Wikipedia talk:WikiProject Mathematics/Archive/2008/May

Émile Lemoine
This recently got promoted to FA. I was late on the scene and was about to raise some serious objections, but the article got promoted before I provided my review. I don't think this would currently pass a mathematics A-Class review (is A-Class review still active?). I've left some comments on the talk page. Have I missed the mark, or do others agree that this article needs some work? Even better, is anyone willing to fix it? Geometry guy 23:52, 24 April 2008 (UTC)
 * As the main contributor to the article, I've responded on the talk page. I'm very willing to address the concerns, and I believe there are fairly simple solutions to about half of them at first glance. Nousernamesleft copper, not wood 00:13, 26 April 2008 (UTC)

Marden's theorem, Steiner inellipse, Complex variables
Concerning links to Marden's theorem, Steiner inellipse: Other things are demanding my attention today; could others help me decide which articles ought to link to these new articles (I just created them) and put the links there? Concerning links to complex variables: it now redirects to several complex variables. But many people use the term to mean complex analysis. Should we make it a disambiguation page? Michael Hardy (talk) 22:54, 29 April 2008 (UTC)


 * I two way linked Steiner inellipse and inscribed circle. I didn't see the circular version of Marden's theorem so haven't touched it. I think the dab page is a good idea, though I think "complex variables" is short for "one or several complex variables", a book title that almost always says virtually nothing about several complex variables, but has a complete introduction to complex analysis of a single variable. JackSchmidt (talk) 00:03, 30 April 2008 (UTC)

Photographs from the Oberwolfach photograph collection
Mathematisches Forschungsinstitut Oberwolfach has released a large collection of photographs under a free license (CC-BY-SA) at http://owpdb.mfo.de/. We can use these without restriction to illustrate articles as appropriate. The photos should be uploaded to commons, not here; I am working out the details of how to track which ones are already uploaded. &mdash; Carl (CBM · talk) 13:00, 18 April 2008 (UTC)
 * That's very good news, but the discussion at de:Portal Diskussion:Mathematik contains an important warning: While most photos in the database are available under this licence, it's not true for all of them. All photos marked "Copyright: MFO", like this one have been released. But the MFO cannot release photos for which it doesn't have the copyright, like this one. --Hans Adler (talk) 13:46, 18 April 2008 (UTC)
 * Thanks for pointing that out. Do you know if there is a category on commons for these images yet? &mdash; Carl (CBM · talk) 13:51, 18 April 2008 (UTC)
 * Apparently not. I suppose it would make sense to create commons:Category:Mathematisches Forschungsinstitut Oberwolfach as a subcategory of commons:Category:Image sources, or something like this. Some German editors talked about uploading to Commons, but it seems they haven't started yet. I didn't see anything in commons:Category:Mathematicians that looks as if it comes from the site. --Hans Adler (talk) 14:40, 18 April 2008 (UTC)
 * The category commons:Category:Pictures from Oberwolfach Photo Collection has been created. --Mathemaduenn (talk) 18:08, 19 April 2008 (UTC)
 * I obtained permission from George Mark Bergman to use the 1888 photographs from OPC on which he holds the copyrights. Where should I record this permission so that we don't bother him repeatedly, or so that we don't sigh and regretfully eschew use of his pictures?  -- Dominus (talk) 18:38, 24 April 2008 (UTC)
 * "Permission" meaning he's releasing them for anyone anywhere to use under an open source or public domain license, or permission meaning he doesn't mind that we use them only within Wikipedia? If the latter, they would fall under our fair use provisions (meaning, it has to be a photo for which no free equivalent can be found, of a dead person, etc). —David Eppstein (talk) 19:57, 24 April 2008 (UTC)
 * Permission for Wikipedia to use them under the terms of the GFDL, which is what the boilerplate letter I copied from WP:ERP said to ask for. -- Dominus (talk) 20:06, 24 April 2008 (UTC)
 * Excellent! I've been adding photos from this collection to the various biographical articles I can find that they match up to, and had several times found good Bergman photos I couldn't use. Now we can. I think where you put the permission statement, on the commons category page, is the right place. —David Eppstein (talk) 06:12, 25 April 2008 (UTC)

