:WikiProject Council/Guide#Assessment and Wikipedia:WikiProject Council/Guide#Peer review (and links therein) for some ideas. I think we should just look around what others do (which I haven't done yet), find something we like, copy the procedure and try it out. One possible problem is that maths is so specialized; there are many articles for which I couldn't possibly comment on their correctness / comprehensiveness etc. -- Jitse Niesen (talk) 04:08, 2 March 2007 (UTC)

I've just stumbles across Wikipedia:WikiProject League of Copyeditors, it might be possible to enlist their help in getting keeping FA status. --Salix alba (talk) 19:43, 5 March 2007 (UTC)

I think it's unfortunate that the quality scale, for articles that will never be on the WP main page for reasons of their subject matter, stops at A. Perhaps we should lobby for an "FA-equivalent" class, meaning "just as good as an FA, but has too narrow a potential audience to put on the main page". For a great many of our articles, that would be the correct goal. While in theory the FA process is independent of subject matter, we all know that in reality they'll never put Stone–Čech compactification on the front page no matter how good it gets. (Note that I'm not saying that particular article is of that quality now, but it could be made so, if we wanted to put the effort into it.) --Trovatore 04:31, 2 March 2007 (UTC)
I don't think we have to be so pessimistic about obscure and impenetrable topics. Laplace-Runge-Lenz vector is FA, as are the articles at Category:FA-Class MCB articles. For several of those, I can't imagine that the population of Wikipedia visitors who had the ability and inclination to read the article broke 1%. And yet, at Wikipedia:Featured article candidates/Proteasome for example, no one complained that the article was too technical, and I don't see a suggestion that it shouldn't make the Main Page. Melchoir 04:56, 2 March 2007 (UTC)
Looking around Military history A class review has

Reviewers should keep the criteria for featured articles in mind when supporting or opposing a nomination. However, please note that (unlike actual featured articles) A-Class articles are not expected to fully meet all of the criteria; an objection should indicate a substantive problem with the article. In particular, objections over relatively minor issues of writing style or formatting should be avoided at this stage; a comprehensive, accurate, well-sourced, and decently-written article should qualify for A-Class status even if it could use some further copyediting.

which seems quite sensible. --Salix alba (talk) 09:17, 2 March 2007 (UTC)

Getting back to Infinite monkey theorem, I announce that my work here is done. The benefit solely from deleting the phrases "the chance is not zero, it must be one", "each individual monkey is finite", and "probably an urban myth" already justify the effort. Obviously I also expect the article to now survive FARC. Melchoir 09:01, 3 March 2007 (UTC)

## How can I draw geometric diagrams?

How can I draw geometric diagrams to include in Wikipedia (with free software)? For example, I would like to be able to make diagrams like those in Penrose tiling. Thanks. JRSpriggs 09:03, 2 March 2007 (UTC)

I haven't used the program, but there's an Open Source project page for a freeware program called "Inkscape" that may do what you have in mind. They have distros for Linux, Mac, and Windows. I see that this image in the Penrose tiling article was generated with Inkscape. The image page even includes the instructions that told Inkscape how to make the drawing. DavidCBryant 12:02, 2 March 2007 (UTC)
Please visit Wikipedia talk:WikiProject Mathematics/Graphics, where you will find some suggestions and can ask for more. Geometric diagrams come in many flavors, with tilings being rather special, and aperiodic tilings still more so. In some cases, specialized programs like Tess or C.a.R will do just what you want; in other cases, programming in MetaPost or PostScript (see Casselman) is more effective; and a catch-all graphics editor like Inkscape can either add finishing touches, or perhaps be the sole tool. (Prefer SVG output, but test to be sure the half-broken librsvg renderer used by MediaWiki produces the output you expect.) The options depend on your needs, platform, taste, and budget (Mathematica is powerful but pricey). --KSmrqT 21:40, 3 March 2007 (UTC)

## B+ rating and Wikipedia 1.0

One of Oleg Alexandrov's bots automatically updates the table Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality statistics. Here is a static version from when this message was posted:

Mathematics
articles
Importance
Top High Mid Low Total
Quality
FA 5 3 2 2 12
A 9 6 1 16
GA 2 7 7 16
B 50 47 31 13 141
Start 22 30 30 29 111
Stub 5 16 30 51
Unassessed
Total 88 98 87 74 347

There is no line for B+ articles here, because WP 1.0 does not include B+ as one of their ratings - it is a project-specific rating. There are currently 38 math articles rated B+, which is about 10% of all rated articles. The math rating template already puts all B+ articles into both the B+ and B-class categories, so B+ articles are included in the B line of the table. But this duplication does not seem to be well known.

The upshot of this is that when an article is rated B+, it is not easy to find that out except by browsing categories. There are several options here:

• Get rid of the B+ rating, and just use the B and A ratings.
• Make a separate bot to generate a different table that does include B+ articles.
• Ignore the problem

I am posting this message here to gather opinions about what to do. CMummert · talk 16:22, 1 March 2007 (UTC)

If we are going to rejigger this system, we should remove FA and GA classes from it; the fewer articles approved by those people we have the better. I defer to the graders whether they make a real distinction between B and B+.Septentrionalis PMAnderson 17:24, 1 March 2007 (UTC)
The standards for FA and the stanards for GA are different and run by different groups, and an article can achieve FA status technically even if it has not gotten GA status. GA is where all the problems are, not FA. JoshuaZ 08:02, 2 March 2007 (UTC)

Here is an example of the type of thing that can be done with a project-specific table. Unlike WP 1.0 bot, this program sorts out the B+ articles and uses backlinks to sort the articles by field. Of course there is room for improvement. CMummert · talk 20:21, 1 March 2007 (UTC)

{{Wikipedia:WikiProject Mathematics/Table}}

Looks cool. But you need to put it on a page different than Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality statistics as that one will be overwritten by WP 1.0 bot. How did you generate the above table? You're very welcome of course to use my bot's code if you find it useful. Oleg Alexandrov (talk) 05:13, 2 March 2007 (UTC)
Yes, it would be inside the math wikiproject namespace. The idea is to be completely independent of WP 1.0. I'll put a comment about the script on your talk page. CMummert · talk 05:46, 2 March 2007 (UTC)
Oh, that's a very nice table. I like it much better. One question, though. Is there a list of e.g. stub-class high-importance articles, or start-class algebra articles, or such? I think there's a tool... catscan or something... that will let me do intersections, but it'd be nice if there were already a category. --Sopoforic 06:36, 2 March 2007 (UTC)
I can certainly generate such a list using the same script. There are tables right now that are maintained by hand, and I don't want to figure out how to parse those. Also, my script does not download any articles or talk pages, so I can't fill in "comments" into the tables. But I can make a simple list. I also have to diagnose some bug in my setup. CMummert · talk 14:30, 2 March 2007 (UTC)
I see that Wikipedia:Version_1.0_Editorial_Team/Mathematics_articles_by_quality is sorted by class and then importance, which takes care of the first part. Is there anything for the second part? --Sopoforic 06:38, 2 March 2007 (UTC)
V nice. Minor point in the second table you will need an unassessed field row. If you working on a bot it might be cool to automatically generate the the field specific tables such as [[4]].
If we are redoing thing, it might also be worth considering a B- rating. While assessing article I've found that there is a big gap between Start and B. Not as useful as the B+ rating but worth a look. The reason B+ articles are currently put in both the B and B+ cats was primarily so WP 1.0 bot could do it thing and also to allow some measure of consistancy with other projects and the global table of all assessed articles. --Salix alba (talk) 07:56, 2 March 2007 (UTC)
For the time being, B+ aticles are still in the B class category; my script takes account of the duplication. I agree that, for the WP 1.0 tables, we might as well lump the B+ articles in with the B articles.
The unassessed field row would be there, except that I took care of all the unassessed articles yesterday. It will appear if there are any unassessed articles. The "none" column should also be suppressed when not needed (Oleg's script does so), but that is slightly less trivial so I didn't do it for the original proof of concept. CMummert · talk 14:30, 2 March 2007 (UTC)

### The real question: which ratings are useful?

The central question here is: What ratings are useful for the project? Let's assume that that ratings themselves are useful, so the question is just how many different grades we need and what they mean. Right now, there are 5 that we can assign, which I understand as follows:

• Stub: trivial coverage, half a page or less when printed
• Start: not a stub, but minimal coverage. Could be called C-class.
• B: Obvious holes in coverage, nonstandard POV, or cryptic writing. But some areas are covered well.
• B+: Roughly equivalent to GA status. Experts will recognize holes in coverage.
• A: Excellent article. Roughly equivalent to FA status.

I find it hard to distinguish between Start class and B class. What criteria could be used to distinguish between Start, B and a new B- class? Wouldn't it be easier to just add some guidance like "When in doubt between B class and Start class, go with Start class"? CMummert · talk 14:30, 2 March 2007 (UTC)

B articles are longer than start, but still missing stuff or written from a narrow/uninformed POV. linas 00:06, 3 March 2007 (UTC)
Start-class only have one decent section, or only a couple of lines on the aspects of the topic. The quality of an article is acontinuous thing, as we're assigning discrete quantities to it, so there will always be borderline cases. Tompw (talk) 22:51, 6 March 2007 (UTC)

## Prime factorization of 1?

I made the following change to the Integer factorization:

By the fundamental theorem of arithmetic, every positive integer greater than one has a unique prime factorization. One does not have a prime factorization because one is not defined as a prime number and therefore can not be written as the product of any prime numbers. [5]

An IP editor reverted this leaving this comment on the edit summary: The empty product is 1 (See explaination in the article on the fundamental theorem of arithmetic)[6]

I don't understand how this makes my contribution incorrect. I understand that 1 is the product of no numbers (like how anything to the zero power is 1). But the question of prime factorization is whether a number can be written as the product of prime numbers, so how does that fact say anything about whether 1 can be represented in such a way?--Jersey Devil 17:52, 2 March 2007 (UTC)

The empty product is a prime factorisation, because all the factors in the empty product are primes (trivially). In other words, 1 can be written as the product of 0 prime numbers. Perhaps slightly confusing at first, but quite reasonable, and it makes everything neater. JPD (talk) 18:06, 2 March 2007 (UTC)
Yoink. Melchoir 18:17, 2 March 2007 (UTC)
There's no point in arguing with the empty-product crowd, Jersey Devil. You can point out to them all day long that the sentence "1 can be written as the product of 0 prime numbers" means the same thing as "1 cannot be written as the product of any prime numbers". And they won't listen, or they'll tell you you're wrong. When you ask them to write down 0 numbers and they don't do it, and then claim that they've already done it, and there's "nothing" to it, you can begin to grasp the difference between that kind of formalistic logic and the kind of thinking you and I do. DavidCBryant 19:03, 2 March 2007 (UTC)
No it doesn't. 0 is not the empty set. Septentrionalis PMAnderson 20:16, 2 March 2007 (UTC)
Does "0 can be written as the sum of 0 integers" mean the same thing as "0 cannot be written as the sum of any integers"? -- Dominus 21:01, 2 March 2007 (UTC)
No, it doesn't mean the same. The first statement is true (because the empty sum is defined as 0). The second one is false. Counter example: ${\displaystyle 3+(-3)=0}$. Ocolon 21:07, 2 March 2007 (UTC)

If you think the prime factorization of 1 is confusing, just try thinking about the prime factorization of 0. It's divisible by every prime power! —David Eppstein 19:06, 2 March 2007 (UTC)

This discussion highlights a phenomenon we've seen many times before. (Until recently, I was involved in a similar discussion about 0^0 at the page Exponentiation.) The point was made there, and I'll make it here, that we here at Wikipedia need not argue about the logic of any given convention. We report what is out there in the literature. On the Exponentiation page, we have a section on 0^0 that describes two different conventions in the literature without judging either as being correct or incorrect. (We mathematicians have a hard time admitting that sometimes two different statements can both be correct, Continuum hypothesis aside, since they are matters of convention.) Why not the same thing here? If there are books that say that 1 can be written as the product of primes, fine. Just report the source of the statement. Alongside it, we absolutely have to report that most books restrict any such statement to integers n > 1, whether they "need to" or not. VectorPosse 23:51, 2 March 2007 (UTC)

Off topic here -- the matters you are discussing are matters of convention; the continuum hypothesis is not. --Trovatore 00:05, 3 March 2007 (UTC)
Fair enough.  :) VectorPosse 00:52, 3 March 2007 (UTC)

For a source, see Hardy and Wright: Number Theory. As far as I know, there is no source which denies that 1 is an empty prime product. Editors can write around this convention if they like, but other editors are likely to follow it; it is simplest. Septentrionalis PMAnderson 03:49, 3 March 2007 (UTC)

Strayer's Elementary Number Theory states the Fundamental Theorem of Arithmetic only for integers strictly greater than 1. Then there is an exercise explaining why the statement of the theorem would be (should be?) untrue for 1. So there's the opposing sources I mentioned above. By the way, I'm not sure a book has to deny explicitly that 1 is an empty prime to be a source for the convention that we should restrict attention to integers greater than 1. I think it's also a matter of debate which convention is simpler. (Simpler in terms of the necessary hypotheses, or simpler for the lay reader?) But maybe this discussion has reached the point at which it should be taken to the talk page. VectorPosse 06:10, 3 March 2007 (UTC)

