# Wikipedia talk:WikiProject Mathematics/Archive 17

## 13-digit ISBNs

Above KSmrq, suggests the use of 13-digit ISBNs. However, since many (most?) sites (e.g. Amazon) can not handle 13-digit ISBNs, using them will make many of the "Find this book" links fail when clicking on the ISBN links. For example clicking on: ISBN 0-7167-0344-0, then clicking on "Find this book" link for the Amazon.com entry under the section "Individual online booksellers" finds this page, while doing the same thing for ISBN 978-0-7167-0344-0, gives this result So we might want to hold off for now on using 13-digit ISBNs. In the future I'm sure some enterprising bot will come along and convert all our ISBNs for us anyway ;-) — Paul August 16:03, 1 September 2006 (UTC)

The future arrives four months from today. Rich Farmbrough has a bot [User talk:Rich Farmbrough/Archive/2006Sep#The bot and ISBN-13 contemplating] an automatic change-over. In the linked discussion I mention a few other issues as well. I'm wondering if it would be too cumbersome to provide both ISBN forms (especially for print). Perhaps the MediaWiki ISBN magic could handle it for online use, like the handling of date formats; but, as always, implementation is not in our hands.
Meanwhile, my feeling is that the ISBN-13 form is future-proof and international, and allows the intended book to be found, even if it doesn't find all the sellers the ISBN-10 form matches. Every ISBN has annoying limitations. A paperback and a hardback have different numbers, as do versions of classics provided by different publishers; and each edition has its own number, which is at times good and at other times an obstacle.
Regardless of which ISBN you prefer, please do take a moment to provide one (and, ideally, check its validity).
Another way to assist readers in finding books is to check against online versions. Some texts can be found at Project Gutenberg, but mathematics is a minority there. Fortunately, we have alternatives.
These sites also include links to others. --KSmrqT 18:19, 1 September 2006 (UTC)

## Good articles

I've been going through the list of mathematics Good articles and I'm not sure that some of them really meet the grade. Riemann hypothesis is what I would consider to be the standard for a good article. My main concern is that the articles are either lacking in any history of the topic failing criteria (3a). Also it would be good to see some illustrations (6).

Moreover, I think there is some need to discuss what makes a mathematics good article so we can establish a standard. Maths articles seem to be a bit of a special case as they are often highly technical, so they are likely to have problems with GA criteria 1a: it has compelling prose, and is readily comprehensible to non-specialist readers. We also seem to run into problems with 2b the citation of its sources is essential, and the use of inline citations is desirable, although not mandatory. Often inline citations are not really appropriate as the topic as a whole will be covered in cited textbooks.

Generally our number of GA's is very low with only 15 articles. Are there any other articles out there which people think are especially good? --Salix alba (talk) 10:37, 3 September 2006 (UTC)

I think the article on knot theory is a good target to turn into a GA, and eventually maybe even an FA. It doesn't try to do too much, and what is there currently should be fairly easy to brush up. I note that the section on Conway notation and planar graph notation is incomplete, but shouldn't take too much time to complete. There are several obvious ways to add good illustrations (and illustrative examples) to the article. --C S (Talk) 11:10, 3 September 2006 (UTC)
There's also quite a bit of bickering going on at Grigori Perelman, but it seems to me that this article has recently undergone a great deal of attention and editing and if all disputes can be resolved, I expect it could become a GA. Perhaps even Poincaré conjecture...but that will require a lot more work, and I've dropped the ball on that for which I apologize. But eventually I'll have a decent writeup of Perelman's proof ("alpha" version is at User:C S/todo/PC proof) and we can rewrite the article around that or whatever. --C S (Talk) 11:21, 3 September 2006 (UTC)
Yes I agree that knot theory could be a good target. Are people happy to defend the article, if so I think it should be nominated.
Grigori Perelman and Poincaré conjecture are probably too volitile at the moment GA 5 It is stable, i.e. it does not change significantly from day to day and is not the subject of ongoing edit wars. , that said it might be a good time to list if there are active contributors.
I'd quite like to create a B+ rating, for articles which are nearly but not quite at the standard of GA, we do have a good number of articles listed on Mathematics 1.0 which would fit this category, for example Pi which is good but has been delisted from GA. --Salix alba (talk) 12:05, 3 September 2006 (UTC)

## Rename "Ordinal number"? God forbid!

User:Salix alba wants to rename (move) Ordinal number which is (in my opinion) one of the most important articles in the general area of Set theory. There are more than FIVE HUNDRED articles which link to it by its current name. Now, admittedly the majority of them would just as well be linked to the article which he proposes to put in its place -- an article on "first, second, third, fourth, fifth, etc.", but there is still a large fraction of them which are important mathematics articles. Please resist this disruptive change by talking at Talk:Ordinal number and elsewhere. Notice that there is already a link at the beginning of "Ordinal number" to the section Names of numbers in English#Ordinal numbers which covers the material in which he is interested. JRSpriggs 02:53, 4 September 2006 (UTC)

I agree, of course: "ordinal number" is correct. You can point him to this book, for example:
Halmos, Paul (1974). Naive Set Theory. Springer. ISBN 0-387-900092 Invalid ISBN-6. (reprint of 1960 classic)
Chapter 19 is entitled "ordinal numbers".---CH 21:17, 6 September 2006 (UTC)

## McNugget number is up for AFD

I've listed McNugget number for AFD. This is the second nom (first was by somebody else in October). AFD discussion page People may be interested in looking over the first discussion, which ended as "no consensus". --C S (Talk) 01:03, 5 September 2006 (UTC)

## Multidimensional Gaussian integrals

User:EulerGamma recently removed a section about multidimensional generalizations from the Gaussian integral article for being "complicated" and lacking sources. The topic is real, but the lack of sources for the details is a valid complaint. Unfortunately, the original author seems to have been inactive for several months. I'm sure some people here are knowledgeable enough to check the content (I'm not); please have a look if you do. Fredrik Johansson 20:40, 6 September 2006 (UTC)

## Leonhard Euler is up for FAC

Please see this page for the discussion. Borisblue 00:39, 7 September 2006 (UTC)

## Mathematical Wikiers in Chinese

Dmharvy, here is your link. zh:Wikipedia talk:数学兴趣小组维基人列表----Hillgentleman 03:41, 7 September 2006 (UTC)

## User:WATARU

New user WATARU appears to me to be almost certainly User:WAREL. However he hasn't yet done any of the things that got him banned before. Let's keep an eye out, but not provoke. "Don't start none, won't be none", as Huey P Freeman would say. --Trovatore 20:30, 9 September 2006 (UTC)

see [1]. --Trovatore 18:33, 11 September 2006 (UTC)

Now he's changed the Japanese link at division ring to something else. I don't read Japanese, so I don't know if it's appropriate or not, but given his history I'm not inclined to trust him. He may well be planning some shenanigans at ja.wiki and making edits here to prepare for them. (It goes without saying that he has long since used up his assumption of good faith.) Would someone with some competence in Japanese please look at this? --Trovatore 21:02, 12 September 2006 (UTC)

And he is insisting on using the Big Omega function on square number, where it is pointless showing off. (See diffs: [2][3].) Given the number of complaints we get for being technical where we have to be, there is no excuse for this in an article that proves that the squares of odd numbers are odd. Septentrionalis 19:48, 13 September 2006 (UTC)

## Articles tagged as too technical

For a list see Wikipedia:WikiProject_Mathematics/Current_activity/Lists#Articles_that_are_too_technical. I've noticed, as I'm sure others have, that sometimes well-meaning editors just go through mathematical articles tagging them as "too technical". For example simple module has been tagged; however, I don't really see why it was tagged other than it looks like "gobbly-gook" to someone who doesn't know what a ring or module is. I can't see how this article can really be improved in a significant way to be accessible to someone without such a background. Perhaps an example built from the ground up would help...but that would seem to be the equivalent of writing a wikibook on abstract algebra. In any case, I believe this article (and some others) have been tagged wrongly.