So if we find a photo that might be useful in one of the articles, and it's listed as copyright MFO, we're free to upload it to commons ourselves? Where should we link to for a statement of the permissions? E.g., I've found this photo and want to link it to Gyula O. H. Katona (it only says "Katona" but it's obviously not the other Katona, from the date): what do I need to do to accomplish this? —David Eppstein (talk) 19:33, 19 April 2008 (UTC)


 * Yes, you can upload it to commons yourself (you'll have to make a account there if you don't already have one). You should be safe if you just copy the formatting from one of the other MFO images, such as commons:Image:Helmut_Hasse.jpg. &mdash; Carl (CBM · talk) 19:40, 19 April 2008 (UTC)

Bergman photographs will eventually be in color
Also relevant: Dr. Bergman (see above) informs me that most of his pictures are actually color photographs, although the scans online at present are grayscale scans. He says that OPC is currently in the process of rescanning these in color, so that OPC will eventually have the color versions online in place of the grayscale ones.

I am going to create a new category, commons:Category:Pictures from Oberwolfach Photo Collection (Bergman), and put the Bergman pictures into it, in the hope that when the color scans become available, someone will remember to replace the grayscale images with the color images.

If anyone reading this has uploaded any Bergman images to commons:Category:Pictures from Oberwolfach Photo Collection, please go to the image page on commons and add the category commons:Category:Pictures from Oberwolfach Photo Collection (Bergman). Thanks, -- Dominus (talk) 18:37, 30 April 2008 (UTC)

Persistent vandal
The IP user 167.206.204.68 has vandalized Joe Harris (mathematician) three times in about a day and a half and been reverted three times by three different editors. Perhaps he should be blocked? Ryan Reich (talk) 18:02, 28 April 2008 (UTC)


 * The talk page says it's a school IP. The edits look like garden-variety vandalism; who knows why he chose Joe Harris. I'll keep an eye out for a day or two, but I agree the IP is working towards a block. &mdash; Carl (CBM · talk) 18:42, 28 April 2008 (UTC)


 * See Administrator intervention against vandalism. JRSpriggs (talk) 15:01, 29 April 2008 (UTC)


 * The IP was blocked by Edgar181 for 48 hours starting this morning. --Pleasantville (talk) 15:20, 30 April 2008 (UTC)

Implicit function
Some folks are making noises over at Talk:Implicit function about possibly renaming the article. Their objection is essentially that the term "implicit function" may refer to one of two things: an "implicitly defined function" or an "implicit relation". The article, they feel, fails to distinguish adequately between these two uses, and so deserves a major overhaul and/or possible move to implicitly defined function (or other unspecified location). I for one think that this is an awful idea. The term "implicit function" is indeed used to refer to a function, given implicitly, or to a single branch of a possibly multiply defined implicit function. The two editors advocating a change seem to feel the lack of rigor or clarity to be a major problem in the article. I'd appreciate another opinion on the matter. Thanks, silly rabbit  (  talk  ) 23:05, 30 April 2008 (UTC)

David M. Young, Jr.
A stub on the inventor of SSOR (which is in every numerical analysis textbook, and was the king of iterative methods in its time) was deleted. Can somebody restore it please? Obviously, "known for SSOR" or something like that which was there was not good enough for that particular admin. Thanks. Jmath666 (talk) 03:55, 1 May 2008 (UTC)


 * Done. I agree that it did not warrant A7 deletion. Will add some more to protect it from future attempts. —David Eppstein (talk) 04:31, 1 May 2008 (UTC)

Proposal - List of mathematics disambiguation pages
Although Category:Disambig-Class mathematics pages has not been created, Category:Mathematical disambiguation has. Over three hundred WikiProjects use the disambiguation talk page to categorize their disambiguation pages. See Category:Disambig-Class articles. Category:Mathematical disambiguation takes the unusual step of using the disambiguation page itself to categorize. There seems to be no reason that Math disambig pages should be an exception by using the disambiguation page to categorize. As indicated in List of mathematics topics, WikiProject Mathematics uses the meta list List of mathematics categories as a way of keeping track of mathematics category pages. To be consistent, the information in Category:Mathematical disambiguation should be placed in WikiProject Mathematics/List of mathematics disambiguation pages to keep track of mathematics disambiguation pages and the disambiguous pages tagged with mathdab instead only should be tagged with disambig. If you agree, please implement this. Thanks. GregManninLB (talk) 14:28, 2 May 2008 (UTC)