I've now posted my thoughts on the matter at Talk:Fundamental theorem of arithmetic and Talk:Integer factorization. Feel free to chime in at either of those places. VectorPosse 06:37, 3 March 2007 (UTC)
Every positive integer less than 11 can be written as 2k·3m·5n·7p for some non-negative integers k, m, n, and p. In particular, 1 = 20·30·50·70. Get the picture? JRSpriggs 12:42, 3 March 2007 (UTC)
Sorry, but I'm not clear who is meant to "get the picture". Are you talking to me or someone else in the thread? For the record, I agree you and with the aforementioned "empty product crowd". I'm talking about reporting multiple conventions, not arguing the logic. My entry on the talk pages listed above should clarify. (A discussion seems to be forming at Talk:Fundamental theorem of arithmetic.) VectorPosse 13:22, 3 March 2007 (UTC)
To VectorPosse: I should have made it clear that I was addressing Jersey Devil and anyone else who might agree with him.
To Jersey Devil: If instead of just thinking of a product of primes, one thinks in terms of a product of powers of all (distinct) primes, then it should be clear that 1 is in no way exceptional. JRSpriggs 11:55, 4 March 2007 (UTC)
I think I get the picture: every integer n is even, since ${\displaystyle n=2^{0}n}$ and so, 2 is a prime factor of n, ergo, n is even. So, for example, 3 is the product of zero twos, and thus, 3 is even. linas 17:03, 5 March 2007 (UTC)
There is much more of a difference between saying something is a product of primes and saying something has a particular prime factor than there is between the empty product and other prime factorisations, so this smart comment really only misses the point. I can understand people objecting to the idea of empty product conventions, but the original question accepted that, and asked how that affected prime factorisations. The fundamental theorem is more importantly about uniqueness of the factorisation achieved than anything else - it is silly to exclude the case where there is no factorisation needed. The more general "product of a unit and (powers of) primes" (for any UFD) covers this without the difficulties of empty product conventions. JPD (talk) 17:56, 5 March 2007 (UTC)

## Creation of a Mathematical Formulas Page

I believe it would be a good idea to add a page with formulas used in mathematics. They could be grouped into categories of different areas of math with explanations and examples of the equation. This would be of great help for many students.--Trd89 23:16, 2 March 2007 (UTC)

Go for it. It shouldn't be hard to list all three of them, lets see, E=mc2, A=pi r2 and I keep forgetting the third one. linas 00:27, 3 March 2007 (UTC)
We do have pages (e.g. the articles at Lists of integrals) like this, which are of debatable value. However, wikipedia probably isn't the place to create a list of formulae for students. Wikibooks, however, might welcome such a page. The problem with creating them here is that such lists generally won't have much encyclopedic value; they may serve as study aids or quick-reference guides, but they probably aren't appropriate for encyclopedia articles. Also, it would be very difficult to come up with appropriate criteria for inclusion. I could probably produce on the order of a hundred very commonly used formulae without half trying, and I know of whole books consisting of nothing but identities which could conceivably be included in such a list. --Sopoforic 00:49, 3 March 2007 (UTC)

This site would be used for formulas and not identities. for example what (a+b)3 factors down to--Trd89 03:04, 3 March 2007 (UTC)

Some more focus would help. A list of formulas is too broad and the content would be overwhelming. See List of formulae involving π for an example of a more specific page of this type, which has nevertheless undergone attempted deletions because some editors feel such lists are not appropriately encyclopedic. —David Eppstein 03:09, 3 March 2007 (UTC)
Would this be better suited to wikibooks? Septentrionalis PMAnderson 03:50, 3 March 2007 (UTC)

Essentially, you are asking us to take virtually all the articles on mathematics (since they all contain formulas) and strip out the words that give context and meaning to the formulas, then combine the resulting mess into one MONSTER article which be would thousands of times longer than the limit for an article. This is the dumbest idea yet. JRSpriggs 12:34, 3 March 2007 (UTC)

Please be civil. Ocolon 18:01, 3 March 2007 (UTC)
Has Political Correctness gone so far we cannot label a dumb idea as such? We all have dumb ideas, some blatantly so, others with hidden defects; it is vital that we recognized these. Claiming an idea is dumb is not the same as calling a person dumb (or worse). Which is more polite, to be told that I have spinach in my teeth, or to walk around all day with everyone noticing and pretending to ignore it? And which is better for the common good, to let a dumb idea go forward, or to kill it quickly?
The main reason I rarely call ideas dumb is cowardice; if I should be proved wrong, if the "dumb" idea leads to worthwhile results (like Wikipedia!), then the one who looks dumb is me. Since my Wikipedia credibility depends on never being wrong and always being Politically Correct, I can't afford to risk it. ;-)
Instead of chastising the language of JRSpriggs, we should applaud the courage and clarity. We are far better off removing the stigma from making mistakes than taking politeness to the point that we won't mention them. In the words of Thomas J. Watson, “The fastest way to succeed is to double your failure rate.” It is not to pretend that failures are successes! In that spirit, I would encourage JRSpriggs to verbally support Trd89's desire to improve Wikipedia while lambasting the present proposal as hopelessly naive and unworkable. Because maybe there's a germ of a good idea there, one never knows; or maybe the next, unrelated, idea will be terrific. And even if Trd89 churns out nothing but bad ideas, we would like to encourage those who might have good ones. --KSmrqT 23:04, 3 March 2007 (UTC)
Okay. Ocolon 09:26, 4 March 2007 (UTC)

I think the idea to add formula only-pages would cause unnecessary redundancy. The formulae are already where they belong to in an encyclopedia — in those articles that handle their topic. Ocolon 18:01, 3 March 2007 (UTC)

Thinking in terms of our users, mathematical formula is probably a common search term, as a jumping off point to Lists of integrals, List of formulae involving π, List of trigonometric identities, would probably help what they are looking for quickly. --Salix alba (talk) 00:00, 4 March 2007 (UTC)
We might have a jumping-off page that links to those existing lists. However, I foresee endless trouble with such a page if some well-meaning user starts adding formulas to the page itself, and others find themselves inspired to attempt to make an exhaustive list of it (there ought to be, somewhere in project space, an essay about the danger of starting lists with unclear inclusion criteria, because someone will always attempt to make them exhaustive). I don't think it would work without a big bold self-reference saying that most formulas in Wikipedia are found only in articles about their subject and not in any list, and that this is intentional and desired. –Henning Makholm 00:08, 4 March 2007 (UTC)

See also Wikipedia:Articles for deletion/List of well known mathematical formulas. Quarl (talk) 2007-03-04 09:57Z

## Formulae articles suggestion

I have made the request elsewhere, but am copying a version here:

When a formula is described on Wikipedia, a one or two sentence non-mathematical introduction is included - aimed at persons who are outside their field with the given topic.

"It was developed by [abc] in [date]. This formula is used in the area of [xyz] and its purpose is to do [def]."

(Can someone archive part of this talkpage - getting slightly long).

Jackiespeel 18:54, 5 March 2007 (UTC)

Good writing, which we aspire to, does include giving English descriptions of formulas. There are a lot of articles that need to be improved, so this goal is not yet met in practice. If you find one that is particularly confusing, you may add the {{confusing}} template, but doing so does not guarantee that anyone will quickly appear to edit the article. This talk page is archived automatically, as explained at the top of the page. CMummert · talk 00:11, 6 March 2007 (UTC)

## Graphs of theorem dependencies, and tables of examples

How feasible would it be to create either a graph of theorems and axioms or a crossindexed table of examples, like the one at the back of "Counterexamples in Topology"? I know it would be quite an undertaking, but either would be pretty great. Prc314 23:40, 6 March 2007 (UTC)

## To do page

I wanted to help, and looked at the Wikipedia:Pages_needing_attention/Mathematics page. Is it possible to sort these items according to topic, i.e. algebra analysis etc. This would help to guide people (like me) with only special knowledge to the articles needing help much quicker. Thanks. Jakob.scholbach 02:06, 7 March 2007 (UTC)

It's not so easy. We need to devise a scheme to decide whether an article is algebra, analysis, topology, etc., and then program it. It's probably possible, but I'm not convinced it's worth the effort. After all, you can just scan the list and pick out the articles in your specialization. Granted, it takes more time and you'll probably miss some, but after you have poked around for a couple of weeks, you'll soon have a list of things that need to be done and (at least in my experience) the list always grows faster than that you can resolve the issues. -- Jitse Niesen (talk) 23:30, 8 March 2007 (UTC)
There is some progress on this front with the {{maths rating}} template. On that there is a field parameter which can be used to indicate the broad field of an article. Quite a rough tool and its not always clear which field to pick, and theres only 350 or so articles which have been graded to date. Anyway you may find Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Analysis and other pages of some help. BTW its probably time we actually did something with the field parameter, say putting those articles in a category or something cleaver with a bot. --Salix alba (talk) 00:11, 9 March 2007 (UTC)
I can say from experience that having a category would be very convenient for automatically determining which articles are assigned to each field. The current method I use to create this table is not theoretically perfect. CMummert · talk 00:55, 9 March 2007 (UTC)

## Structure theorem for finitely generated modules over a principal ideal domain

Could someone review Structure theorem for finitely generated modules over a principal ideal domain? It has been recently created and caught by our bot as copyvio, but apparently it is a false positive (and would like a member of this project to review it and decide if it is notable enough for Wikipedia (as the only reference is a PDF). If it is suitable, please tag the article appropriately. If it is not, please prod, afd or inform me so that I can proceed. Thanks in advance! -- ReyBrujo 03:08, 7 March 2007 (UTC)

Took a quick look, so i can't vouch 100% for its contents. But this looks like the classic decomposition theorem for modules. I would guess it's already in some other article though. --C S (Talk) 03:19, 7 March 2007 (UTC)
I think in that case it would indeed at least deserve a renaming (or if it is somewhere else being either deleted or transformed into a redirection). I leave it to you since I suck at maths ;) -- lucasbfr talk 17:52, 7 March 2007 (UTC)
I'm not sure why it would be renamed. Despite the long name, that is what it's called. And while the article could use a little work, it's certainly notable and important, and therefore deserves an article. VectorPosse 19:03, 7 March 2007 (UTC)
Ok, I will remove it from the copyvio watchlist. Thanks for the help! -- ReyBrujo 20:56, 7 March 2007 (UTC)

## Jimbo Wales' proposal for credential verification

Recently there has been a small media storm (e.g. [7]) over the revelation that Essjay, a bureaucrat and Wikia community manager, has misrepresented himself, in particular his credentials as a professor of theology at a university. Jimbo Wales initially stated that he regarded this as only utilizing a pseudonym; after learning more details, Jimbo came to the conclusion that Essjay had used his false credentials to bolster his arguments in editorial discussions and so asked him to resign his positions of trust (which he did). Essjay has subsequently left Wikipedia[8].

Jimbo has on his talk page proposed an optional procedure similar to Amazon's "real name" mechanism. Editors wishing to verify their credentials may do so. Jimbo envisions a related policy whereby someone stating unverified credentials would somehow be discouraged for doing so.

Now what does have to do with us? And why am I posting these comments? Well, I've been reading the comments on Jimbo's talk page with regards to this proposal. It struck me that there are several issues that our community is quite unique and perhaps suggestive of a model of how the ideal verification system should work.

Let me basically break up these issues into two groups: 1) trust-based editing, 2) dealing with cranks.

1) There have been arguments against Jimbo's proposal because people understand this (perhaps wrongly) to be about using credentials to bolster one's editing, e.g. "Your edit should be reverted because you don't have a Ph.D. and I do!" I'll try and abstain as much as possible from getting into the issues of whether this is a correct understanding or not of the ramifications of the proposal; my desire is only to explain why our WikiProject experience is relevant to the proposal. In our WikiProject we have a number of credentialed (or near-credentialed :-) ) experts. Somehow we manage to give these people the necessary respect without kow-towing to their authority, and conversely these expert editors manage to not act like such, but utilize policy to justify their edits and decisions.

One explanation for this is that such experts manage to show their expertise in their edits and are generally good at learning the relevant policies in a timely fashion. The expertise is viewed favorably by other editors, who often make the transition to Wikipedia easier for these editors. Speaking for myself, I judge an editor based on his/her edits, but find that credentials often help in understanding someone's background and expertise.

Another explanation is that we are sufficiently insulated from the rest of the community (including a number of trolls and vandals) that we don't have the same issues. This explanation is partly bolstered by the increasingly frequent disconnect between mathematics editors and long-standing non-mathematical editors in discussions on citations, articles reviews, etc. On the other hand, my experience with the second set of issues suggests that the occasional problematic editors we do deal with often require as much effort or even more effort than non-math editors deal with.

2) A number of project members have experience (either directly or indirectly) of cranks, particularly on Wikipedia. A common argument going on right now on Jimbo's talk page is whether policy by itself can handle cranks adequately. Some suggest that the use of credentials can be useful for say, mediators, in determining crankiness. It seems to me that some project members have dealt with such cranks for often very extended amounts of times (with some ongoing). This suggests that it is not as easy for experts to deal with cranks as some have asserted in response to Jimbo's proposal. In my experience, the hardest cranks to handle are the ones that offer myriad citations, sometimes to hard to obtain documents, that can take days or weeks to investigate (by going to the university library, waiting for interlibrary loan, or whatever) and refute.