The unfortunate thing about all this is that it makes it hard to find the actual overly-technical articles that can be made much more accessible. As a first step to making articles more accessible, therefore, I suggest that some people take some time and untag as many articles as they can -- those that are very advanced topics or seem to have been made as accessible as possible. --C S (Talk) 02:30, 11 September 2006 (UTC)

I added a sentence about graphical projection to Projection (linear algebra) and removed the tags. There wasn't anything in the talk page about why the tags were added. User:ST47 who added the "technical" tag was bot assisted. User:Srleffler added the original tag didn't leave any explanation. It seems Srleffler's attention was drawn to the article through graphical projection; they also left the same tag on projection (relational algebra) which Jon Awbrey summarily removed. Guess it's just another example of what you're talking about. (I know it's just one article. Sorry.) Lunch 23:15, 12 September 2006 (UTC)
got a bunch more. btw, it seems the current activity list hasn't been updated in a couple of weeks. did the bot run out of gas? Lunch 04:58, 24 September 2006 (UTC)

## page move?

the article on Robert Berger, the mathematician, was linked to by several film-related articles mentioning the writer robert berger. i changed those to refer to Robert Berger (writer). might it be a good idea to move Robert Berger to Robert Berger (mathematician) and put a redirect in its place? how does one go about doing this? tia. Lunch 03:38, 11 September 2006 (UTC)

The easiest is to use the "move" tab at the top of the article to move Robert Berger to Robert Berger (mathematician). This will automagically leave a redirect in its place. --LambiamTalk 05:31, 11 September 2006 (UTC)
But looking at this stubby article, I think there is not enough info to merit having a separate article here, as was noted by others on its talk page. --LambiamTalk 06:16, 11 September 2006 (UTC)
Two points here: (1) Are you sure that these are two different people? Sometimes one person does work in two completely unrelated fields. For example, Dorthy Lamour (hope I remembered the right actress) Hedy Lamarr was both a film actress and the inventor of a method of encryption. (2) There is no point in moving the page unless you replace the redirect with a disambiguation page listing various people named "Robert Berger" and giving links to their pages. JRSpriggs 07:05, 11 September 2006 (UTC)
Try Hedy Lamarr for the inventive star. --LambiamTalk 10:09, 11 September 2006 (UTC)
My thanks to Lambiam for the correction. JRSpriggs 05:26, 12 September 2006 (UTC)
According to his entry at the IMDB, the writer Robert Berger was credited as "Robert H. Berger M.D." for being a consultant for the movie Final Analysis. As that movie is about a psychiatrist, that Robert Berger is very likely too a shrink. Citations of (Berger, Robert. "The undecidability of the domino problem". Memoirs of the American Mathematical Society, 66, (1966), 1–72) all appear not to give a middle initial. --LambiamTalk 10:35, 11 September 2006 (UTC)
This Robert Berger seems not to have an entry in the Library of Congress, but he IS in the Harvard library catalog! He is given as Berger, Robert (born 1938), author of the AMS memoir on domino undecidability. They don't know his middle initial. I also looked up the memoir itself, and it includes no middle name, middle initial, thesis advisor, and no acknowledgments that I could find. There were four references, including one to a paper of Hao Wang. WP's entry for Wang says he was at Harvard from 1961 to 1967, so it's reasonable he could have been Berger's advisor. AMS MathSciNet does not seem to have any papers by this Robert Berger besides the domino memoir. EdJohnston 19:36, 11 September 2006 (UTC)

the harvard library catalog lists several holdings under the title "the undecibility of the domino problem." one of them is the AMS publication. another one of them is a copy of his dissertation. the title page there probably has his advisor's name. i'll be visiting there at the beginning of november; if i get a chance, i'll look it up. (i'm also morbidly curious to see ted kaczynski's dissertation, too, so i might actually take the time. :) UMI has him listed at harvard in 1965, too, but they don't have a copy of his dissertation (not even the abstract).

what originally brought me to the article was just a haphazard meandering. i saw the article on the list of "too technical" articles and was curious why it was there. when i looked at the list of "what links here," i noticed the three (four?) links to the movie writer/producer. although a quick check through IMDB now makes me think there are at least three robert bergers of note: the mathematician; Robert H. Berger, M.D., the writer/consultant for "final analysis"; and robert berger, the producer. this last fellow was making films as far back as 1962 so unless the mathematician robert berger was also a rookie film-maker during his harvard days, they're not the same person. (and incidentally, robert berger has produced almost three dozen movies; maybe there should be an article on him.) that doesn't rule out that the mathematician went out and got an M.D. and got into the film business, but i'd hazard a guess that didn't happen.

anywho, all this attention seems way out of proportion, but i'm glad to see some other amateur sleuths out there too.  :) i s'pose my two bits is that i go back an un-wiki-link robert berger, the writer/consultant of final analysis; make a stub on robert berger, the producer; and move robert berger, the mathematician. whaddya all think? too much?

thanks. Lunch 20:21, 11 September 2006 (UTC)

(oops, kaczynski did his PhD at michigan. he was an undergrad at harvard. oh well, maybe some other time.) Lunch 17:27, 22 September 2006 (UTC)
OK with me. The Harvard library catalog shows many, many Robert Bergers. But this man is the most famous of the mathematical Robert Bergers. Google Scholar still shows 216 citations to the domino paper, so he is notable. EdJohnston 22:55, 11 September 2006 (UTC)
The plan sounds fine. Just be careful of the other mathematician named Robert W. Berger who wrote quite a few papers, mostly in German. His genealogy can be found here. I don't know how notable he was/is.
By the way, this book review (a postscript file) asserts that the Robert Berger we have been discussing was indeed Hao Wang's student. Michael Kinyon 23:10, 11 September 2006 (UTC)

thanks. (i think the link is [4] for the postscript or [5] for the pdf, but i think the pdf got chopped off.) to address lambiam's early point, should the robert berger article mention all three since separate articles would be too short? i started a stub for Robert Berger (producer); potentially it could be much longer (he was rather prolific), but isn't long now. i dunno how long the article on robert berger the aperiodic tiler could be, or how long the article on robert w. berger could be. Lunch 00:12, 12 September 2006 (UTC)

## WP:BLP violation at Louis de Branges de Bourcia

I've changed to a far better version while trying to incorporate some of the recent factual additions. But the previous version definitely had way too much speculation, ramblings, and just poor sourcing. Given the number of people (although maybe some of the IPs are really the same person), who have edited it into this state, I think it's wise if people keep an eye on this page. --C S (Talk) 06:04, 11 September 2006 (UTC)

Some of the details are from Sabbagh's book, but I have not seen it recently enough to edit. Septentrionalis 20:32, 11 September 2006 (UTC)

## What does it mean?

I find that many math articles give definitions in a way that is 100% accurate but only 10% useful. (This is true of math writing beyond Wikipedia.) For example, until recently the definition of symmetric matrix simply stated that ${\displaystyle A_{ij}=A_{ji}}$. That's all well and good—it correctly defines the term—but it does not answer the question "what does it mean for a matrix to be symmetric?". As best I can tell, the answer is "it means the eigenvectors are orthogonal", which I added. After all, this is what mathematicians think when they think "symmetric".