 * Somehow that seems like a lot of work for a system that is slightly worse (as it would be more fragile). Why would you recommend this, other than for conformity with other projects? CRGreathouse (t | c) 14:42, 2 May 2008 (UTC)


 * I think the main argument in favor of the present way of doing things is the stability. Anytime an appropriate category is added to a page, the page is added to the List of mathematics articles. Anytime Template:mathdab is added to a page, it is recognized as a disambiguation mathematics page. It would be more fragile to require a second template to be added to the talk page to do this, and would also be redundant to the pre-existing article categories. &mdash; Carl (CBM · talk) 15:01, 2 May 2008 (UTC)


 * If a disambiguation page has some links to mathematical articles and some links to non-mathematical articles, then do we use the "mathdab" template or not? JRSpriggs (talk) 16:34, 2 May 2008 (UTC)


 * I think we should reserve mathdab for pages that are (almost) entirely about mathematical topics, like Whole number. Pages that are more mixed should just get the regular disambig tag. This is similar to this issue with disambiguation pages for school names.
 * As a proof of concept, I made a list at User:CBM/Sandbox5 of all disambig pages that link to a mathematics article - this can be done without any special tagging of disambig or talk pages, using the list of mathematics articles, and I think it is much more likely to be reliable than manual talk page tagging. So I think the only benefit of mathdab (if there is one) is to mark disambig pages that are particularly mathematical. &mdash; Carl (CBM · talk) 17:48, 2 May 2008 (UTC)
 * That came up recently at Quadratic. I wasn't sure what to do.  -- Dominus (talk) 18:36, 2 May 2008 (UTC)


 * I made an error in my earlier query. The list is actually much longer, and is now divided over User:CBM/Sandbox6 and User:CBM/Sandbox7. The point remains that the list can be generated without the necessity of tagging any pages beyond what is already done. &mdash; Carl (CBM · talk) 02:34, 3 May 2008 (UTC)

Here's another related question (but probably not a very important one). Why are just a few of the pages at Category:Mathematical disambiguation called "Foo (disambiguation)"? VectorPosse (talk) 18:27, 2 May 2008 (UTC)
 * Well, in general you're supposed to use foo (disambiguation) when there's one overwhelmingly primary encyclopedic meaning of foo, that should get the undisambiguated title. On the other hand foo itself should be a disambiguation page if there are two or more meanings that are reasonably competitive with one another. I haven't tried to evaluate how well the math dab pages conform to that principle. --Trovatore (talk) 18:34, 2 May 2008 (UTC)

Template:CSB/Math
Now what should we think of CSB/Math and Category:Mathematics-centric? WP:POINT? This is getting out of hand. --Lambiam 22:59, 2 May 2008 (UTC)

Interpretation (logic)
There is a mathematician who believes that an interpretation in logic does not have to assign unique names to each object in the domain of discourse, also believes that it is objects that we assign, not truth values. Third party requested. Pontiff Greg Bard (talk) 17:10, 30 April 2008 (UTC)


 * This is a somewhat interesting dispute. Cokaban writes (in response, essentially, to the above): "It is the other way around: unique object for every name." and "How can you name all real number, for example, using only words in English alphabet (words of finite length)?".
 * I don't follow the discussion on objects vs. truth values, though.
 * CRGreathouse (t | c) 17:21, 30 April 2008 (UTC)
 * I found it interesting too (for only a short while however). So everyone knows that you can't put the reals into one to one correspondence with the naturals. So with a finite alphabet, a formal language has that type of limitation. I don't think logicians who use this type of interpretation have a problem with that. I am pretty sure about the definition that I have promulgated on this Wikipedia. Pontiff Greg Bard (talk) 17:30, 30 April 2008 (UTC)