I think it would be helpful for people to go to Jimbo's talk page and explain their experience, particularly with respect to these two kinds of issues. Somehow we've struck a right balance between relying on credentials but also on a person's body of editing. I think this is something the rest of Wikipedia can learn from, or at least to consider why it may not be viable for all of Wikipedia. --C S (Talk) 21:04, 6 March 2007 (UTC)

Yeah; one of the more troublsome cranks was highly credentialled - the problem was that he (Carl Hewitt) was an overly agressive self-promoter with no self-control. linas 01:11, 8 March 2007 (UTC)
The Carl Hewitt problem was deeper still. Earlier in his career he made substantial, valuable contributions to computer science at MIT. The MIT AI Lab, and MIT generally, can nurture individuals who are bright and unusual. One well-known example is Richard Stallman, who founded the Free Software Foundation, and who arguably marches to a different drummer than most. For MIT at large, a famous example is Noam Chomsky, whose major contributions to linguistics are accompanied by controversial and outspoken political views. But Carl drifted so far out of the mainstream that his own field was unwilling to follow him. He is convinced he is correct, and often asserts priority, both vigorously. Perhaps history will prove him right and everyone else wrong, but at the moment that seems unlikely. Carl is not a common crank, despite a similar disruptive pattern of behavior.
Research is often portrayed idealistically as a pure search for knowledge, innovation, and improvement. With experience, one sees that the search is not completely pure. Human beings have egos and ambitions and insecurities and complex social dynamics, as well as a broad spectrum of intellectual strengths and weaknesses. Whenever we talk, write, or listen, we are dealing with a person, not an abstract machine, and it is helpful to keep that in mind as we evolve our systems and procedures. The (impossible) goal is to support the remarkable good each person may be able to contribute, while protecting ourselves from the not-so-good.
One theory of sociology says that every group draws a boundary around itself, separating acceptable from unacceptable, with ways to (attempt to) enforce the distinction. Similar ideas appear in cultural anthropology. No doubt Wikipedia's ways will provide fertile raw material for a number of doctoral dissertations in these fields. Meanwhile, we must muddle on.
My only suggestion is vague: to combine common sense with compassion, to regard the facts dispassionately while never forgetting the humanity behind them.
We may eventually find that the mathematics community here appears to work well only because it has not been challenged to the same extent as other parts of Wikipedia. Some folks also make that claim about the remarkable scarcity of worms and viruses for the Mac OS compared to MS Windows — and have been making the same claim for decades. My suspicion in both cases is that the communities are at least as important as the systems. --KSmrqT 06:10, 8 March 2007 (UTC)
I don't know if this adds anything, but when a new user, User:LBehounek, arrived and started editing stuff on T-norms, a quick google told me that he was a graduate student or something in the Czech Republic. After noticing a couple more edits were good, I found I didn't have to watch too closely, as he liked to make many small edits at once. Its a sort of "trust, but verify" thing. What made it much easier, though, was that the user used part of his name in the username. I think that this is more common in some communities (math, science?) than in the general population. This openness makes a big difference. Smmurphy(Talk) 06:41, 8 March 2007 (UTC)
The 2 problems with EssJay were (1) that the credentials he claimed to have on Wikipedia got taken as fact and falsely-asserted off Wikipedia and (2) that he asserted credentials to try to gain the upper hand in a content dispute. I don't care how many Ph.D.s someone has; "trust me" is not acceptable verification for Wikipedia articles. Everyone has to cite a reliable source for content asserted in an edit. And let's say that a non-expert makes an edit that they, in good faith, think makes the article better, but unfortunately introduces a subtle error. Then the response is that the person who catches the error fixes it (hopefully in a way that still addresses the first editor's concern) and maybe leaves a polite note on the editor's talk page encouraging them to keep editing but to discuss potential changes on the article talk page first. That's the system now, and I think that it works fine. If the credential verification procedure happens, people are going to be afraid to edit sections created by someone with a higher credential, and I don't want that to happen. Do we have to create a rule or procedure every time some (insert not-nice word of choice here) finds a way to abuse the Wikipedia system?
Anyway, the problem has now been resolved, and now we're all aware to not take someone's asserted credentials at face value. That whole "fool me once..." etc. thing. I'm going to go post this at Jimbo's talk page now. Thanks for bringing it to our attention. --JaimeLesMaths (talk!edits) 07:11, 8 March 2007 (UTC)
Trust. When wikipedia works is it is when there is trust among the editors, trust that editors put NPOV above personal objectives, trust that people do not make false claims about their credentials. When wikipedia breaks is when the trust fails. Either when the user breaks the trust or when the administration fails to trust the users. It would be a sad day when the trust is replaced legislation. --Salix alba (talk) 09:13, 8 March 2007 (UTC)

## cleanup of "independent variable" and "dependent variable"

Both of these pages begin by suggesting that the design-of-experiments usage is the principal topic of the article. That is ridiculous. Then they treat the usage that everyone learns in high school, and independent variable gives a stupid definition by non-essentials: the variable plotted on the x-axis.

Also, there should be a conspicuous link to statistical independence, since that is where the topic of independent random variables is treated.

I'm leaning toward (1) redirecting "dependent variable" to "independent variable" and making the latter to into a disambiguation page.

• An independent variable is
• in mathematics, an argument (input) to a function, the dependent variable being the value (output);
• in design of experiments and various other areas of statistics, a variable controlled by the experimenter or at least one whose causal consequences one wants to consider;
• possibly some computer-science meanings too?

Another problem is how to direct the many links to these pages. I suspect some of them are already pointing to an inappropriate place.

Michael Hardy 22:54, 9 March 2007 (UTC)

I think the notion "dependent" in dependent versus independent variable in the design of experiments and statistical hypothesis testing is not related to the notion of statistical independence of random variables. It is an unfortunate coincidence that the same word is used with unrelated meanings in somewhat related contexts.  --LambiamTalk 17:25, 10 March 2007 (UTC)

It's not compmletely unrelated, but it's certainly quite a different thing. Hence the need for a disambiguation page. Michael Hardy 02:54, 11 March 2007 (UTC)

Isn't it sufficient to put dablinks at the top of the relevant articles? By the way, I followed a few what-links-here links backwards, and about half of those were completely misdirected, involving a meaning of "(in)dependent" independent of that of any the articles under discussion here.  --LambiamTalk 05:34, 11 March 2007 (UTC)

OK, I've reorganized it, and NOT as a disambiguation page. I moved "independent variable" to dependent and independent variables and redirected "dependent variable" to the latter, after pasting some material from "dependent variable" into "dependent and independent variables". I put in a dablink to statistical independence, where the concept of independent random variables is treated. Michael Hardy 23:49, 11 March 2007 (UTC)

## References

In lots of math articles in the Wikipedia, theorems etc. are stated without proper reference. (E.g. the properties of Étale cohomology). In research articles, ideally all statements (except those the author believes to be known by everybody) are cited very concretely, i.e. [..., Theorem ...] etc. I would propose this for Wikipedia articles, too. What do you think? Jakob.scholbach 05:32, 8 March 2007 (UTC)