I propose a concerted effort to get answers of this form into the definitions of math terms—answers that allow readers to think like a mathematician rather than stare at syntax. Perhaps a template Template:what_does_it_mean? —Ben FrantzDale 23:35, 11 September 2006 (UTC)

As for the statement you added, it wasn't quite correct, so I fixed it in the article. (It turns out to be exactly the symmetric matrices that have orthonormal bases of eigenvectors which makes your addition even more appropriate to this particular article.)
As for your suggestion, I agree with you in principle but not in practice. A mathematical definition is just that--a definition. While it may be equivalent to any number of conditions, some of which are intuitively more appealing than others, the definition is usually the more straightforward one. In this case "symmetric" means literally that the matrix entries exhibit some kind of symmetry, in this case with respect to the matrix transpose. That's why we have a whole article to follow; the article should explain "what does it mean". A good article probably does not need any additional template if it's doing its job correctly.
Having said this, thanks for your contribution and suggestion. We do need to make sure that the math articles fully explain the "why". VectorPosse 00:26, 12 September 2006 (UTC)
what do you mean by "mean"? ;) that there is a complete set of orthonormal eigenvectors of a symmetric matrix (along with real eigenvalues) is usually called a theorem, and the symmetry of matrix entries is usually called the definition. of course, it is equivalent to do the reverse. (and there are several other definitions that result in equivalence.)
but the symmetry of matrix entries is by far the simplest definition, and the eigenvector/value property is listed shortly thereafter in the article (and this is good practice). also, the symmetry of matrix entries does have significance: if two vectors are related by multiplication by a symmetric matrix, then changes in entry i wiggle entry j as much as entry j wiggles entry i. symmetry is also preserved under a congruence transform (as like with change of coordinates applied to a quadratic form - not to be confused with a similarity transform, a change of coords for a linear system). physicists love these sorts of things. (as do mathematicians, engineers, and a whole party of people. :) but i'd stick this in a list of properties...
i guess my point is that people usually go with the simplest possible definition and stick equivalent definitions under "properties" or "lemmas/theorems". Lunch 00:43, 12 September 2006 (UTC) (oops. edit conflict.)
maybe i'd add that "simplest" doesn't always mean "most intuitive" or "most informative about why this is useful/interesting/wheretheheckdidTHIScomefrom". you're right in thinking that an article on such a subject deserves a bit of history/motivation in the leading paragraph(s). or maybe i'm not thinking what you're thinking. Lunch 00:54, 12 September 2006 (UTC)
Lunch, I think we are on the same page when you say “‘simplest’ doesn't always mean ‘most intuative’...". In the case of this example I'd argue that the obvious definition of symmetry, while important, is essentially intuition-free and so not very helpful for newbies. That's why I like the format "X is defined as y but really a mathematician is thinking z." Overall I'd like to see a move towards systematically answering “wheretheheckdidTHIScomefrom”. —Ben FrantzDale 02:40, 12 September 2006 (UTC)
you mean you didn't like my wiggling components analysis?  ;) not to beat a dead horse, but as a mathematician who spends a lot of time doing linear algebra, i do think in components often enough. imho, the component-wise definition of a symmetric matrix is a good one and does have intuitive appeal. (i'd also add that linear algebra is almost always first introduced to students from a components point of view -- and with good reason.) Lunch 19:47, 12 September 2006 (UTC)
VectorPosse, as for the template idea, to clarify I was thinking a cleanup-style template not an infobox—something to tag an article with when it feels like it's skirting the "mathematician's intuition" definition. —Ben FrantzDale 02:40, 12 September 2006 (UTC)
Oh, I see what you mean now. Well, I'm not sure that changes my opinion much. I'm rather new here myself so I don't know much about templates; nevertheless, I suspect there's already a common template to indicate that an article needs more explanation or clarification. I'll leave that to more experienced editors to decide. I still agree, of course, that any "mathematical intuition" should be explained in the article (but not in the definition). VectorPosse 04:44, 12 September 2006 (UTC)
I'm not sure this is really necessary. Mathematical objects can have many properties, and one of them is not necessarily more important than others. We have a whole article to explain these properties and what is useful/interesting about them, and the intro should summarise the article. JPD (talk) 08:08, 12 September 2006 (UTC)
I agree that what does it mean? is really context-dependent. We would probably not say that Rn means "cofunctor of an abelian variety". A symmetric matrix may appear in several contexts without reference to spectral properties. pom 15:06, 12 September 2006 (UTC)
A distance matrix is symmetric. This is an easily understood elementary property. Few mathematicians will think: "Oh, I know what that means. It has an orthonormal basis of eigenvectors!'  --LambiamTalk 15:11, 12 September 2006 (UTC)
Good point, and good example. I assume the eigenvector symmetry property isn't interesting in that case because the matrix isn't used as a transformation. For a distance matrix, it seams that symmetry is a trivial and not-too-interesting fact. The distance matrix page could do with some "what does it mean" love itself, actually; it says what one is and the fields in which they are used but not how they are used.—Ben FrantzDale 18:09, 12 September 2006 (UTC)
Symmetry isn't trivial or uninteresting in this case: it's one of the three key axioms defining a metric. —David Eppstein 21:28, 12 September 2006 (UTC)
I've been bold and added a Mathematical intuition project sub-page to try to address this issue. —Ben FrantzDale 18:14, 12 September 2006 (UTC)

I created extension (mathematics) as a new disambiguation page with more than 30 entries. I think it ought to get organized into sections and subsections. Could Wikipedia's many mathematicians please help? Michael Hardy 21:31, 12 September 2006 (UTC)

I put them into some vague sections, people should feel free to subdivide further. Of course, most of these are algebra. -- Deville (Talk) 22:02, 12 September 2006 (UTC)

Does anyone else think it's a little weird that Extension problem is strictly about group extensions, while the stub Group extension mentions fields and other algebraic structures? Michael Kinyon 18:25, 15 September 2006 (UTC)

Yeah, I thought it was weird, so I changed Group extension to mention only groups and added a link at the bottom to Ring extension. This is a stub that could be greatly expanded. The article Extension problem actually has a lot of the material I would put in Group extension if it were up to me. Ah, if I only had the time... VectorPosse 19:03, 15 September 2006 (UTC)
What problems would result from just switching the names around? Michael Kinyon 20:07, 15 September 2006 (UTC)
I like it! If we did that, we would need to restore the few words I removed (probably with some editing), but I think this is a great idea. The page Extension problem ought to be a small-ish, more general page about any kind of extension problem. Then its links direct readers to the particulars of specific kinds of extensions. There is something in the page's discussion about calling it Extension (algebra) (which currently redirects to Group extension) and I think that would be necessary for this solution. Otherwise, one would have to include material on extension problems in all fields and that would be the same list that started this thread to begin with. VectorPosse 23:23, 15 September 2006 (UTC)
It seems fine to me. I am going on a Wikibreak for a bit more than a week starting tonight, and you have thought in more detail about what would be needed than I have. So my "vote" is: go for it! Anyone else have any thoughts about this? Michael Kinyon 03:47, 16 September 2006 (UTC)

## Discussion at Euclidean space

There is a discussion occurring at Euclidean space concerning how best to write the introduction to be more accessible (see: Talk:Euclidean space#Obnoxious article and following). Interested parties may wish to join the discussion. Paul August 23:23, 12 September 2006 (UTC)

## Peer review: Boy's surface

Boy's surface (talk) is up for peer review. Please offer any insights (there, not here).—msh210 21:36, 13 September 2006 (UTC)

Martingale paradox has been put up for deletion: Wikipedia: Articles for deletion/Martingale paradox. The author has spent a lot of effort on Usenet at promoting this material, e.g. [6] (see User:AntiochCollege for suspiciously similar material). --C S (Talk) 00:21, 15 September 2006 (UTC)

## What happened ?

I created a page for Pierre Rosenstiehl yesterday. It just disappeared today (even the traces of the changes I made). I am sure to have saved it after editing and the page is still in my watchlist... If it has been deleted, it would have been fair to post some message on my talk page. Otherwise, what did happen? pom 10:26, 15 September 2006 (UTC)

Here's the entry from the deletion log:
Go complain. --KSmrqT 12:13, 15 September 2006 (UTC)
I put a message on Gustafson's Talk page asking him to consider restoring it and, if he still thinks Rosenstiehl is non-notable, putting the article up for AfD so that the rest of us can have some input. Michael Kinyon 12:42, 15 September 2006 (UTC)
Speedy deletion under A7: unremarkable people or groups/vanity pages. An article about a real person, group of people, band, or club that does not assert the importance or significance of its subject. If the assertion is disputed or controversial, it should be taken to AfD instead. I think that was wrongly applied. Charles Matthews 13:31, 15 September 2006 (UTC)
I think the "proper" method would be to take it to DRV. Or you could just recreate it with a {{hangon}} tag. But asking the deleting admin for reconsideration is always in order.
The page came back and I put a {{hangon}} tag. Actually, I am not sure it should be kept as I am not aware of the threshold considered by Wikipedia for notability. Whatever decision is taken does not care too much. However, deletion / restoration without a slightest explanation from an admin is an attitude which does not encourage editing at all. pom 16:05, 15 September 2006 (UTC)
Notability is well known to be a difficult concept to apply in practice. A better question: who would consult Wikipedia as a reference about a given person (excluding family, friends, colleagues)? For a member of Oulipo, it is easy to see that many people might look here. It is an argument you could all there-are-no-minor-poets: of course almost all poets are 'minor', as almost all mathematicians fail to be 'major'. But if someone likes a poem and has only a name, then, yes, they might use a reference work to discover more. Charles Matthews 21:44, 15 September 2006 (UTC)
Ok, but from a practical point a view, what should I do if I want to start to write pages on living combinatorists? Should I consider there is limit on the number of bigraphies and that I should prioritize the additions. If so, what would be the order of magnitude of this limit? pom 22:34, 15 September 2006 (UTC)
Mr. Gustafson pulled the trigger on the article (and perhaps should have known better), but an anonymous user User:151.200.246.168 was the one who tagged the article for speedy deletion in the first place. In the span of just over two hours, they tagged 18 articles for speedy deletion. It wasn't quite vandalism; many of the articles were marginal at best, but didn't quite seem like candidates for speedy deletion either. Weird. Lunch 17:18, 15 September 2006 (UTC)
Weird, indeed. In good faith, perhaps it is just someone who doesn't understand the speedy deletion criteria. In any case, I think this WikiProject can congratulate itself on how this was handled. (But will our backs hurt from patting them so hard?) Michael Kinyon 18:15, 15 September 2006 (UTC)

## Etymology

Some unusual updates have been made to the etymology at pentagon (disambiguation), heptagon and polygon. I'm no expert, but I never heard that these terms had a Sanskrit origin before, so I am rather doubtful about the accuracy of these updates. Any comments ? Gandalf61 10:31, 15 September 2006 (UTC)

Here are some etymologies from the OED:
pentagon In A, ad. L. pentagon-us, a. Gr. pentagwn-oj pentagonal, five-cornered, f. penta- penta- + -gwn-oj from stem of gwnia angle. In B, ad. L. pentagon-um, Gr. pentagwnon, the neuter adj. used as sb. Cf. Fr. pentagone sb. (13th c. in Littré), whence the Eng; form in -gone.
penta- penta, before a vowel pent-, a. Gr. penta-, combining form of pente five, occurring in many words in Greek as a variant of the earlier pente-, and forming the initial element in various modern technical words adopted from Greek, or formed from Greek elements or on Greek analogies.
I'm not convinced that those articles need any etymologies, much less ones that seem to have little support in standard references. It may be possible that the words came to Greek from Sanskrit, but without any documentation I think it is better to just remove the anonymous edits instead of correcting or expanding them. CMummert 10:49, 15 September 2006 (UTC)
The Greek did not "come from" Sanskrit any more than the Sanskrit came from Greek. I've removed these changes. --LambiamTalk 17:19, 15 September 2006 (UTC)
I asked on wikitionary and got
Er – no, it's wrong. All these related ‘shape’ nouns are from Greek. The Greek suffix was -γωνος, literally ‘angled’, and in this case combined with πεντα-, from πέντε ‘five’. The Sanskrit forms are cognate (i.e. both Sanskrit and Greek are descendants of Proto-Indo-European *penkʷe ‘five’), but Sanskrit is not the immediate source of the English word. Very few words in English come from Sanskrit. -- Widsith
So now we know. --Salix alba (talk) 17:44, 15 September 2006 (UTC)
There was a habit of calling Proto-Indo-European "Sanskrit" a century ago, before the decipherment of Hittite and the present understanding of IE vowels. It should be suppressed where found. Septentrionalis 18:48, 15 September 2006 (UTC)

## Polar coordinate system

Hi everyone! An article that I've been working on quite a bit, Polar coordinate system, has just become a good article. We've requested a peer review to find out how it can be improved to featured article status, and it's great so far. Any other comments would be appreciated. Thanks. — 14:20, 16 September 2006 (UTC)

## Subcategory for geometric graph theory?

I've been working on a few pages lately that have the flavor of geometric graph theory — that is, about graphs that are either embedded in a geometric space themselves, or that arise from configurations in a geometric space. I'm wondering whether it would be appropriate to make a new category for them, as a subcategory of both geometry and graph theory.

Evidence that organizing things this way is not just my own hobby horse: Pach's edited collection Towards a Theory of Geometric Graphs (to which I contributed a paper on geometric thickness, a subject that would fit here as well but one that I think someone else should add if it deserves adding).

Anyway, this seems a widespread enough change that I felt I should open up the question for debate here rather than just going ahead and doing it. So, does anyone have an opinion on this possible reorganization? —David Eppstein 21:30, 17 September 2006 (UTC)

Category:Geometric graph theory sounds good to me. --Salix alba (talk) 21:14, 17 September 2006 (UTC)
I don't know if it will be so easy to make the distinction between Geometric Graph Theory and Topological Graph Theory. For instance: the usual crossing number is of topological nature, while the rectilinear crossing number is of geometric nature. Don't you think it could be better to (at least temporarily) merge the two in a Topological and Geometric Graph Theory subcategory? Of course, there are purely topological or geometric results (rotation system / Erdős–Szekeres theorem) but most have several aspects. Graph drawings may rely on spectral analysis or poset related properties (like track drawing). The classification of theoretical results may also be problematic (e.g.: Schnyder's theorem is about planarity, poset dimension, decompositions into particular forests, and induce a straight line drawing on a linear grid). All of this does not mean I am against subcategories, but rather that I am afraid by the number of topics which will cross the boundaries of categories. pom 21:59, 17 September 2006 (UTC)
To me the distinction seems clear enough: topological graph theory concerns graphs embedded on 2-manifolds such as the Euclidean plane, with vertices as points and edges as curves, while geometric graph theory either considers similar type embeddings with edges as straight line segments or other restricted geometric curves (polygonal paths with few bends, or circular arcs, though I doubt there is much already in WP that mentions these), or graphs coming from other geometric constructions (intersection graphs, visibility graphs, arrangements, etc). But of course there is overlap between the two; fortunately WP allows entries to have multiple categories. Perhaps I shouldn't have included Crossing number (graph theory) above since it's about the topological version of the problem; it's a long article so it might make sense to have a separate article on Rectilinear crossing number or Geometric crossing number (two different names for the same thing). Fáry's theorem seems like a good example of an article that overlaps both categories since it states that a topological graph has a stricter geometric representation; Scheinerman's conjecture is also of that type. —David Eppstein 03:20, 18 September 2006 (UTC)
You are fully right. pom 05:41, 18 September 2006 (UTC)

## Can we put the Leonhard Euler FAC nomination on the project page?

Leonhard Euler is nominated for Featured Article status. I know that the nominator of the article has already posted this 10 days ago on this talk page but I think it would also be worth putting the info more prominently on the welcome page of the project. There's not that much work left to do on it to push it up to the desired quality and it's clearly a goal that should be among the project's priorities. Pascal.Tesson 23:44, 17 September 2006 (UTC)

In related news I've put Ackermann function on FA review. I think it lacks in laymans explination and is not up to current FA standards. --Salix alba (talk) 00:03, 18 September 2006 (UTC)
Speaking of which the primitive recursive article is also in a very sad state. But I digress. Pascal.Tesson 06:17, 18 September 2006 (UTC)

## the apes are in question

I just contributed here calculating something. It would be nice if someone could verify what i wrote, because it seems the article contains a mistake. Nerdi 17:50, 18 September 2006 (UTC)

I was going to move the link to the musical ensemble The Exponents from list of exponential topics to exponent (disambiguation) and add this (using the "dablink" template, since the various "otheruses" and "alternateuses" templates are an odious and execrable abomination abhored by all good people):

But the latter page does not exist. This caused me to notice that the list of exponential topics is quite incomplete as a list of Wikipedia articles already existing that belong there. Here's what needs to be done:

• Enter "exponent" in the search bar and click "search", not "go".
• Add to the list of exponential topics the mathematics articles that belong there.
• Add to a new exponent (disambiguation) page the many "exponent" topics on non-mathematics topics, and also add the list of exponential topics to that page after a few of the most prominent mathematical senses of the word, with a note saying the list is fairly long.