I guess it couldn't hurt to include theorem numbers in footnotes if the latter are already present. Melchoir 05:56, 8 March 2007 (UTC)
Étale cohomology, like all articles, should at least list some good references at the end so that readers know where to go to find an authoratative treatment. Please feel free to add some if you are familiar with the area. As with many topics, an untrained reader is likely to be unable to easily comprehend these references, even though the article itself may be understandable.
A lot of discussion has gone into the purpose and utility of inline citation in math articles. There are guidelines that document the project consensus on the issue. In practice, the consensus in the math project favors correct and useful articles with few citations over short, less useful articles that give a citation for every sentence. In practice, if you ask politely for a citation of a particular result on the talk page, somebody will usually be able to give you one (or, better, explain why the theorem is true). CMummert · talk 12:36, 8 March 2007 (UTC)
The following is a vigorous endorsement of what CMummert just said. (It is also long-winded; mea culpa.)
Something I have not seen discussed is effort. When I write on a topic I know, my first focus is on the writing. Who is my audience, what must be said, how best to say it, and would a figure help? Often I do a little research for inspiration, completeness, and fact checks. (That includes jogging my memory with things I wrote in the past!) I also like to include at least a few good references, for various reasons; WP:V, Wikipedia's peculiar approach to reliability, is not one of them. Finding and documenting those references can be a great deal of additional work beyond writing the article.
Editors who do not know a topic, who write by copying out of a text with little understanding and no knowledge of context in the field, presumably start with a reference and work forward. For some topics, this describes me, too, though perhaps having more "mathematical maturity" helps always.
Wikipedia grows in both ways. I worry that those who can only copy will force their limitations on the experts. I far prefer a solid well-written article with no references to a citation-studded article that is poorly done.
∗ Some will be shocked that I claim an article can be valuable even with a theorem that is not meticulously correct. Welcome to reality. The peer-reviewed literature contains mistakes. We don't like it, we try to avoid it, but it happens and we can usually recognize the errors and find a correction. (Though I would not like to have been in Andrew Wiles shoes before he found the fix to his famous mistake!) A well-written article serves as a kind of error-correcting redundancy; for, the better we understand what was meant, the easier it is to spot and fix slip-ups. Moreover, an appealing article will attract more readers, and more eyes will spot more problems.
References do not make a good article, they are simply one more positive factor, like figures or examples or meticulously correct theorems. In fact, my approach to references is very much like that of creating a good figure or finding a good example; what will best benefit the reader?
As to the proposal of the poster, consider two scenarios. In one, a copier found a definition or theorem somewhere, transcribed it (correctly, we hope), and included a reference. In the other, an expert patiently explained as one might teach a class, in a manner unlikely to find its way into a formal publication. Do not imagine that upon consulting the references that the clouds will part and illumination will shine through. Do not underestimate the value of an expert explanation.
Mathematics has a considerable reservoir of underground literature, such as lecture notes and unpublished manuscripts, as well as many face-to-face conversations recorded nowhere. After all, when only a handful of people in the world are investigating a specialty, these informal methods of communication are more cost-effective. Even when formal publications do exist, finding a copy can be next to impossible.
Fortunately, mathematics has one significant advantage over, say, paleontology or comparative literature. We don't necessarily need a reference to verify or refute a claim.
What we do need is clear, compelling writing, so we can understand the topic and take an interest. If sometimes that means the references are not all we might hope for, so be it; they may never be, despite our best efforts. --KSmrqT 22:58, 8 March 2007 (UTC)
CMummert, KSmrq, the choice between attributed, inadequate explanations and thorough explanations off the top of the editor's head is a false dilemma and, I think, dangerously misleading. One can build prose that is both thoroughly explained and thoroughly sourced; the catch is that it requires more thinking and more research than one will ultimately communicate or cite. We are beginning to build examples that show that the extra effort is worth it.
On the other hand, if you think you can most efficiently contribute to Wikipedia by personally adopting a different methodology, that's fine; someone else will build upon your work. But please don't discourage other editors from being the best they can be. Melchoir 23:25, 8 March 2007 (UTC)
Sigh. Lest silence be taken to connote assent: your representation, Melchoir, of what I wrote above is a gross distortion. (I do not presume to speak for CMummert.) And I might sadly note: yet again. CMummert and I support the guidelines for appropriate references; you do not. Let's leave it at that. --KSmrqT 07:30, 9 March 2007 (UTC)
You ask us to "consider two scenarios"; surely you will admit that is an incomplete treatment of the issue?
No, let's not leave it at that. I support the application of those guidelines of which I am aware, including WP:SCG. You, on the other hand, supported[9] just last week maintaining the Featured status of an article with zero secondary citations[10] that made concrete mathematical claims in direct contradiction to the published literature. So much for not necessarily needing references. Melchoir 07:48, 9 March 2007 (UTC)
Two more paragraphs, three more distortions; yet another waste of our time. --KSmrqT 09:25, 9 March 2007 (UTC)
Let me guess; in your defense, you didn't actually read through Infinite monkey theorem before casting your drive-by vote-on-principle. Therefore you can't be held responsible for the details of that situation? Melchoir 09:50, 9 March 2007 (UTC)
Woah guys, can we be WP:COOL, this discussion is fast aproaching that of two pissed off monkeys. --Salix alba (talk) 11:44, 9 March 2007 (UTC)
I was perfectly happy to let it go when KSmrq called the FAR "madness"; it was just one edit to a fairly obscure page. But I was definitely pissed off by what I saw in that article. There was pettiness, speculation, and plain old inaccuracy. This from a Featured Article that had been written and maintained by some of our best editors. The bit about the zero-one law, for example, is inspired by Michael Hardy's original version of the article, which made a rather conservative statement about historical usage. Eventually, in late 2004 — I don't have the diff handy — it was explained in a badly inaccurate way by an editor whose contributions include almost no other mathematics articles, and who apparently lacked the habit of precision. The new explanation survived for more than two years, during which the article was Featured and widely read. It wasn't attributed to a reliable source, but then again, neither was anything else, so it didn't stand out. Even when its veracity was challenged on the talk page, there was no source to consult, and the error was not caught or corrected. It took someone (me) to systematically go through the article, cite what's possible, and throw out the rest in order to get rid of the problem. Every other editorial mechanism failed at this most basic of purposes: not being wrong.
I'll cool down if KSmrq acknowledges that in practice, sometimes you really do have to demand a source for something, and you can't be satisfied just because an expert thinks it's self-evident. We can go from there. Melchoir 12:29, 9 March 2007 (UTC)
Actually, I had no plans to respond further. I felt obliged to note that Melchoir had distorted my statements, but one might as well get upset with the sun rising. If he feels the voices trouble him less when he wears the foil hat, there is not much hope of convincing him to remove it. (Here's a classic example.) Having wasted far too much time in the past trying to reason with him, I do not wish to travel that road again, nor to drag others through such an ordeal. --KSmrqT 00:05, 10 March 2007 (UTC)
I admit that I handled that situation badly, and I would do things in a very different order if a similar situation arose today. Regardless of my social missteps, I did manage to improve 0.999... in several dimensions, and I'm not talking about citation count. In the end, everybody congratulated me on a job well done. If you care about results, you can't be sore over that article. Melchoir 00:53, 10 March 2007 (UTC)
Behold a stark demonstration of the folly of arguing with foil-wearers; their inner voices overwhelm the sounds from outside. In his mind, the problem is not his bizarre idea of what falls under WP:OR, but merely his social skills in failing to convince all those who disagree. And he goes on to insist (to me, no less) that he "improved" the article and that everybody offered congratulations! It may seem harsh to refuse to debate such a person, but in fact it is hopeless to try. --KSmrqT 12:02, 10 March 2007 (UTC)
My idea of what falls under WP:OR was stated and applied to 0.999... in an unpopular fashion. I am sorry for that, although I can't apologize for the outcome.
I have no idea what it will take to placate you on this matter. I, and at least one other editor here, have attempted to discover what elements of the old version you would like to restore, and why. To no avail. I've tried to explain that I learned from the experience; you choose not to care. Apparently even the passage of time has done nothing, and you have expressed no wishes for the future. Is there anything that might convince you to stop cherishing an old wound?
And in the event that you refuse to acknowledge that question, what do other people think I should do? Melchoir 20:57, 10 March 2007 (UTC)
Whatever the case, we can hopefully agree that Étale cohomology needs some references, if only for further reading. Also, some form of acknowledgement of the intellectual achievements of the founder(s) of the theory (Deligne? Grothendieck? Serre? Verdier?) would seem in order.  --LambiamTalk 13:42, 9 March 2007 (UTC)
Charles Matthews wisely stayed out of the fray and added two. (Actually, the article already referred to SGA 412, with a link to our article which has extensive bibliographic information.) I have fleshed out the first two references, added more, cleaned up the equation formatting somewhat, and inserted a passing mention (per Springer) of the Künneth formula. I have not made any attempt to review the content of the article, for which not even 200 references can substitute. I would far prefer to see those who know the topic well devote their time to that than to peppering the article with citations. In that spirit, I thank Charles Matthews and R.e.b. for creating the content in the first place, with or without references. --KSmrqT 00:05, 10 March 2007 (UTC)
KSmrq, please note that your motivations may differ from others. Whenever I write about topics that I know very well, I rarely add references, because I simply don't have them any more; I'm working from memory. I think this describes others who write on topics they know well (e.g. Charles Matthews). However, I don't much like writing about things I know very well (they bore me; I do so only out of pity for some sad article); I prefer writing about things I am learning/re-learning/reviewing. These are easy to cross-reference, because I have three texts in my lap all at once. The result is a referenced if perhaps inelegant/stilted article. So it goes. linas 00:55, 10 March 2007 (UTC)
Good point. Here's another. Some topics that I know too well I avoid touching here as much as possible, because I know what can happen to them. The little warning at the bottom of the page says "If you don't want your writing to be edited mercilessly …, do not submit it." Too true. But, motivations aside, you have repeated the two modes of creation I described early. And, as I said, I am in favor of both. --KSmrqT 12:02, 10 March 2007 (UTC)
Gee, Linas. You must have a big lap. Or some skinny textbooks. Maybe both? ;^>
I think I can see both sides of this issue. On the one hand, if a relatively simple mathematical idea is explained well, there's hardly any reason to give a reference; either the reader is going to understand say Euclid's proof that there is no largest prime number, or else he hasn't got a future in mathematics. On the other hand, well-written articles about less familiar topics begin to look too much like OR if they don't contain at least a couple of references.
Today I spent some time researching the Hartman-Grobman theorem. I had never heard of it before, but it seemed intuitively appealing, once I understood it. I figured that the best references would not only explain the theorem – they would also indicate how the theorem got its name. Eventually I found what I was looking for. I found an open on-line copy of a contemporary peper that builds on the result of P. Hartman and D.M. Grobman, and also cites the original papers (from 1959, and 1960). I also added the references to the older papers, only one of which is available on-line (via JSTOR, and therefore not freely available to most readers).
There, I think, is the rub. An awful lot of good math papers are available on-line, for \$24 a pop (unless you're a subscriber to JSTOR, or IEEE, or ACM, or Springerlink, … or you have free access somehow). Most of our readers aren't in that boat. So finding good references for a free on-line encyclopedia is a challenge. Maybe we ought to focus more on helping each other solve that problem and worry a bit less about the exact number of references a given article theoretically ought to have. DavidCBryant 02:59, 10 March 2007 (UTC)
The irony of the distortion of my remarks is that I explicitly said I like references, properly used. And as the Hartman-Grobman research story reinforces, it often takes considerable time and effort to track down the ones we want.
I may be deluding myself, but I have the impression that I am often more successful at locating information on the Internet than are many around me. Search strategies can make a big difference.
• For example, if I search for 'Hartman-Grobman theorem' I miss the sources that reverse the names. If I omit the hyphen, as in 'Hartman Grobman theorem', I get both orders. In either case the information I want may be drowned in a sea of irrelevant hits; an effective response is to insist on the phrase, '"Hartman-Grobman theorem"', not just the individual words.
• Soon I find that Hartman (1982) published Ordinary Differential Equations, 2/e, Birkhäuser, alleged to contain the theorem. If I have a good library or bookstore nearby, perhaps I can have a look, as it seems likely to be a good reference. Otherwise, it's back to the Web. But wait, perhaps it's on Amazon.com, and anyway I'd also like the ISBN.
• So I search for 'Hartman 1982 "Ordinary Differential Equations" ISBN'. Notice that the title is quoted and the ISBN is explicitly requested; in my experience both of these small details are remarkably helpful in quickly locating exactly what I want. Also, here the date helps me restrict to the second edition (and is more effective than trying to say "2nd edition"). I discover that SIAM reissued the book in paperback in 2002, March 4, with ISBN 0898715105, and that the author's first name is "Philip".
• Using this handy online tool, I quickly obtain a correctly hyphenated ISBN-13, namely ISBN 978-0-89871-510-1. Sometimes we get lucky, and Amazon lets us browse inside a book; not so here, but it's a tip worth remembering, especially when all we need is a page or two. (Another tip is to look for author preprints of journal papers.)
• Nothing I have described so far requires any subject knowledge. Sometimes that can make a dramatic difference as well. For example, this seems to be a not-too-exotic topic in ODEs, and I can locate this online book by Gerald Teschl, which discusses the theorem in §7.3. Incidentally, I deliberately did all this without looking at what DavidCBryant chose for the article.
This by no means exhausts strategies, but perhaps it gives a feel for the hunt. It is time-consuming, even online, and sometimes frustrating. There is no guarantee that any good reference is available, no matter how hard we look, for a variety of reasons. In fact, we have not discussed how we judge "good", except implicitly to prefer material that is freely available on the Web.
Both linas and DavidCBryant have told us that successfully researching, learning, and explaining a topic can be gratifying; I concur. I would add that even researching a familiar topic can bring pleasant surprises, as every day more material — both old and new — shows up on the Web. Sometimes one also has the guilty pleasure of discovering that one's own work has been put to new uses.
Let me conclude with a brief mention of how I have been writing up references. My primary guide has been WP:CITET. Although these templates are more verbose than just typing in the data, they spare me the trouble of consistent formatting, and help other editors do the same. I am currently trying the {{citation}} template, which covers books and journals and so on all together. It also supports automatic links from {{Harv}} (and {{Harvtxt}}) citations, the style I prefer. (Am I the only one who hates microscopic lists?!) It's too bad we don't yet have a Wikipedia-wide BibTeX system, but apparently the rest of the world still struggles to catch up with standard practice in the mathematics community. ;-)
One last tip: AMS may be able to help decipher those mysteriously abbreviated journal names, with this online guide.
Example: In the theory of ordinary differential equations, the Hartman–Grobman theorem, as described by Hartman (2002), characterizes solutions in the vicinity of a hyperbolic fixed point (Grobman 1959).
• Grobman, D. M. (1959), "Homeomorphism of systems of differential equations", Doklady Akademii Nauk SSSR (in Russian), 128: 880–881, ISSN 0002-3264
• Hartman, Philip (2002), Ordinary Differential Equations (2nd ed.), SIAM, ISBN 978-0-89871-510-1
(Incidentally, I have used an en dash, not a hyphen, in the theorem name — a stylistic nicety.) Enjoy. --KSmrqT 12:02, 10 March 2007 (UTC)

(KSmrq's comment and mine are both pretty long and have the same indentation level, so I'm putting this line here to separate them. The following comment is mine, Sopoforic's)
DavidCBryant notes that many of our references are not available (to most people) for free, online, and suggests that we work to overcome this. I think that a part of this would involve collecting a list of useful online sources, of which I know there are a few (Diestel's book Graph Theory comes to mind, for that subject). A second part, though, would be providing access to those sources which are legally available, but not practically available. I have occasionally cited works that are in the public domain due to their age, but which were rather hard for me to acquire, due to being in storage, or only available through ILL, or on microfilm, or whatever other difficulties may arise. We could conceivably provide access to these sources by scanning them and linking, but I personally am not sure how I would go about it--supposedly commons is the place to go for things like that, but they don't support PDFs, and JPGs of individual pages aren't as helpful as I'd like.
I don't know whether others would be willing to put in the extra time to scan out-of-copyright sources, but I wouldn't mind doing it, if only I knew what I ought to do; it's a crime that so many public domain works are locked up in subscription services, but without some guidance, I can't help solve that. So, does anyone have any recommendations? I've access to a scanner and a university library, and I've got enough free time to scan things in. If someone will help me to learn what I ought to do, I'd happily scan in relevant sections of books and things.
But that is only one idea. I'd love to hear any suggestions others may have. --Sopoforic 21:37, 10 March 2007 (UTC)
Thank you for the generous offer. There are some details we would want to discuss (proof of copyright status, where to store, format — DjVu+OCR or PDF, cataloging, overlap with existing sources), but let's begin with: can you point us at an online catalog for the library?
Meanwhile, here are three links that may be of interest: Cornell monographs, Internet archive, UPenn list. --KSmrqT 22:31, 11 March 2007 (UTC)
I attend West Virginia University, and the catalogue is here; I believe it is accessible to the public. Of course, I'm not limited to only those books/journals owned by this library. I can also request these things via ILL, so in practical terms I can probably get access to any article or book published after about 1850 (in fact, it would probably be easier for me to get journal articles that aren't owned by the library, due to a number of factors, although that is no strict statement). Actually, I don't know what the license for JSTOR is like, but they have many articles that are out-of-copyright; if the license permits, I (and others, I'm sure) could post those articles somewhere also. I'll get in contact with whoever is in charge of the JSTOR license at my school and see what's what. --Sopoforic 03:52, 12 March 2007 (UTC)
I have the impression that JSTOR already allows public access to out-of-copyright material, and that it only restricts more recently published content. At least, I haven't always had to go through my campus's VPN to gain access to old papers on JSTOR. —David Eppstein 05:12, 12 March 2007 (UTC)
It doesn't seem that it is. I just had someone check who isn't on the campus network, and he got a copy of the first page of the article and a message telling him to subscribe for access. For reference, I gave him this url to an article in the first issue of the American Journal of Mathematics, from 1878. --Sopoforic 05:35, 13 March 2007 (UTC)

I've finally got round to creating a Wikipedia:WikiProject Mathematics/Resources page. The aim of this page is to list good sources to help in referencing of mathematics articles. --Salix alba (talk) 09:44, 12 March 2007 (UTC)

## LaTeX to Wikicode translation

A raw version of a translator is available, by joint effort of User:Oleg Alexandrov and myself. Jmath666 06:57, 25 February 2007 (UTC)

"Joint work" here means that I did the original hack of several lines and then Jmath666 took the effort to make this actually output something usable. This is an interesting way to create articles, surely much faster and more efficient than using the textbox and the "Preview" button. Oleg Alexandrov (talk) 07:08, 25 February 2007 (UTC)

If you insist on getting inline TeX out of this thing, can you at least use \scriptstyle when it's inline? Michael Hardy 03:15, 28 February 2007 (UTC)

Please explain. Jmath666 22:18, 8 March 2007 (UTC)
How about the reverse - Wikicode to LaTeX? Tompw (talk) 16:25, 1 March 2007 (UTC)
The basic stuff (sections, equations, <ref></ref> to \bibitem, but no pictures or links) would not be so hard either. I wanted LaTeX to Wikicode translator for myself, because over time I wrote some introductory material in LaTeX that may be useful. And citations are so much easier if I can just pull them from existing BibTeX databases. Jmath666 22:18, 8 March 2007 (UTC)
Not even speaking of the convenience of a wysiwyg editor instead of hacking the source. Jmath666 01:20, 9 March 2007 (UTC)

By the way, is there some permanent place to make a link on Wikipedia to such tools? Jmath666 22:18, 8 March 2007 (UTC)

There is now a separate user page for the translation. Jmath666 00:09, 15 March 2007 (UTC)

## WikiProject

I've started something called the Mathematics Construction WikiProject (not in development yet), which focuses on making sure that information on an article is verifiable and attributed with reliable sources. If we can do something like this on this WikiProject, it'd be great! Sr13 (T|C) 03:03, 10 March 2007 (UTC)