I'll be back later to participate in this, but maybe not till tomorrow. Michael Hardy 21:20, 18 September 2006 (UTC)

## Ackermann function

Ackermann function is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 15:46, 19 September 2006 (UTC)

## 256^(4.7*10^9) on prod

It's not in any math categories, so it won't show up on current activity; listing here. --Trovatore 21:15, 19 September 2006 (UTC)

and current activity hasn't updated for a week; is something wrong? Septentrionalis 23:25, 19 September 2006 (UTC)

## Tagging talk pages and assessing articles

Wikipedia Assessments within AWB. Click on the image to see it in better resolution

Hi. If you still have work to do tagging talk pages and assessing articles, my AWB plugin might be of interest to you.

The plugin has two main modes of operation:

• Tagging talk pages, great for high-speed tagging
• Assessments mode, for reviewing articles (pictured)

As of the current version, WikiProjects with simple "generic" templates are supported by the plugin without the need for any special programatic support by me. I've had a look at your project's template and you seem to qualify.

Hope that helps. If you have any questions or find any bugs please let me know on the plugin's talk page. --Kingboyk 14:01, 20 September 2006 (UTC)

## Manifold Destiny (article)

It has been suggested to me that this page, dealing with a controversial New Yorker dirt-digging story about Perelman, needs semi-protection. I can't quite see that it fits the guidelines at Wikipedia:Semi-protection policy, although there have been some anons making edits there that could get WP into legal trouble. In any case this page is potentially something very troublesome. Charles Matthews 21:28, 21 September 2006 (UTC)

I think you've been mislead by Lubos Motl's comment on your talk page [7]. Look through the history of the article. In particular, look at all the anon edits. I don't see what is trouble some about them; the worst I can see is a new user (not anon) that added an unsourced statement that Tian had never spoken to the New Yorker, but it was later removed by an anon.
I think given that this article exists, the edits that have been made by new or anonymous users thus far, are in fact of decent quality, certainly better than some by registered users! So I don't see any valid reason someone could want the page semi-protected.
Whether this page should exist is another issue. I didn't used to think so, but given the media coverage, it seems to me that this article is sufficiently notable. Some may not like what is going on, or that dirty underwear is being aired, but this kind of thing is par for the course on many topics. The mathematical community does not have any special protection on Wikipedia against this kind of stuff and shouldn't. Sure, the article could be potentially troublesome, but that is true of many controversial articles. We should deal with it like any other. Keep an eye on it and make sure people don't turn it into a version of their blog. --C S (Talk) 10:56, 22 September 2006 (UTC)

Thanks for filling me in. As I said, after I had been asked my conclusion was not to semi-protect. As you say, watching should be enough for the present. Charles Matthews 11:08, 22 September 2006 (UTC)

## Order 3 groups are cyclic proof

Order 3 groups are cyclic proof is up for deletion. Chime in at the appropriate spot. Michael Kinyon 00:28, 23 September 2006 (UTC)

## Gleason's theorem

This page was tagged as needing attention. It was a stub which simply stated the theorem in question. I have expanded it quite a bit, and removed the tag; I hope that my edits were sufficient to do so! My expansion has centred mainly on the application of the theorem, in quantum mechanics and the philosophy thereof. On the talk page, someone suggested sketching an outline of the proof of the theorem, which could be a worthwhile addition at some stage, but since most references to the theorem are centred on its uses and implications, this is probably not necessary at the moment (the proof is also hideously long and complicated, and not easy to summarise for an encyclopaedia article). Anyway, I wanted to find out the following. Now that the tag is gone, does your magical bot remove the page from the "needing attention" lists your project maintains? Or should I do that manually? I didn't want to just go ahead and do it, in case it interferes with the bot somehow...do let me know! Byrgenwulf 18:06, 23 September 2006 (UTC)

thanks! the article certainly no longer is a stub (and the "expert needed" tag was probably misplaced). and don't worry, the 'bot will eventually pick up on the tags. Lunch 05:12, 24 September 2006 (UTC)
Maybe this should be raised on the article's talk page, but I don't get the bit about P(y) being 1 for every lattice point y. Is 0 not also a lattice point? Doesn't this require y to be the sum of n (instead of any r) orthogonal atoms? And if true, isn't "the probability is fixed" a weak way of saying: the event is almost sure? --LambiamTalk 07:36, 24 September 2006 (UTC)
That's a typo...the "=1" shouldn't have been there (it's gone now). So: any y can be expressed as the union of some (not necessarily n) number of orthogonal atoms xi. The probability P(y) is the sum of the probabilities P(xi) (all r of them). "The probability is fixed" simply means "uniquely determined" in this context. Byrgenwulf 10:19, 24 September 2006 (UTC)
Regarding the bot, there is some problem with the computer on which it runs. I'm on the other side of the planet and can't reach the computer remotely. I should be able to bring it up next week after I return to my office. Sorry about the problems (but it is nice to see that people are noticing). -- Jitse Niesen (talk) 14:45, 27 September 2006 (UTC)

## Ear curve

Ear curve is up for deletion. Opine at its AfD page. Michael Kinyon 11:22, 24 September 2006 (UTC)

## number needs attention

The section on real numbers is quite weak and maybe even misleading. Michael Hardy 02:15, 25 September 2006 (UTC)

I do agree that it is weak. Did you have something particular in mind when you say it's misleading? VectorPosse 02:39, 25 September 2006 (UTC)
I don't know what Michael Hardy had in mind; but the real numbers section conveys the impression that some of them (e.g., 0.1010010001...) are not constants. That is definitely misleading. JoergenB 13:31, 25 September 2006 (UTC)
While we're at it, the "Infinitary extensions" subsection is very misleading, and the "Transcendental numbers and reals" subsection is worth a look (the first paragraph does not deal with transcendental numbers at all). -- Meni Rosenfeld (talk) 10:49, 25 September 2006 (UTC)

It was less misleading after my edit, just before I posted this comment. It was written so as to make it appear that a real number is by definition a decimal expansion. I suppose in some ways that's no worse than saying a real number is a Dedekind cut, or that it is an equivalence class of Cauchy sequences, or any of various other members of that same isomorphism class, but the prevalence of popular errors about the definition of rational and irrational numbers (thinking that those concepts are defined in terms of decimal expansions) makes me cringe at that way of introducing the idea. Michael Hardy 19:47, 25 September 2006 (UTC)