Um… starting a whole new WikiProject might look suspiciously like a schism. How about making it a "department" of this Project instead, something like the examples at Category:WikiProject peer reviews? Wikipedia:WikiProject Military history seems to be pretty well-organized. Melchoir 04:44, 10 March 2007 (UTC)
Sure, that would be a great idea! Sr13 (T|C) 09:34, 10 March 2007 (UTC)
Not a good idea, unless you are looking for political trouble. Instead, focus on making sure the information in each article is correct and complete, with references that follow our guideline. That is what we really want, while what you propose is a controversial Wikipedia methodology that pretends to be equivalent. Empirical studies have shown that the more inline citations an article contains, the less likely it is that anyone will actually verify everything. (OK, so I'm not aware of any actual studies; but I feel confident that's what they would find.) We must also guard against the bystander effect. I find it telling, and troubling, that you did not propose that articles actually be verified. This is cargo cult behavior. --KSmrqT 12:39, 10 March 2007 (UTC)
Making sure that an article is correct and complete is surely the most important consideration when deciding how to reference an article, but it is not the only thing that "we" really want. Articles should also be written to be robust against the introduction of error by future editors, to simplify accuracy disputes on talk pages, and to aid our readers in their own research. These goals are the responsibility of an interactive encyclopedia, and they aren't met just by producing a version of a given article that is true.
Given that we don't have empirical studies yet, why prejudge Sr13's idea? The worst that could happen is that the department is ineffective and gets shut down. Melchoir 00:10, 11 March 2007 (UTC)
I see...so what you are saying is that verifying should not be a specific group's commitment, but rather each Wikipedian's obligation, and this is what makes an interactive encyclopedia. Sr13 (T|C) 08:45, 12 March 2007 (UTC)
KSmrq's cargo cult idea lit up my imagination: just like a coconut radio carved by a primitive tribe might start working if only its only carved realistically enough... "if we can only add enough ref's, then surely any article can become become factually correct..." .. this thought made me smile. Not understanding that high-tech is important for creating a functional transistor radio is like not understanding that meticulous research is needed for factual accuracy in an article. Just adding references is not enough to make it true.
It took me a bit to understand the bystander effect: just as a mob of bystanders will fail to help a victim in need of help, so an article that is obviously in failing health and factually incorrect might not be helped because it already has so many references and footnotes "standing by"... . linas 00:35, 13 March 2007 (UTC)
It depends on how you interpret the crime in this case how you can apply the bystander effect. KSmrq and you both seem to agree that having so many references "standing by" will cause people to neglect their duty to do some real research on the article. It is certainly the case that in order to take a generic math article and elevate it to something that even Brittanica would be proud to publish will take a lot of work, and that adding piecemeal references will not contribute to this. Most of our articles are not near this state, however, and in fact have no referneces at all. Even adding standard citations (you know, putting Hartshorne chapter and verse in every basic algebraic geometry article) will at least improve them to the point that they are useful as references. At least they will tell you where you might go. It will also provide a basis for further improvement, which brings me to the other interpretation of the bystander effect: I claim that in this case, the crime is indifference and that we are all bystanders, no one making even a first attempt to do something useful in the way of references. Even your and KSmrq's objections to this project (something like "people should improve articles deliberately") reflect a bystander effect: you want editors to self-select to be the one to "save" the article. But it seems to me that the philosophy of Wikipedia is that multiple incremental improvements will lead to a high-quality product, not that an article is not worth being written if it is not going to be written perfectly. I think we should not stand in the way of someone hoping to industrialize the process of making initial increments in citation. Ryan Reich 03:02, 13 March 2007 (UTC)
I have pretty much every math logic article on my watchlist; many of them are in a bad state. I can say from experience that bystanders do make edits to correct errors in these articles; many errors are corrected by anonymous IP editors or by newly registered users with very few edits.
You might be interested in this list of unreferenced math articles. I think it is unreasonable to go through and add references I have never looked at to articles whose content I am not completely familiar with. But I think it would be very appropriate, for example, for someone with a background in algebraic geometry to go through those articles. I would add the crucial caveat that the topic of the article should actually be discussed in some depth by the references added. CMummert · talk 18:56, 13 March 2007 (UTC)
Even if you're not familiar enough with an article to verify it against a reference, you could always add potential sources under a "Further reading" section. Melchoir 19:51, 13 March 2007 (UTC)
Yes, I didn't think about that. The key distinction I make is whether the editor has actually seen the reference or not (at least an online version); I feel very bad adding references to books whose existence and content I am taking on faith. CMummert · talk 13:44, 14 March 2007 (UTC)
Potential sources? I can just see it: thousands of Wikipedia articles chock-full of potential facts "verified" by citing the entire contents of the Library of Congress as potential sources.
Standard rules in academia say if you haven't personally used the original source, even if it is just a reprinting (and especially if it is a translation), you should acknowledge the source you did use; otherwise we risk a game of "Rumors". This proposal goes far beyond that nuance, into total madness. "Potential sources" is a potential disaster. Kill it now. --KSmrqT 05:14, 15 March 2007 (UTC)

## Formatting of categories

Is there any consensus how to format categories? Sometime one sees ${\displaystyle \mathbf {A} }$ (mathbf) or A, sometimes ${\displaystyle {\mathcal {A}}}$ (mathcal). Jakob.scholbach 22:49, 13 March 2007 (UTC)

And worst of all, in some articles (e.g. monoidal category) one sees ${\displaystyle \mathbb {C} }$. Ryan Reich 04:48, 14 March 2007 (UTC)
To add to my comment. ${\displaystyle \mathbb {C} }$ is clearly wrong because it conflicts with well-established notation (my personal opinion is that blackboard bold should be reserved for well-established notation, which is essentially exclusive to the various number sets ${\displaystyle \mathbb {N} ,\mathbb {R} ,\mathbb {C} ,\mathbb {A} }$ (the latter is the adele ring), and so on). There is a reasonable case that A is preferable to ${\displaystyle \mathbf {A} }$ on account of typesetting aesthetics (and an equally reasonable case that the opposite is true on account of the fact that the latter reflects a semantic distinction, namely "math variables", whereas the former is merely formatting), whereas ${\displaystyle {\mathcal {A}}}$ can be said to be preferable on account of being unlikely to conflict with anything at all (calligraphic characters are, as far as I know, not standard notation for anything, whereas bold characters are not infrequently stand-ins for the equivalent blackboard-bold character). I would endorse either A or ${\displaystyle {\mathcal {A}}}$ without preference (though of course consistently in an article) given that the overlarge PNGs we get from TeX markup are actually quite distracting. Ryan Reich 05:04, 14 March 2007 (UTC)
My preference to denote categories is sans-serif boldface, Cat.
Please note that we do not have enough alphabet and style variations to give every type of entity in every specialty its own unique look. My choice, for example, conflicts with the recommended substitution of bold for blackboard bold inline, as in R instead of ${\displaystyle \mathbb {R} \,\!}$ for the real numbers. We try to write each article as clearly as possible, adapting notation where we must, and trusting our stalwart readers to compensate for our inadequacies. --KSmrqT 05:21, 15 March 2007 (UTC)
Yes, this is my preference, too. \mathcal is problematic with categories like Ab and for things like the reals the \mathbb seems to be much more often used than \mathbf. Should a recommendation be part of the style-guideline of math-papers? Perhaps it is also possible to introduce a tag like \cat{...}, at least in the Latex code. (If I write a paper in good old-fashioned offline Latex, this would be the first I would do. If I later need to change the layout, this is done by changing one line of code). Jakob.scholbach 16:11, 15 March 2007 (UTC)

## Inductive symbol

Has anyone ever heard of this? Or should we put it up for deletion as un-notable? JRSpriggs 06:18, 22 February 2007 (UTC)

I'm from Australia and I've never come across it. darkliight[πalk] 06:35, 22 February 2007 (UTC)
We also find in the article:
• Spoke 4: The portion of the number system for which the proof holds, e.g. n=J+ (positive integers)
Universal notation for integers is Z, not J. The creator contributions consist solely of this article, this image, and a new section about it added to mathematical induction (since removed). The image should die as well. --KSmrqT 09:51, 22 February 2007 (UTC)
Spacepotato (talk · contribs) un-PRODed inductive symbol without any explanation or substantive change. JRSpriggs 08:35, 27 February 2007 (UTC)
Well, you can do that -- prod is supposed to be for noncontroversial deletions, so anyone who objects can remove it. Just means you have to go the long way around, unless there's a speedy criterion that fits. At a three-second glance the article looks like a goner, but I haven't put any more effort into it than that, so who knows. --Trovatore 08:40, 27 February 2007 (UTC)
Not that it matters much, but Spacepotato is apparently part of a crew that goes around un-PRODing everything that's proposed for deletion. Why, I'm not sure. DavidCBryant 01:16, 28 February 2007 (UTC)

Oh, a propos of nothing much, I do recall the "J" notation for the integers, from high school. I think the Houghton–Mifflin series of books use it. --Trovatore 08:42, 27 February 2007 (UTC)

I tried to put it up for deletion at WP:AFD (which I have never done before), but I think that I messed the process up somehow. Can someone fix it, please? JRSpriggs 09:58, 27 February 2007 (UTC)
The AfD process seems to be in order. I would suggest an effort to clean up mathematical induction which is not much better than the this one. The intro has too many advanced topics. The informal statement should state induction for the positive integers, not infinite sequences. The worked out example unnecessarily introduces the confusing notion of an empty sum (just start with n=1), and the rest of the article is an unorganized jumble of ideas.--agr 00:12, 28 February 2007 (UTC)
As you can see at Wikipedia:Articles for deletion/Inductive symbol, it was deleted. And now, its associated image is also up for deletion as an orphan image. See Wikipedia:Images and media for deletion#Image:Inductive.gif (see old discussions for March 4). JRSpriggs 04:56, 8 March 2007 (UTC)
The image itself was deleted[11], although somehow the image page still exists.  --LambiamTalk 09:51, 15 March 2007 (UTC)
I have to agree with agr that the mathematical induction needs cleaning up. The current mess is a disgrace! It should focus on the simple case of induction on the natural numbers, possibly also including structural induction, but all talk of transfinite induction needs to be moved to the transfinite induction page. Which also could use some cleaning up, but that is a topic for talk:transfinite induction perhaps. I admit I am hesitant to dive in and do something here; afraid of sticking my hand in a wasps' nest. Hanche 17:54, 17 March 2007 (UTC)

## Back to manual archiving

I removed the Werdnabot invocation. I have been following Werdnabot closely; and it just has too many bugs that manifest themselves in unexpected ways. Like on Tuesday, it did not put any edit summaries into its edits for no apparent reason. Thus we go back to manual archiving. JRSpriggs 08:10, 7 March 2007 (UTC)

By the way, Werdnabot (talk · contribs) has been down (blocked) and appears likely to stay that way. However, there appears to be another bot that we might use for archiving — MiszaBot II (talk · contribs). Has anyone had experience with MiszaBot? JRSpriggs 09:07, 16 March 2007 (UTC)
I looked into it a little yesterday because it looks promising. The code is still under development, and the bot was speedily approved when WerdnaBot was discontinued. The talk page User talk:Misza13 shows one or two bugs in the last two days. So maybe we should wait a couple of weeks until the kinks are worked out. CMummert · talk 11:43, 16 March 2007 (UTC)
OK. And thanks for doing the manual archiving here. JRSpriggs 07:13, 17 March 2007 (UTC)

## Silly pictures

2 or 3 years ago, before Wikipedia was as popular/well known/... as now, I looked at the Mathematics and Computer Science articles and was extremely impressed. I remember noting a correction of a fault in a Taylor/MacLaurin series. It was no more than minor proof reading but within a day somebody had replied "True, why didn't you correct it yourself?"

A couple of years on it all seems to be going seriously downhill. Hard to believe but it just might be better to divide the subject into "Mathematics" and "Popular Mathematics". In the Mathematics section there are NO links to JAVA/COBOL/IGNORANT animations - that sort of nonsense can be viewed in "Popular Mathematics".

2 more possible rules -

• No pictures unless it is Euclidean Geometry.
• No links to Tom, Dick or Harry's website.

Colin M Davidson 62.251.121.16 20:01, 12 March 2007 (UTC)

I do tend to agree about the animations. While they do add value in explaining some points, they can also be very distracting and constantly draws the attention. The other day I removed an animation Image:Vortex-street-animation.gif from spiral only to find that it was actually a featured picture. I've been thinking about ways to present the animations without them being distraction, posibly with a sub-page or with a show/hide box. Animations also gobble up bandwidth. --Salix alba (talk) 21:53, 12 March 2007 (UTC)
Its not just pictures or animations. Popular math articles tend to accrete a varity of unhelpful, cloudy, useless statements, formulas, and templates, and not just bad pictures or websites. This is particularly true for any subject that is "hard" and has a cachet, such as Einstein's theories about spacetime, or quantum mechanics. It seems that novices wish to demonstrate thier ability and intelligence by "improving" these articls in dubious ways, garnering bragging rights by having "written" the WP article on general relativity. (Careful: this is exactly the same thing that the experts do; only that experts get fuzzy at a higher, more abstract level).
I think the Essjay/Jimbo Wales accreditation issue feeds into this. The difference is that I think the only viable mechanism is to have "stable versions": allow this wikiproject to mark a particular version of an article as "acceptable", whereas other version are caveat emptor. linas 00:55, 13 March 2007 (UTC)
"No pictures unless it is Euclidean Geometry" - are you serious ? Would you really remove the images from bifurcation diagram, elliptic curve, blancmange curve, catastrophe theory, topology, braid group, pretzel knot, crosscap, Möbius strip, Klein bottle etc. etc. ? I think these articles would be much poorer as a result. Gandalf61 13:57, 13 March 2007 (UTC)
What about this: An essentially technical article should only have illustrations that help to understand the material presented in the text. As always, such a rule should not be applied rigidly, but the tendency to add images just because it looks good, however tenuous the connection, should be countered.  --LambiamTalk 14:34, 13 March 2007 (UTC)
I have no idea what the original poster meant by "no pictures unless..." as that is clearly ludicrous (and also casts doubt on the rest of his statements). What you say is more reasonable, but I would be averse to such a rule at all. Is the adding of images really a problem? It seems to me there really is a lack of images, especially ones that "look good". Many math animations I've seen, such as at dunce hat (topology), have added considerably to the article. Perhaps this is all in reference to some problem I've not come across, like people adding a picture of Britney Spears holding a doughnut to solid torus. --C S (Talk) 15:33, 13 March 2007 (UTC)
I should add that my favorite example of an image whose inclusion has seemed ludicrous to more than a few but in my opinion is actually instructive is the cartoon in Bring radical. Perhaps this is more along the lines of what the OP thought was taking Wikipedia downhill. --C S (Talk) 15:40, 13 March 2007 (UTC)

### 2nd and last attempt to remove silly pictures.

Klein's bottle (or surface) is historically important. There should be some reference in any self respecting body of knowledge. - More so if it has lead to an interesting branch of mathematics. I am very disturbed by the "silly picture". The picture is 2nd rate (JAVA/COBOL?) and very misleading. We can only be grateful for the writer's text - something along the lines of "But don't try to do this in 3 dimensions."