Two remarks:
• the "needs attention" note is still in. It would help if you could copy-and-paste your detailed explanation to the talk page, so people can have a shot at fixing it.
• defining real numbers as (equivalence classes) of decimal expansions, and rational numbers by properties of such expansions, is correct, if awkward.
• I'm not aware of a definition of real numbers that's better than the one via decimal representations, but still has some connection with non-mathematical culture, and can easily be grasped by non-mathematicians. Dedekind cuts and Cauchy sequences, I'm afraid, are right out for that.
RandomP 20:03, 25 September 2006 (UTC)
Saying real numbers correspond to points on a continuous line certainly can be grasped by non-mathematicians. Michael Hardy 20:06, 26 September 2006 (UTC)
For most people, formally defining any kind of number is a strange ritual. Does a definition of positive integers in terms of sets or successors connect with non-mathematical culture? Mathematics itself was very slow to make numbers formal objects. But in terms of historical development, there is evidence that the Dedekind cut idea is the earliest of the four major approaches. (These are: cuts, decimals, sequences, field axioms.) Cuts are also technically simple, while decimals are a beast. However, the number article should mostly leave the formalities to specialized articles, and concentrate on the big picture, which is that real numbers — however defined — "complete" (fill in the gaps of) the line (rationals). Concretely, what's the diagonal of a unit square? What's the area of a unit circle? --KSmrqT 14:54, 26 September 2006 (UTC)
This may be OR, but I've found that a good way to explain real numbers is by a sequence of shrinking intervals – possibly of zero width, although that's not essential – [Li, Ri] with Li ≤ Li+1 and Ri ≥ Ri+1, and Ri − Li → 0. The claim is that this determines a unique real number x that is contained in all intervals: Li ≤ x ≤ Ri. It is easy (for us) to see that this induces a Cauchy sequence as well as a Dedekind cut. There is no need to require the Li and Ri to be rationals when explaining the idea. The point is, rather, to formalize the notion that "there are no gaps", a closure property. I've found that for psychological reasons I can't explain the notion of an interval shrinking "in the limit" to zero is easier to grasp than limit in general, even for a monotonic sequence. --LambiamTalk 22:13, 26 September 2006 (UTC)
You and your students might appreciate Archimedes' proof that the area of a circle is the same as that of a right triangle with base equal to the circumference and height equal to the radius, found in "Measurement of a circle". (See Heath's translation, ISBN 978-0-486-42084-4.)
We want to be careful about the distinction between conveying intuition, which "number" should do, and establishing a workable definition, which "real number" should do. Working from the definition alone we need to be able to do arithmetic, comparisons, and proofs. That's one reason why Dedekind cuts are more appealing than decimal expansions for formal work. Compare with the modern definition of "compact space" in topology, where the "finite subcover" idea is less intuitive but more effective than "closed and bounded".
Back to your original point: Mental models are important for teaching; they are also important for functioning in the real world, a theme that artificial intelligence research has explored under the names "naive physics" or "qualitative reasoning". (See Smith and AAAI for sample reading.) --KSmrqT 15:56, 27 September 2006 (UTC)

## In which subject areas is the term basis function used?

There seems to be disagreement over whether the term basis function is used in functional analysis. I don't know enough about the subject to have an opinion. Could someone comment at Talk:Basis function? --Jtir 13:04, 25 September 2006 (UTC)

There is a problem with the weakness of the article. There must be several areas, eg wavelets, where this is a relevant concept. Charles Matthews 13:12, 25 September 2006 (UTC)
Correct. I looked at the what links here list and found wavelets, plus articles in chemistry, physics, engineering, and business that link to Basis function (I've put a culled, classified, and alphabetized list of linked articles at Talk:Basis_function). A wikipedia search finds many other examples of the term being used. It is starting to seem to me that making the article a dab would be preferable to trying explain all possible uses of the term. I don't have enough WP experience, though, to know what the implications are. --Jtir 21:26, 25 September 2006 (UTC)
A dab page makes mainly sense if we have separate articles on different meanings of the words "basis function". In mathematical use, isn't there a common meaning: an element of some basis of a vector space whose elements are functions? The main problem of the article may be that it starts with the words "In functional analysis" instead of "In mathematics". --LambiamTalk 22:38, 25 September 2006 (UTC)
an intro sentence might be, "In mathematics -- particularly analysis -- a basis function is an element of the basis for a function space. The use of the term is analogous to basis vector for a vector space." (NB: some of those words are dab pages so the links are Analysis (mathematics) and Basis (linear algebra).) Lunch 00:56, 26 September 2006 (UTC)
With this formulation, couldn't all the technical content of the article be removed? Basically the article is saying that basis function is a synonym for basis vector in some usages. If so, the article could become a redirect to basis (?) which could parenthetically note the same thing. --Jtir 16:10, 26 September 2006 (UTC)

I don't think a simple redirect to Basis is a good idea. When dealing with bases in function spaces, a Hamel basis (which is what that page focuses on) is usually not the tool of choice. Instead one typically deals with a Schauder basis or, in the more specific Hilbert space setting, an orthonormal basis. Sometimes the word is stretched a bit, such as in the context of Riesz basis (which I think is really just a frame). Michael Kinyon 16:20, 26 September 2006 (UTC)

(I'm gonna CC the conversation here to the basis function talk page. There's some good stuff here that hasn't been mentioned there, and vice versa (along with some repeats). Come on over and join in!) Lunch 19:04, 26 September 2006 (UTC)

## Should "Recursively presented group" redirect to "Presentation of a group"

Both finite and recursively presented groups are defined on the page "Presentation of a group". At present "Finitely presented group" redirects to "Presentation of a group" but "Recursively presented group" is just a fairly minimal stub. It would make more sense to me if it too redirected to "Presentation of a group". Bernard Hurley 20:38, 25 September 2006 (UTC)

Yes, it would. I think I created the article, and wasn't aware of that (probably because I thinko'd and created it under the wrong title - sorry, I was just upset we didn't have those articles when rereading Rotman).
RandomP 20:53, 25 September 2006 (UTC)
Well, merge and redirect. Charles Matthews 09:36, 26 September 2006 (UTC)

## 'Determinants' is a featured article on the French Wikipedia

Are we allowed to steal from the other language Wikipedias? See [10] for a rather nifty treatment of Determinants. It's 111K (vs the 55K of our own English article) and has some nice color illustrations. The language used is not 100% familiar to someone whose linear algebra is several years in the past, but maybe this is the latest thing.

Here are the opening sentences:

"First introduced in algebra to determine the number of solutions of a system of linear equations, the determinant reveals itself as a very powerful tool in numerous domains (study of endomorphisms, search for eigenvalues, differential calculus). It is in this manner that we define the determinant of a system of equations, the determinant of an endomorphism or the determinant of a system of vectors.
"For many operations, the determinant can be defined by a collection of properties (axioms) that we summarize by the term "alternating n-linear form". This definition allows us to make a complete theoretical study and to enlarge further its field of application. But the determinant may also be conceived as a generalization to n-dimensional space of the notion of oriented surfaces and volume. This aspect, often neglected, is a practical and illuminating approach to the properties of the determinant." EdJohnston 23:59, 25 September 2006 (UTC)
I believe that the other language wikipedias use the same license which we have here. So you can use their content freely provide that you give them credit for it and offer it to others under the same condition. In other words, go ahead and copy any of their text and translate it into English. But make sure that you attribute it to them in your edit summary -- specify that it was the French wikipedia and name the article, so that anyone can look in their revision history to see who put the material into it in the first place. JRSpriggs 05:50, 26 September 2006 (UTC)
Yes, you can translate and use here freely. Charles Matthews 09:38, 26 September 2006 (UTC)

Actually, translation is not just permitted (and as far as I can see often not accompanied by credits), but encouraged. Read e.g. Wikipedia:Translations into English. JoergenB 10:13, 26 September 2006 (UTC)

You ought to give credit, though. Anything else is risky under the GFDL. Remember that the original authors still hold copyright, even though they've licensed it to you. If you don't comply with the terms of the license (which requires attribution) you could be infringing. --Trovatore 06:43, 27 September 2006 (UTC)
Well, this sounds reasonable; and 'there are some nice templates', which make it very easy to inform the reader of sources from sister Wikipedia, and which you may place under the heading references. It might be a good idea to use them whenever material is translated, which is seemingly not done now. Not only the determinants article lack such information. JoergenB 13:51, 29 September 2006 (UTC)
Regretfully, I'll have to qualify the statement there are some nice templates. After having been around at the template pages a little, getting more and more confused, but finally finding some adequate explanation, I'l have to rephrase it there are two nice templates (namely Template:German and Template:Polnish). I accidently started by looking at a list of recently translated articles from German to English, and then assumed that I knew the pattern... However, there may be other such templates without proper categorisation (and of course they should not be too hard to create, I suppose, if we want to encourage translators to give more credit).
That discussion perhaps should move to another page, though. JoergenB 16:43, 29 September 2006 (UTC)

## Something has gone wrong with LaTeX interpreter

Being realtively new to wikipedia I'm not sure where to post this so it's going here. Something has gone wrog with the LaTeX interpreter on wikipedia so that maths pages are full of lots of raw LaTeX. Bernard Hurley 23:27, 26 September 2006 (UTC)

It seems that the server of formula PNGs (http://upload.wikimedia.org/) is unreachable. As a consequence, PNG formulas only appear in their HTML version. pom 23:52, 26 September 2006 (UTC)
Some images also seem to be broken. I suspect this is a tempory problem which will be fixed in a few hours. Its happened before. --Salix alba (talk) 00:29, 27 September 2006 (UTC)
Have you tried control-shift-R? For several days now, I have occassionally been seeing the formulas unconverted. But they always become correct after control-shift-R. JRSpriggs 06:13, 27 September 2006 (UTC)
That is curious because the LaTeX interpreter is on the server. I can't test this because the problem seems to have gone away, but thanks for the suggestion. Bernard Hurley 08:29, 27 September 2006 (UTC)
If you visted the page while the PNGs are not accesible, the HTML version could be stored in the cache and so appear even after the problem is gone. Purging the cache when everything is working again would fix this problem. JPD (talk) 10:31, 27 September 2006 (UTC)

## Spurious dashes

Hmm. Gleason's theorem, at least, still has issues with spurious dashes, though. Does this happen to anyone else? RandomP 02:11, 27 September 2006 (UTC)

Yes, I noticed it an hour or so ago in Character theory. Michael Kinyon 06:37, 27 September 2006 (UTC)

This is a bug in the LaTeX interpreter on wikipedia. The LaTeX interpreter seems to add a dash to the end of formulas containing certain letters and ending in certain other characters. So in the following paragraph "B(m,n)" gets an extra dash:

Let ${\displaystyle n,m\in \mathbb {Z} }$ where ${\displaystyle m}$ is odd, ${\displaystyle n>10^{78}}$ and ${\displaystyle m>1}$, and let ${\displaystyle B(m,n)}$ be the free m-generator Burnside group, then every non-cyclic subgroup of ${\displaystyle B(m,n)}$ is SQ-universal in the class of groups of exponent ${\displaystyle n}$.

If I change it to "B(x,y)" it is OK:

Let ${\displaystyle x,y\in \mathbb {Z} }$ where ${\displaystyle x}$ is odd, ${\displaystyle y>10^{78}}$ and ${\displaystyle x>1}$, and let ${\displaystyle B(x,y)}$ be the free m-generator Burnside group, then every non-cyclic subgroup of ${\displaystyle B(x,y)}$ is SQ-universal in the class of groups of exponent ${\displaystyle y}$.

A fix seems to be to add a LaTeX space at the end of the formula but in this case the formula gets displayed with a larger font! So using "B(m,n)\ " we get:

Let ${\displaystyle n,m\in \mathbb {Z} }$ where ${\displaystyle m}$ is odd, ${\displaystyle n>10^{78}}$ and ${\displaystyle m>1}$, and let ${\displaystyle B(m,n)\ }$ be the free m-generator Burnside group, then every non-cyclic subgroup of ${\displaystyle B(m,n)\ }$ is SQ-universal in the class of groups of exponent ${\displaystyle n}$.

Incidentally you can get the larger font by including a LaTeX space so:

• "a" gets interpreted as ${\displaystyle a}$
• "a\ " gets interpreted as ${\displaystyle a\ }$

Bernard Hurley 08:23, 27 September 2006 (UTC)

And a thinner space by using \,: "[$a\$]" gives "[${\displaystyle a\ }$]", while "[$a\,$]" gives "[${\displaystyle a\,}$]". --LambiamTalk 10:27, 27 September 2006 (UTC)
There is a bugzilla bug on this. Vote for it to encourage a quick fix. I'd recommend against short term fixes in articles. --Salix alba (talk) 08:27, 27 September 2006 (UTC)
Guys it's totally about the caching. When wikipedia sees an equation it's seen before it re-uses the old image. Sometimes they change the image renderer so you get a version from an old renderer. e.g.: ${\displaystyle B(m,n)}$ ${\displaystyle B(x,y)}$ ${\displaystyle B(asixhux,sdkcjnjzz)}$. So it seems ${\displaystyle B(m,n)}$ is from the old renderer. ${\displaystyle B(mmmnn,nnn)}$ Here's another example: ${\displaystyle \oint }$. Oh look it's broken. That one's cached. But with the new renderer: ${\displaystyle Babcasisxajnsx\oint }$. I think that last one got fixed when they switched over to dvipng. When you do experiements like this you should always insert random text to trick the caching. 'course I could be wrong about all this, it's just a theory. Dmharvey 12:45, 27 September 2006 (UTC)
That seems to make sense. It would be nice if there were some mechanism to force the re-caching of a formula, but I suppose that could be open to abuse, it would also break any pages that rely on an incorrect old rendition. Bernard Hurley 13:02, 27 September 2006 (UTC)
I did a checkout on phase3 (is this the correct tree?) and was able to reproduce the bug with a fresh mw installation. I found a problem in render.ml, and after fixing it, the problem went away (it was necessary to clear the math table, of course). However, this can't explain why the bug does nolonger occur for new formulas. For details, see bugzilla.--gwaihir 16:25, 27 September 2006 (UTC)
Good stuff. Have you tried running with the preference set to MathML if possible. This has the effect of rendering simple maths as html and for these I'm getting the same problem without a image being used anywhere, so $B(m, n)$ produces the html <span class="texhtml"><i>B</i>(<i>m</i>,<i>n</i>)-</span>. --Salix alba (talk) 17:48, 27 September 2006 (UTC)
Ah the cache issue explaines the difference of apprearance, in some equations
${\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{2}x^{2}+a_{1}x+a_{0}}$.
${\displaystyle ((\ldots (a_{n}x+a_{n-1})x+...+a_{2})x+a_{1})x+a_{0}\,}$.
to me the first looks good, but the letters in the second seem rather blury. I guess the first is cached using an old renderer, but the second is generated using a new renderer. --Salix alba (talk) 08:43, 29 September 2006 (UTC)

## Good articles and inline cites

On Wikipedia talk:Good article candidates they have been reworking the criteria, which now currently require the use of inline cites. This resulted in all 11 of our mathematic GA receiving a message warning that the articles may be up for review. Lots of other articles also received the same messages and the physists especially have visiforously protested against the change. Theres now an atempt to reach a consensus on the issue. This particularly affect maths articles as we tend not to use inline cites for the main mathematical content, in Wikipedia:Featured article review/Eigenvalue, eigenvector and eigenspace use of manitory inline cites was contested.