Restricting pictures to Euclidean geometry is clearly extreme but it seems a better starting point than accepting anything that Tom, Dick or Harry throws into the mill.

Colin M Davidson 62.251.121.16 20:42, 15 March 2007 (UTC)

Which image specifically in the Klein bottle article do you find "silly"? I take it you don't mean the still frame from Futurama since your objection is to a computer-generated image. (How does one use COBOL to generate an image, btw?)
And what about the images is "very misleading"? That the images in the article depict immersions of a Klein bottle? The use of immersions is made rather explicit in the text and in the caption to the first image. Lunch 21:37, 15 March 2007 (UTC)

When you put quotation marks around the words "silly picture", that means either that someone called it that or that someone would call it that but you wouldn't. Yet your words make it appear that that's not what you meant. Michael Hardy 23:50, 15 March 2007 (UTC)

I'd also find it easier to understand if Colin M. Davidson would say WHICH picture he has in mind. Michael Hardy 23:56, 15 March 2007 (UTC)

I can't tell which picture Colin M. Davidson is talking about since they all look good to me. The top one is the standard image of this particular surface, looks like it was done with Mathematica, illustrates exactly the key feature of this immersion. Aside from the two other Mathematica pictures, we have a square-folding diagram, a photograph of a "real" Klein bottle, and the Futurama comic. I find the other two Mathematica pictures quite useful, though the one illustrating dissection of the Klein bottle into two Möbius strips could, I suppose, use a better angle; in particular it's nice to have alternative embeddings shown in the article since, as it is impossible to depict the surface accurately in three, let alone two dimensions, and only one picture. Really, the pictures may be the best part of the article, especially for someone interested just in an overview of the surface. Ryan Reich 00:24, 16 March 2007 (UTC)

The figure-eight one is really a little hard to follow. I can't see where the self-intersection is supposed to be. To me it just looks like a torus where someone grabbed a bit of it and turned it 180 degrees. --Trovatore 00:56, 16 March 2007 (UTC)
You might find it helpful to start with a cylinder with a figure eight base: 8 x [0, 1]. Now glue the top to the bottom but with a half-twist so that opposite parts of the eight get glued together. Also helpful to see this last part is to orient the top and bottom 8's in opposite directions. The twist makes sure the orientations match in the gluing. --C S (Talk) 01:26, 16 March 2007 (UTC)
OK, I can see it now. --Trovatore 01:35, 16 March 2007 (UTC)

From Colin M Davidson's other edits and remarks (e.g., at Talk:Dijkstra's algorithm#EWD would have cried) I deduce that he might be referring to the 'external links' of the Klein bottle article. (Indeed, they lead to one animation and one home page.) Colin, if this is correct, you could have said so from the beginning... The natural thing was to look for pictures in the article itself, since this is what your text seemed to indicate. JoergenB 20:17, 17 March 2007 (UTC)

## Symbols in non-latex code

Is there a page depicting all commonly used symbols like ℤ or ∪ (not in the < math >... < / math> environment) -- and also how to type them? It always takes me an eternity to find them on other pages like union (set theory) etc. Thanks. Jakob.scholbach 16:13, 15 March 2007 (UTC)

Try User:KSmrq/Chars. —David Eppstein 16:35, 15 March 2007 (UTC)
Some are also in the edit characters below the edit box. — 20:46, 15 March 2007 (UTC)
Yeah, but wouldn't it be better to use the < math >... < / math> environment, and let the mathml convert these to the proper symbols? That way, at least one gets a uniform look-n-feel. linas 23:34, 15 March 2007 (UTC)

No, it wouldn't always be better. If we were using TeX in the normal way, it would be better. But often on Wikipedia when TeX is inline, it gets misaligned or is far too big with comical effect. Michael Hardy 23:48, 15 March 2007 (UTC)

Agreed, for Wikipedia in the present state. But hopefully the rendering of math formulas will be fixed in due time and hopefully Wikipedia will be around for a long time. So it might be better to do the right thing and expect it will look good eventually even if it looks bad right now. In other words, the problem is incorrect rendering of math formulas in the web environment; ad-hoc fixes will only make it worse in the long run. Jmath666 03:02, 16 March 2007 (UTC)
J.M.Keynes said, "In the long run, we are all dead." I think we ought to make the pages look as good as possible right now. If the graphics engine ever gets fixed, the in-line HTML will still look OK, and it will be relatively simple to cut everything over to TeX. So we can either (a) make it look OK now, and better eventually, or (b) make it look bad now, and better eventually. Which makes more sense? Think of the readers! DavidCBryant 17:03, 16 March 2007 (UTC)

I nominated one of us, CMummert, for admin. If you are familiar with his work, you can comment/vote at Wikipedia:Requests for adminship/CMummert. Oleg Alexandrov (talk) 03:16, 16 March 2007 (UTC)

## Uniformization of notation at Cyclic group

New user Greg Kuperberg is giving Grubber a hard time at Talk:Cyclic group, arguing about the best notation to use in the article. It seems Greg Kuperberg wants to push for a certain notation because he uses it and it is used in some current research papers.

My understanding of wikipedia policy is that we always use the most common notation. We copy standards, we do not create them. For articles in mathematics, the most common notation is the notation used in authoritative textbooks on the subject. Perhaps someone can point me to a relevant wikipedia policy or provide some backup for Grubber. MathMartin 16:50, 16 March 2007 (UTC)

There isn't an explicit policy on math notation (but see WP:MSM). You are correct that we describe the "real world" rather than recreating it here. So if there are multiple common notations in the real world, we should just describe them, pick one to use, and get on with things. Discussion on the "best" notation tends to go around in circles. In this case, it looks like both involved parties agree that Z/nZ is acceptable. CMummert · talk 18:28, 16 March 2007 (UTC)
Uh, Kuperberg has been editing here under that name since 2004, judging by the history of his talk page. He's hardly a new user. —David Eppstein 05:07, 17 March 2007 (UTC)
Yes, he is not a new user. I should have checked more thoroughly. MathMartin 13:21, 17 March 2007 (UTC)
Hmm. There is a Greg Kuperberg who claims to have coauthored a paper with you, "Fat 4-polytopes and fatter 3-spheres". On the down side, he claims to have a doctorate in mathematics from U.C. Berkeley, which may have brutalized his sanity; and U.C. Davis has a well-known enology program, which may also have had adverse effects. Any comments on his sanity or sobriety from your experience? ;-) --KSmrqT 06:44, 17 March 2007 (UTC)
I don't recall that I've met him in person, just corresponded electronically on that paper and other matters. I have no reason for thinking him any less sane or sober than the typical mathematician. —David Eppstein 06:49, 17 March 2007 (UTC)

## Proposed deletion of "list of cycles"

See list of cycles and Wikipedia:Articles for deletion/List of cycles. Michael Hardy 22:24, 18 March 2007 (UTC)

## A-class review proposal

As several editors have expressed an interest in it, I have created a proposal for an A-class review process for this project. If you are interested, please discuss it at the associated talk page. CMummert · talk 00:36, 6 March 2007 (UTC)

We now have the first article for review Addition see Wikipedia:WikiProject Mathematics/A-class rating/Addition. --Salix alba (talk) 10:14, 9 March 2007 (UTC)

I have moved the proposal to Wikipedia:WikiProject Mathematics/A-class rating. Please feel free to nominate articles! CMummert · talk 13:08, 20 March 2007 (UTC)

## Rating importance calibration

We've been having a discussion on calibration of the mathematical importance rating system over on Talk:Penrose tiling that might be of more general interest to the participants here. —David Eppstein 18:40, 17 March 2007 (UTC)

Using the criteria set forth there, I am tempted to say that Limit (mathematics) has top or high importance, not the mere mid importance it has been dealt.  --LambiamTalk 20:11, 17 March 2007 (UTC)
I agree, as one of the foundations of calculus and many other uses, high seems to be the appropriate value. I've changed the template accordingly. --Salix alba (talk) 22:04, 17 March 2007 (UTC)

David: Your proposed criteria at Talk:Penrose tiling seem excellent at first, but I am worried about them. It seems to me that the principal criterion you have offered for judging the importance of an article is whether you would be embarassed to find that the article was not in the encyclopedia. This seems initially like a reasonable idea, particularly since your examples all elicit about the same level of embarrassment for me as you say they would for you. But I worry that not everyone will be similarly embarrassed by the same things.

If personal embarrassment is used as a criterion, and if there is a consensus about the degree to which individuals would be embarrassed by the hypothetical ommission of articles, then all is well. But I fear that using embarrassment as a criterion will only turn the vague and subjective arguments about "importance" that we have now into equally vague and subjective arguments about personal embarrassment. Nothing will have been gained, and perhaps it will be even worse, since the terms of the discussion will encourage participants to rant and flame about about their personal emotions. Consider how much worse it would be to describe the importance of an article in terms of the rage and fury you would feel if the article were omitted---it should be clear that this way of framing the issue would be unlikely to promote respectful, rational discussions. Using embarrassment as the measure, rather than of rage, would ameliorate the potential problem here, but not eliminate it, I think.

I do not have a useful alternative to offer, but I am concerned that bringing embarrassment into the official guidlines is a step in the wrong direction, and could turn out to be a grave mistake. I hope that the WP:M community can come up with something less likely to promote flame wars. -- Dominus 13:50, 19 March 2007 (UTC)

I would be happy to have a less subjective scale. But the crucial thing for me is that it should not quantify importance only with respect to current mathematics research or pedagogy, but rather importance as a part of an encyclopedia, taking a broader view of connections to nonmathematical topics as part of that quantification. —David Eppstein 15:16, 19 March 2007 (UTC)
The biography importance characteristics do attempt for something more objective bassed around the importance of the topic cross discipines, top is something like big influance over a wide range of topics, high influence on topics outside of the domain (i.e outside of mathematics), mid influence across a number of fields within the domain, and low being of interest primarially within the field. (or something to that effect) see [12]. I find a certain appeal to adapting this to suit maths articles. --Salix alba (talk) 20:16, 19 March 2007 (UTC)

## E8

The E8 (mathematics) lie group hit the news today, which coverage of a full enumeration on the BBC and slashdot, see talk page for links. The article is very technical and could do with some attept to describe it in laymans terms, especially the meaning of the new result. --Salix alba (talk) 20:04, 19 March 2007 (UTC)

This could make a better movie than A Beautiful Mind; read David Vogan's narrative of the project. This site is a good starting point for other info. --KSmrqT 22:44, 19 March 2007 (UTC)
Here's a press-release: http://web.mit.edu/newsoffice/2007/e8.html. Note that Jeffrey Adams, who, as said in that release, is the project leader, has made a Wikipedia account, at User:Jeffreyadams. Nice. Oleg Alexandrov (talk) 03:41, 20 March 2007 (UTC)
Hmmm, compsci heroics. But we need to have more on the mathematics of it. Charles Matthews 10:56, 20 March 2007 (UTC)

## Attention: Probability Theory

I was browsing through the list of vital articles, and found out to my dismay that most (almost all) content has been removed from Probability theory. I have already left some comments at its talk page, but I would like additionally to alert as wide a circle of mathematics editors as possible. Arcfrk 03:25, 21 March 2007 (UTC)

Serious work has started on Probability theory. However, we need experts in probability theory and/or statistics to map out the article (urgent) and contribute high quality content (as the time permits). Arcfrk 04:10, 22 March 2007 (UTC)

## Sobolev space

I would like to attempt to rewrite Sobolev space. This article, which is quite important, is written in a messy manner (in my opinion). Some points which I would like to stress are described in User:Igny/Sobolev space (they are somewhat mentioned in the article, but like I said it is a mess). In particular I would like to stress the connection to the Fourier transform of distributions, which, by the way, deserves a separate article in my opinion. I will appreciate any input from other editors, in particular a blessing to proceed. (Igny 19:17, 21 March 2007 (UTC))

Yes, the article could be better. If you undertake such project, could you please allow for multiple definitions of Sobolev spaces? Perhaps you could structure it as section "Definition of Sobolev spaces", with subsection(s) for definitions, so that more definitions can be added in future. Because:
• different definitions do not always give equivalent spaces
• simple definitions though maybe not as satisfactory have an important place in teaching and are very suitable for encyclopedic purposes. In order of accessibility:
• definition by completion of a space of smooth function (requires only the concept of completion of metric space)
• definition by ${\displaystyle L^{p}}$ weak derivative (requires Lebesgue integral but neither Fourier transform nor distributions)
• the distributions/Fourier transform way goes the whole mile but is the least accessible
• the definition by Fourier series on an interval is a good example for teaching and sometimes a nice trick to know
And yes, distributions should have their own article. So should interpolation of spaces.
Also, it would be good to have at the top of the article something simple yet specific even if maybe not 100% accurate so that people without much background get the correct idea what the topic is (i.e. without knowing what ${\displaystyle L^{p}}$ and multiindex are and so on). Many math article are done this way. Maybe something like this: Sobolev space is a normed space of functions. The norm on Sobolev space of order n involves the value of the function as well as its derivatives of order up to n. The Lebesque spaces ... are a special case of Sobolev spaces of order zero. Negative order Sobolev spaces are defined as dual spaces to spaces of positive order, and Sobolev spaces of non-integer order are defined by interpolation of normed spaces (which is not the same as interpolation of function). The importance of Sobolev spaces lies in the fact that the smoothness of a function is measured by in which Sobolev space it is, and solutions of PDEs fall naturally in Sobolev spaces." Then the example of the most common space, ${\displaystyle H^{1}=W^{2,2}}$, in 2D, with all partials written out, and saying that the derivatives are suitably generalized for this whole thing to work, then the TOC and then the messy technical stuff. Thanks for taking this up! Jmath666 01:12, 22 March 2007 (UTC)

Well, I would have to say that the draft article is not written in a very friendly style. We are constantyly asked to have more explanation for the general reader. There is also a constant pressure from experts to remove verbal explanations, replacing them by 'precise' statements and formulae. The difficulty is that articles then lose all chance of access by non-experts. It is fairly typical that an explanatory comment

The Sobolev spaces are the modern replacement for the space C1 of solutions of partial differential equations. In these spaces, we can estimate the size of the butterfly effect or, if it cannot be estimated, we can often prove that the butterfly effect is too strong to be controlled.

was removed by someone in January 2006 claiming it was 'original research'.

Charles Matthews 08:02, 22 March 2007 (UTC)

This is not a draft per se, it is a collection of elements of the future draft. I was just writing things, which the current article lacks or states poorly (again in my opinion). In anyway, I will continue working on my version (make it friendly and so on), which I hope at some moment will be good enough to replace the current version. I just want other editors know about this effort, and contribute with advice if possible. (Igny 13:22, 22 March 2007 (UTC))
Are you sure the desired improvement cannot be attained by a sequence of piecemeal edits – in general a more desirable approach?  --LambiamTalk 14:24, 22 March 2007 (UTC)

Yes explanatory statements for non-experts are needed but the butterfly was a bad one no matter how catchy it sounds; please see the discussion why it was removed. And indeed it was missing references. The reason why Sobolev spaces exist is simply that solutions of PDEs are in general not in the classical ${\displaystyle C^{n}}$ spaces. For example, in 2D and 3D linear elasticity, there are functions with finite deformation energy (=solutions of the elasticity equations; Nature settles to the lowest energy state) that are not bounded and so not even in ${\displaystyle C^{0}}$. One can construct such function as a special kind of spike (this makes a nice picture for the non-specialist), which also shows why point constraints make no sense in >1D, even if engineers merrily keep putting point constraints in their Finite element models all the time. Jmath666 15:21, 22 March 2007 (UTC)

Well, I know why it was removed. I don't care about the butterfly. I do care about the general principle of making things comprehensible. And citing OR about helpful heuristics, which are clearly just that and not assertions, is too much on the silly side for me. Everyone knows that some heuristics are 'folklore'. Charles Matthews 18:00, 22 March 2007 (UTC)

I agree. It is very important to make things comprehensible. I do not think the butterfly statement was helpful heuristics, though. More like an attempt to push the right buttons than to give a clue about the subject. And for me at least it sounds so specialized I would have liked a reference. Jmath666 18:25, 22 March 2007 (UTC)

I don't have time to write anything just now, but I think th first chapter of Susanne C. Brenner and L. Ridgeway Scott, "Mathematical Theory of Finite Element Methods", Springer-Verlag, 1994 (ISBN 0-387-94193-2) is a particularly nice introduction to Sobolev spaces. It ought to be accessible to anyone having had a first course in analysis at the level of, say, Rudin or Hewett and Stromberg. Greg Woodhouse 18:34, 22 March 2007 (UTC)

## Cross-project help part 2: Concluding Vandalism Study 1

Hello again! Wikipedia:WikiProject_Vandalism_studies's first study is finally about finished. We loved you guys' help a few weeks ago in giving some eyeball time to how the study was composed math wise, and now that we're almost done, we're wondering if you wouldn't mind checking over the results. The study's end results themselves are here, and the discussion of what this means for the conclusions is here. We are keeping in mind that measuring is easy, but knowing what you are measuring is the hard part. Any and all comments, critiques and math angles not considered would be much, much appreciated. We want this to be as tip-top as possible before reporting our findings to the community at large. Thanks everyone. JoeSmack Talk 23:59, 24 March 2007 (UTC)

I'm curious what the math community has to say about the proposed merger of several key Wikipedia principles into one: Wikipedia talk:Attribution/Community_discussion. I can't see that it really changes much about the way we do things around here, but I would like to know if there are issues to consider. (Would we have to fight battles over inline citations all over again, for example?) VectorPosse 10:02, 25 March 2007 (UTC)

User:SlimVirgin has written an explanation of why the change was proposed. My personal opinion is that the current wording of WP:ATT is better than WP:V. CMummert · talk 11:25, 25 March 2007 (UTC)
See WP:ATT#How_to_cite_and_request_a_source. We will have to watch this; it used to mandate inline citation, but the present language may be adequate to deal with the inline enforcers. One of them seems to misread it, however, here. You may want to comment on this when you !vote. Septentrionalis PMAnderson 15:16, 25 March 2007 (UTC)
Like SlimVirgin, I see WP:ATT as a needed step forward, if not a panacea. Sadly, there is a heavy thumb on the scales; see these comments by Jimbo Wales. (And, yes, I checked the edit history because his views seemed so startling I wondered if they had been spoofed!)
Perhaps next we can focus on the task of actually checking each article for correctness (and maybe a few other things, such as completeness, clarity, neutrality). Of course, it is meaningless to "certify" an article that "anyone can edit" two seconds later. [If Wikipedia is serious about becoming a trustworthy source, an obvious model is the software community, where lack of reliability can have dire consequences. FreeBSD, for example, is used by businesses that could suffer severe economic and legal harm if their operating system let them down. So, how to allow development and manage the risk? Standard practice is to offer two versions: one "stable" and one "bleeding edge". If you want (or need) to use the latest and greatest features, you may be willing to accept the risk of the experimental version. Wikipedia today gives you no choice. How can a responsible teacher point students to Wikipedia, when at any moment the geometry article, say, might look like this? (Check the edit history; this is hardly an isolated example.)] Happily, efforts are afoot to address this need, so I remain optimistic.
Meanwhile, clearing away Wikipedia's bizarre take on "verifiability" and "original research" can only be seen as a Good Thing (even if we never manage to hunt down and exterminate all members of the "inline citation squad", who insist every statement must have a footnote). --KSmrqT 16:39, 25 March 2007 (UTC)

## KSmrq deletion of other's comments

To KSmrq (talk · contribs): Since you appear to be unable to refrain from accidentally deleting the comments of other users, which you did again to Lambiam and Oleg Alexandrov recently, I suggest that you make a practice of checking the revision history after you save your edits and immediately repairing any damage you caused. JRSpriggs 12:10, 25 March 2007 (UTC)

I find it outrageous that you continue to make the daily temperature swing through such excessive ranges throughout the year, with consequent damage from floods and fires; please desist at once or take steps to correct the damage you cause.
Do I make myself clear? Your personal attack is irrational and offensive. If you want results, pressure the developers. I will be happy to work with any developer who wants to track down this issue.
I am fairly sure that the consequences of this bug are far more deleterious to me than to anyone else, and I have already publicized the problem (as you apparently know) and tried a number of changes in practice to try to work around it.
Frankly, it looks like an flaw in maintaining database integrity through multiple overlapping transactions. I don't know if you know anything about the design of database software, but this is the kind of thing that must be carefully built in and regression tested for bugs in any system that is expected to confront such complexity. It is easy to handle one "atomic" transaction at a time; it is much harder to handle multiple simultaneous transactions with unpredictable event sequencing. --KSmrqT 15:04, 25 March 2007 (UTC)

I am not the one who is being irrational here. Nor am I asking you to do anything which I do not already do myself — I almost always check the revision history after I do an edit to be sure that I did what I meant to do. I would also point out that your edits (together with the bugs you mentioned) have caused this problem as often as all other editors on this project put together. A possible factor in causing this is that your edits are often very lengthy, providing more opportunity for edit conflicts. If you want this to happen less often, you could write your messages off-line and then cut and paste them in quickly to reduce the window for edit conflicts. JRSpriggs 05:17, 26 March 2007 (UTC)

Can you take further discussion of this issue to the user talk space?  --LambiamTalk 07:08, 26 March 2007 (UTC)

I see a reference in Wikipedia:Wikipedia Signpost/Newsroom/Suggestions#Academic paper on Wikipedia to a research paper "Assessing the value of cooperation in Wikipedia" by Dennis M. Wilkinson and Bernardo A. Huberman.[13]. The paper finds that article quality is correlated with both number of edits and number of distinct editors. Is it just me, or is some of the mathematics and statistical techniques a bit off?  --LambiamTalk 14:05, 26 March 2007 (UTC)

## Welcome template for mathematics

The recent welcoming of a new mathematics editor led me to wonder, what would be most helpful to tell a newbie to our mathematics community? Information could go in a new mathematics-welcome template, or on the project page, or both. So, aside from the usual Wikipedia welcome, what might we say?

In particular, what did you find most helpful? Most difficult to discover? What do you find yourself wishing most new editors would do or avoid doing with regard to mathematics articles (that we can teach)? Other comments?

• In the difficult discovery category, I would hate to go back to life without popups (with popupRevertSummaryPrompt=true); the ability to hover over a linked technical term and see its lead paragraph is an incredible timesaver.
• The Help:Formula page is essential, showing the parts of TeX supported by the MediaWiki texvc software. I also found it handy to have my own page of characters; but newbies need help configuring their system to display them all.
• We should continue to expand the reference resources page; I'd love to see a wiki version of a BibTeX-style database across mathematics articles (perhaps bot-assisted).
• Newbies often need illustration assistance; we could be more helpful than Wikipedia:How to create graphs for Wikipedia articles. (A recurring example: commutative diagrams.)
• Beyond WP:MSM, I have suggested some writing tips that I wish were more widely followed.

Our target audience will include a gamut from professional mathematicians to young students; each needs to be told different things (for the former, Wikipedia is not a technical journal; for the latter, there is more to mathematics than you have seen). A good orientation could bring rich rewards. --KSmrqT 06:22, 17 March 2007 (UTC)

This sounds a great idea. --Salix alba (talk) 09:07, 17 March 2007 (UTC)
I am in complete agreement. If I had to choose a list of resources that took me a while to find, those that would have been helpful from the start, I would have listed exactly the resouces KSmrq has proposed above. VectorPosse 10:02, 17 March 2007 (UTC)
One more quick note. I might recommend that the math welcome be constructed in such a way that it supplement the normal welcome template instead of replacing it. (Actually, this is probably what KSmrq already has in mind.) It is likely that the math-specific editors we're targeting will have already received the standard welcome. Besides, the regular welcome has important general Wikipedia info that is indispensable. VectorPosse 10:08, 17 March 2007 (UTC)
I would suggest making a subpage of WP:WPM with resources for new editors, and then making the talk page message a welcome with a pointer to the subpage. Then we could also link to the subpage from WP:WPM and refer to it ourselves as a resource. CMummert · talk 18:28, 17 March 2007 (UTC)
I'd call it something like "Editor resources for mathematics articles", without the word "new", since they are also useful to seasoned editors. As far as I'm concerned KSmrq's buried essay, with a bit more structuring and emphasis on an editor's problems when writing a mathematics article, can be made into one of these resources.  --LambiamTalk 19:56, 17 March 2007 (UTC)
So anybody actually willing to create it? :) Oleg Alexandrov (talk) 03:37, 18 March 2007 (UTC)
Yes, I will begin soon if no one beats me to it.
Some questions:
1. Are we agreed to accumulate the resources on a subpage of the project, and to make our template a minimal augmentation of the standard welcome template?
2. Any other must-have items?
3. Perhaps we should use the "Resources" subpage for this, moving its current contents to "Reference resources".
4. Apropos of which, can our bot-master whip up something to go through the mathematics pages and collect all the references, so that we can begin to massage them into a coherent database? Lazily, I envision beginning with a simple accumulation of exactly what appears in each article, then sorting like entries together, then eliminating duplicates and converting each entry to a standard form, then filling in missing information like ISBN-13, then checking each entry and marking it as confirmed correct (with respect to the data in the entry, without regard to the use of the citation), then taking over the world. This is obviously a naive strategy that may be overwhelmed by size, but it is otherwise easy and incremental. Or perhaps something better already exists of which I am unaware? Or is the consensus that this is a crazy idea that only a fool would undertake?
Continuing suggestions still welcome, of course! --KSmrqT 09:20, 19 March 2007 (UTC)
I will start a thread below on the fourth bullet; it wouldn't fit here. CMummert · talk 12:13, 19 March 2007 (UTC)
One thing to point to is Wikipedia:WikiProject Mathematics/Participants. Not everyone finds their way there. For example CMummert — unaware or just shy? Paul August 05:21, 19 March 2007 (UTC)