People might like the add their views at on the issue at Wikipedia talk:Good article candidates. --Salix alba (talk) 18:03, 27 September 2006 (UTC)

There is also discussion on Wikipedia talk:Citing sources. This is very relevant as the proposed GA standards would make it difficult for math articles to receive GA status. And there is also discussion on Wikipedia talk:WikiProject Physics. CMummert 03:23, 28 September 2006 (UTC)

## Category:Math wars

I nominated this for deletion. The discussion is at Wikipedia:Categories for deletion#Category:Math wars. Comments are welcome. Oleg Alexandrov (talk) 01:51, 28 September 2006 (UTC)

## Intro line to analysis

In Areas of mathematics, I think it is misleading to say that analysis is primarily related to rates of change. Many aspects to the theory do not arise in this way. I think it would be better to say that analysis is the study of inequalities, because this is the theme that runs through every branch, at least it seems to me. To quote Krantz (from a book review of 'A Companion to Analysis: A Second First and First Second Course in Analysis') "Analysis is dirty, rotten, hard work. It is estimates and more estimates. And what are those estimates good for? Additional estimates, of course. We do hard estimates of integrals in order to obtain estimates for operators. We obtain estimates for operators in order to say something about estimates for solutions of partial differential equations. And so it goes." Any comments? I tried to change it initially myself, but instantly got reverted. :) I should have started here I suppose, thanks to Oleg for pointing this out to me. Thenub314 03:29, 28 September 2006 (UTC)

Whatever it is, it should match the Mathematical analysis article. (I personally have no really clear "intrinsic" concept of analysis - I know what would be considered analysis amongst the things I know, but if confronted with some mathematics that was totally unknown to me, I might be in doubt as to whether to consider it analysis.
Right now, the areas of mathematics article claims
"Analysis is primarily concerned with change. Rates of change, accumulated change, multiple things changing relative to (or independently of) one another, etc."
which appears to me to be based on real analysis in one variable. Mathematical analysis has:
"Analysis is a branch of mathematics that depends upon the concepts of limits and convergence."
which is what I would consider more appropriate for describing topology. Of course, one approach would be to define analysis historically, as that branch of mathematics that begins with the study of "nice" real functions, integration, and differentiation.
RandomP 03:58, 28 September 2006 (UTC)
Jordan would have probably have considered the "Analysis is... limits and convergence" definition to be correct, but at that time topology did not exist as a separate area of study. It's a matter of historical perspective. The contents of undergraduate analysis courses seem to have been fixed for about the last 50 years, but apart from that it would seem quite difficult to define.
Bernard Hurley 09:31, 28 September 2006 (UTC)
Part of the problem is that "analysis" is actually at least two fields: functional analysis and something which I might term "higher calculus". The former does often concern itself with limits and convergence, but in function spaces rather than spaces like ${\displaystyle \mathbb {R} ^{n}}$. The latter considers individual functions on ${\displaystyle \mathbb {R} ^{n}}$ using calculus-like ideas such as the derivative (of course, in many variables). Then there is the mysterious realm of PDE's, which bleeds into differential geometry, while perhaps the entire field is haunted by the ghost of operator theory. Perhaps the best one-sentence summary is that "Analysis is the field of mathematics which studies functions or spaces of functions using techniques related to the notion of limits and convergence." If I wanted another sentence, I would write, "Although all of its techniques, such as differentiation, integration, Fourier analysis, and so on, have seen vast generalizations (for example, p-adic analysis, generalized measure theory, and harmonic analysis on an arbitrary locally compact topological abelian group), it is over the connected, locally compact, and complete metric spaces ${\displaystyle \mathbb {R} ,\mathbb {C} }$ that they wield the greatest power and demand the most extensive use." This sentence disposes of the vast confusion that arises when you try to generalize about "analysis", since it is now so big. On the other hand, I'm not an analyist, and it seems that by doing this I might be doing the moral equivalent of saying "Algebraic geometry, although generalized to work over arbitrary commutative rings and to answer questions of number theory and even algebra itself, is essentially the study of complex algebraic varieties." Ryan Reich 13:33, 28 September 2006 (UTC)
Funny that this came up; a few days ago, a professor of mine remarked "It's not an exaggeration to say that analysis is the study of estimates". I think there might be some merit to incorporating that word in the definition. Fredrik Johansson 13:36, 28 September 2006 (UTC)

## History of Analysis article

I am not a historian, so I probably should not really comment, but is the history section under Mathematical Analysis article seems a bit too good to be true. I did some reading up on the MacTutor math history site. It doesn't seem to indicate that calculus was known in india in the 12th-14th century. Is this really true? In terms of verifiability all I found in any of the articles was a link to some physics prof's web site. Does anyone know more? Thenub314 00:30, 30 September 2006 (UTC)

## Citation issues

Lately, there have been many discussions of how to cite science and math articles at WP:GA and WP:CITE. In particular, there are editors out there in Wikipedia-land which would like to see every line in Wikipedia-articles cited. That would include, for example, line-by-line citations for mathematical proofs which I think would be ridiculous. There is currently a proposal at WP:CITE to include an important modification to the guidelines that would state that elementary facts should not/may not be cited. I tried to qualify this with a statement of what things I think (and maybe others think) should be cited in science and math articles and what things should not (and why). Please read, comment, and modify this work here. --ScienceApologist 05:53, 29 September 2006 (UTC)

There is little point giving citations for 'well-known' facts, anyway. Putting a huge effort into that is not going to solve the issue of references for genuinely recherché facts, which are those for which it is valuable to give pointers. Charles Matthews 07:00, 29 September 2006 (UTC)
I would go further. Peppering an article with extra citations is harmful, not helpful, for readers.
Extremists at Wikipedia insist otherwise.
One distorting force is the use of inline citations to address the reliability of our articles, which I believe is a fundamental mistake. Editorial debates belong on a talk page, not an article page. A reader should be able to have confidence that the Wikipedia quality control process has done its job, so that they can safely focus on absorbing content from the article.
Excess citations make it impossible to assess salience. If we cite both for "1+1=2" and "the Riemann hypothesis is true", a reader has no indication that the former is trival and uncontroversial while the latter would be a major claim. Nor will many editors wish to verify dozens and dozens of such citations, so garbage can easily creep in.
If only common sense were more common … --KSmrqT 17:49, 29 September 2006 (UTC)
agree with above, c.f. 0.999, where every trivial thing, it seems, is cited. Mct mht 00:45, 30 September 2006 (UTC)
I encourage people with views like those above to follow and contribute to the discussions at WP:CITE and WP:GA. Discussing this here won't help to convince the editors who recently revised the GA guidelines. "Consensus" was reached on the changes because nobody from the sciences was contributing to those discussions. CMummert 17:57, 29 September 2006 (UTC)

## GA status for Addition?

To my eyes Addition seems to be a good quality article. It might be an idea to put it forward to Wikipedia:Good article candidates, if anyone willing to defend it. BTW it is well cited with both inline and overal cites. --Salix alba (talk) 16:30, 30 September 2006 (UTC)

## Citation guidelines proposal

I know you've been having similar concerns about citations and Good Articles here as we have over at Wikipedia:WikiProject Physics. I have a proposal to deal with this debacle. Let's establish, by consensus within the project, a set of guidelines for referencing physics and mathematics articles in Wikipedia. Then, at least, we will have a set of clear guidelines and an established consensus to refer to if we start having problems with WP:GA and WP:FA. I think if we write a reasonable set of guidelines, which respect WP:V and WP:CITE, we'll get little argument from the vast majority of the people over there.

I have already written a proposal, available here: Wikipedia:WikiProject Physics/Citation guidelines proposal. It definitely has a whiff of the first draft about it (some sentences seem pretty tortured), but I'm confident we can bang it into something that is clear and concise. I've tried to write the guidelines in such a way that they don't apply just to physics, although the examples are (by necessity) taken from articles I'm familiar with. I'm hoping that we can get the editors from both WikiProjects (physics and mathematics) to form some kind of a consensus for referencing our articles, which would give it increased legitimacy: we could incorporate the guidelines into both our projects.

To keep the discussion (semi-)unified, please comment at Wikipedia talk:WikiProject Physics or Wikipedia talk:WikiProject Physics/Citation guidelines proposal. –Joke 16:59, 30 September 2006 (UTC)

I urge the participants here to go over the proposal and help reach concensus. I expect it will carry more weight if it is a joint proposal of two active WikiProjects.  --LambiamTalk 23:16, 30 September 2006 (UTC)

## History of mathematical notation - peer review

History of mathematical notation is seeking peer review. --Salix alba (talk) 19:02, 30 September 2006 (UTC)