One was created a couple months ago: User:C S/welcome. I didn't like it much though, which is why I haven't really used it. Perhaps having something concrete to critique will help. --C S (Talk) 05:40, 19 March 2007 (UTC)

I put something online at Wikipedia:WikiProject Mathematics/Editor resources. Everyone should feel free to add or remove things or criticize what is there. CMummert · talk 13:00, 19 March 2007 (UTC)

### Extracting references from articles

Extracting references from articles is not trivial. It would be relatively easy to get a list of all the instances of {{cite book}} and friends. It would be much harder to automatically deal with hand-formatted references. I could get the contents of every "References" section (there are about 4500 of them), but it would take a lot of massaging. I'm not sure what plan you have in mind for the information. But anyway, I started the program to update my cache of math articles, which is going to take about 12 hours. I can extract whatever data is requested. CMummert · talk 12:13, 19 March 2007 (UTC)

### Interest?

A while back I started writing Wikipedia:WikiProject Mathematics/Editor resources. Is there still interest in this sort of page? It would not be difficult to write Template:maths welcome to point to it. CMummert · talk 11:35, 29 March 2007 (UTC)

Ah, I was looking for that page the day before yesterday but I forgot why I was looking for it before I had found it. The "Editor resources" is very useful to point editors to. I hardly use welcome template myself (information overload) so I'm not really interested in that. -- Jitse Niesen (talk) 12:40, 29 March 2007 (UTC)
Although WP:WPM has an info box mentioning "Editor Resources", it does not link to WP:WPMER.  --LambiamTalk 14:11, 29 March 2007 (UTC)

## Citizendium content

Citizendium is now live, and I thought I'd spend a few moments looking at their mathematics.

[14] is an article about Kummer surfaces, and is more detailed than what we say by quite some way. It is marked GFDL, so let's assume there is no problem in principle if we wanted to import it.

The problem in practice is that one wants to import the wikified content, but to 'edit' (get the marked-up version) one needs an account, and there are procedures for that (real name, CV, etc.). My question is: does anyone in this WikiProject already have an account? Would anyone actually want to create an account for the purposes of importing material here? Charles Matthews 20:49, 26 March 2007 (UTC)

http://en.citizendium.org/wiki/User:Oleg_Alexandrov --Pjacobi 21:16, 26 March 2007 (UTC)
http://en.citizendium.org/wiki/User:Mark_Jason_Dominus --Dominus 22:54, 26 March 2007 (UTC)
Caution. I can't tell what the copyright status of that article is; the notice at the bottom is not clear about how to determine it. It might be better to wait until CZ gets their act together before we start copying from them. I think I have seen comment by Sanger where he suggests that their "to be determined" license may be incompatible with GFDL, and it would be a pain to revert articles because of "contamination". There are some active discussions about licensing at the CZ forums. CMummert · talk 21:22, 26 March 2007 (UTC)
I agree with CMummert. Let's wait with the copying of material. — 21:24, 26 March 2007 (UTC)
Here is a quote from the CZ forum that reinforces what I was saying: "We should not underestimate the potential ills resulting from WP's ability to take CZ content." [15] I don't know that such opinions are representative, but the quote points out the need for caution. CMummert · talk 21:28, 26 March 2007 (UTC)
The current position at Citizendium is summed up by "We are definitely undecided (about the license)". They'll use GFDL for articles derived from Wikipedia, and either cc-by-sa or cc-by-nc for home-grown articles. These are Creative Commons licenses; cc-by-sa is similar to GFDL and would probably allow us to copy their articles; cc-by-nc differs in not allowing commercial redistribution, and thus that would prohibit copying their articles. So, yes, we better wait with copying their stuff. By the way, I also have an account there. -- Jitse Niesen (talk) 00:56, 27 March 2007 (UTC)

Is it OK to link to their articles from ours as we might with MathWorld? JRSpriggs 07:16, 27 March 2007 (UTC)

Personally, I can't see why we can't link to them as a reference or external link. CMummert · talk 12:14, 27 March 2007 (UTC)
Certainly we can link. I have no objection if this new source is treated as just another web site, but perhaps we should allow them to establish credibility before we genuflect. Consider MathWorld, one of the early sources for broad mathematical information on the Web; we have learned over time to be cautious in relying on content there. --KSmrqT 14:25, 27 March 2007 (UTC)
Yeah, let's hope that their licence won't be incompatible with GFDL. I assumed that they wanted to differentiate themselves by having a "better"/different way of doing collaborative editing than Wikipedia, such an attempt is of course laudable, whether it turns out to work or not. Making content transfer a one-way street however, would make it harder to decide later whether they were successful because they had a better model or because they were able to take advantage of Wikipedia content without giving anything back. Oleg Alexandrov (talk) 15:15, 27 March 2007 (UTC)
I don't quite follow. How can they use WP content and then license it under an incompatible license? Doesn't GFDL forbid that? --Trovatore 15:20, 27 March 2007 (UTC)
They can't; it's the material that originates at CZ that they haven't decided how to license. They decided a while back not to take everything from WP, but only take articles when someone will immediately edit them. Some editors will just start from scratch. CZ has a way of marking which articles contain WP content, but I don't know that it's very accurate yet.
This is all a matter of copyright, not intellectual priority. If a CZ article covers something that the corresponding WP article doesn't, we are free to write our own material about it so long as ours is sufficiently different than theirs, regardless of copyright. This is no different than the situation with Brittanica, which has no sort of open copyright. So I find the idea that a closed license will prevent us from using their material to be misleading. CMummert · talk 15:45, 27 March 2007 (UTC)
Heh. It is much easier to write an article by doing a copy and paste from somewhere and going from there, then starting from scratch, even with good references. So I'd think it does matter if their license is compatible with GFDL. Now, the people at Citizendum seem concerned that free sharing would be more advantageous to Wikipedia than to them. I'd doubt that. For example, we've been borrowing a lot from Planetmath, and they copy stuff from us sometimes too, and that benefited both sides and disadvantaged nobody. Anyway, it will be fun to see if Citizendium turns out successful. Oleg Alexandrov (talk) 03:06, 28 March 2007 (UTC)

## Work on probability theory

I have added a Classification section to the probability theory, your comments/updates on it will be useful. To me it also seems that major portion of the article needs extensive copy editing... I am gonna propose this as a candidate for collaboration of the week. Cheers --Hirak 99 15:59, 28 March 2007 (UTC)

hm, would most probabilitists agree that one can "classify" in this way? seems kinda unlikely. i would recommend folks take a look. Mct mht 19:49, 28 March 2007 (UTC)

## Geometric Median

I've created an article on Geometric median, please feel free to improve by adding more information in your free time. Is there a formal way to request for a diagram? Cheers --Hirak 99 16:03, 28 March 2007 (UTC)

It's not formal, but you could leave a request on Wikipedia talk:WikiProject Mathematics/Graphics. By the way, if geometric median is unique, and 1-dimensional median is a special case, then it is also unique, quod non. Same problem in higher dimensions for a set of collinear points of even cardinality, with the empty point set as an obvious case.  --LambiamTalk 08:02, 29 March 2007 (UTC)
Thanks, updated the uniqueness portion in the article. --Hirak 99 10:17, 29 March 2007 (UTC)

## Corollary

I noticed recently that corollary is a redirect page to theorem. I thought someone here might want to make a proper article out of it.--Jersey Devil 01:15, 29 March 2007 (UTC)

• It could be an attempt at humour, similar to the tired old joke of making Self-reference redirect to itself. Terry 02:04, 29 March 2007 (UTC)

I cleaned up Theorem a little a long time ago. The main difficulty is finding any sort of canonical reference for the terminology, in order to get the articles to be more than dictdefs.

Personally, I think it would be useful to make a single article "Theorem, Lemma, and Corollary" that discusses these terms. It would also be nice to do something with Mathematical terminology. But then, a lot of things would be nice.

Here is a quick summary of the various articles on mathematical terminology:

CMummert · talk 02:13, 29 March 2007 (UTC)

## Mathematics now a featured article candidate

Mathematics has been made a featured article candidate.  --LambiamTalk 07:37, 29 March 2007 (UTC)

## Disambiguation for M23, M24, and a few other numbers

A couple of Mathieu groups are listed on a few disambiguation pages that I have edited or will edit soon (e.g. M23, M24). The description of these number given at Mathieu group is incomprehensible to the average person. (Note that I have a Ph.D. in astronomy.) Could someone leave a short (one sentence) description of what these numbers are supposed to be on my talk page so that I can write reasonable entries for these numbers on the disambiguation pages? Thank you, Dr. Submillimeter 10:50, 30 March 2007 (UTC)

The description given at Mathieu group might not have much meaning if you do not know what a group is, but it pretty clearly says that M23, etc. are groups, and doesn't at all suggest that they are numbers. The entry already at M24 seems fairly reasonable to me - a disambiguation page is not the place to have long explanations. It could be reworded to "M24, a Mathieu group (a type of mathematical object)" or something like that. JPD (talk) 11:07, 30 March 2007 (UTC)
Thank you. I will try working with this, although something in even simpler terms would be better. Also, is it possible to write an introductory paragraph to Mathieu group that explains the concept in less technical terms? Dr. Submillimeter 11:28, 30 March 2007 (UTC)
It might be worth trying to get a less technical introduction in the article, but I'm not sure what you mean by simpler terms for the disambiguation. "M24, a Mathieu group"/"the Mathieu group M24" simply tells you its name(s) and provides the link, and "mathematical object" is the simplest way to describe what sort of thing it is. Anything more would either be more technical or would become the sort of long explanation that doesn't belong on a disambiguation page. JPD (talk) 11:43, 30 March 2007 (UTC)
What you have suggested may be the best that can be done for disambiguation pages. It would just be nice for the average reader to understand what it is if they come across the disambiguation pages. That may not be possible, so just "M24, a type of mathematical object called a Mathieu group" may be the only realistic solution. (I hope I have not caused any offense.) Dr. Submillimeter 12:14, 30 March 2007 (UTC)
I had a go at writing a standard dab for the five Mathieu groups. Geometry guy 15:02, 30 March 2007 (UTC)
I made some minor stylistic changes (removing parentheses and periods), but I will otherwise use Geometry guy's dab text. Thank you, Dr. Submillimeter 15:09, 30 March 2007 (UTC)
Yes, that's much better, but it's not going to be possible to give people an idea of what they are unless they already know some group theory, any more than a dab page should explain what a lenticular galaxy or Taoiseach is. JPD (talk) 15:26, 30 March 2007 (UTC)
But hopefully they would be defined sufficiently precise to disambiguate them from other entities sharing a moniker with lenticular galaxies and the Taoiseach. And it is really not much effort to write: [can refer to:] "the Taoiseach, the leader of the Irish cabinet". It may save the reader a click, because that may be just all they needed to know.  --LambiamTalk 13:54, 31 March 2007 (UTC)
I would consider reorganising the first and second paragraphs. To a layman the most interesting thing about them is that they are some of the exceptional cases in the classification of finite simple groups. Once the motivation for why these are objects worth study the reader might be encouraged the to read the more technical details. --Salix alba (talk) 20:21, 31 March 2007 (UTC)

### Addition to the math style manual

Well, I see good agreements above that something needs to be said in the math style manual about this issue. I started a section, Wikipedia:Manual of Style (mathematics)#Choice of fonts. It is just an initial write-up, which I hope reflects the sentiment above. Changes to it and comments here on it are very welcome. Oleg Alexandrov (talk) 15:20, 24 March 2007 (UTC)

There is a certain amount of overlap with the subsubsection Font formatting, which is a bit confused as to whether it is about markup or about typesetting conventions.  --LambiamTalk 18:37, 24 March 2007 (UTC)

### Italic Greek letters

The principal discussions of this have been whether to use italics on Greek names; for example in the article Constantinople. There has been agreement not to do that, because

• the Greek text already stands out from running Roman text,
• our Greek italic font isn't very good, and the bold Greek is worse.

I'm not sure how much this should apply to mathematics; but I see no reason to use α (''α''), when α works fine. Septentrionalis PMAnderson 15:39, 24 March 2007 (UTC)

This is another place where I would like to see flexibility and not policy. Any guidance on the use of fonts for Greek names simply does not apply to mathematics, any more than the use of Roman letters for Roman names implies mathematical variables should be in Roman. I actually think the italic Greek letters look better for variables and they more closely resemble the TeX form (for similar reasons, I tend to use \varphi and \varepsilon rather than \phi and \epsilon in TeX - but \theta rather than \vartheta). Also I sometimes find it helpful to distinguish π (a number celebrated on 14th March in the US and 22nd July in the UK :-) ) from π (e.g., a bundle projection in geometry and topology). Geometry guy 18:48, 24 March 2007 (UTC)
To my surprise, I discovered that the current Manual of Style is rather prescriptive on this point. I searched for some previous discussions, but found nothing. So for the moment, I will edit the MoS to make it less emphatic (excuse the pun). If someone wants to continue this discussion in a new section, I will be happy to contribute! Geometry guy 18:37, 30 March 2007 (UTC)