This is an amusing discussion. Most discussions are difficult to judge, because both parties make sensible statements, in spite of their dispute. This one is different however: I think the last point should be enough reason for Pontiff Greg Bard to no longer edit the page in question, and leave it to other editors to clean up the page by concensus.
 * Cokaban is entirely right;
 * Pontiff Greg Bard is entirely wrong, or more precisely most things said do not make much sense at all;
 * the current article is a complete mess, in spite of the fact that the MathWorld article to which it refers to (twice) is fairly clear;
 * most other participants in the discussion disagree with Pontiff, as long as they manage to not get tangled up in their own phrases

I am a mathematician not specialised in logic, but I know that a first order formal language is something like the language of elementary group theory: there are names for constants (the neutral element) and functions (the inverse (unary) and the product (binary)), predicates ("=") and variables; terms can be formed by applying functions to the required number of arguments (constants, variables or the result of other function applications), and these can be combined by predicates, logical connectives and quantification to sentences like &forall;x&forall;y: x*y=y*x; some sentences are given as axioms. Now giving an interpretation of the first order language of group theory means just giving a group: specifying the domain of discourse means giving the undelying set of the group; to each name one should assign an element of that domain (in the case of constants, so one should specify which element is to be called the neutral element) or a function of one or more values in the domain to the domain (so the symbol for inverse should correspond to a function from the underlying set to itself, and the product symbol should correspond to function mapping a pair of elements to another element), and every predicate should similarly correspond to a relation on the domain (for "=" the equality relation). Thus each sentence will get a truth value, determined by the meaning of logical operations; and it is required that the given axioms get the value "true". Other sentences could have any truth value, for instance the mentioned sentence &forall;x&forall;y: x*y=y*x will be true if the group happens to be commutative, and false otherwise. Note that Marc van Leeuwen (talk) 12:02, 1 May 2008 (UTC)
 * An interpretation does not change the language (the language of group theory is independent of any particular group), in particular it does not add any names
 * There is no need for all elements of the domain to correspond to some name; indeed most theories have very few explicit names (which does not prevent variables from ranging over anonymous elements)
 * There is no need for different names to refer to different elements: for instance in the elementary language of rings the names "0" and "1" could refer to the same element (in the interpretation given by the zero ring)
 * Names for functions correspond to actual functions with arguments and results in the domain (not truth values)
 * Names for predicates corresposond to relations: functions with arguments in the domain and as result a truth value
 * Only (closed) sentences correspond directly to truth values
 * That's pretty harsh there Marc. Listen, I didn't pull this stuff out of my a**. There are several sources that I provided, and I learned this stuff formally in a class, not independently. It seem that there is different terminology out there, and as usual that's fine with me to include all of it, but it's not okay by you guys. If there is different terminology, then it should be accounted for, not omitted. If you notice I got at least one show of support in the discussion. It says something about possibly you guys have missed the point entirely. Be well, Pontiff Greg Bard (talk) 21:49, 1 May 2008 (UTC)
 * The diff you provide supports unique objects for every name, not unique names for every object. I thought Cokaban suggested the former and you the latter...?
 * Unique objects for every name would mean that j mean Joe and not Jim, but that Person("Joe Smith") could also refer to Joe. Unique names for every object would mean that if j meant Joe than Person("Joe Smith") would have to be someone else, but j could refer to Jim as well.
 * CRGreathouse (t | c) 22:37, 1 May 2008 (UTC)
 * If you look at the whole discussion, he was intending to say that its obvious that we need unique names for each object because that's the whole point of putting it into a formal language. He clarified that here. Pontiff Greg Bard (talk) 22:59, 1 May 2008 (UTC)
 * I don't think that's what he was saying at all -- though he does concede that "when starting from scratch" synonyms "fall to the wayside". I'm slightly confused by your position, though, Greg.  I mean, what would ontology be without multiple names of uncertain providence?  I would think that a philosopher would be most interested in the case of multiple names (though perhaps that is just my own metaphysics bent). CRGreathouse (t | c) 02:17, 2 May 2008 (UTC)
 * I think we covered this on its talk page. The whole point of putting this concept of an interpretation into a formal language, is that we can deal with the issue rigorously. (He agreed on this point). It would make no sense to set out creating an interpretation with two different names for one object. However it is logically possible that there happen to be to objects which we discover are identical to each other, and therefore we find that really there are two names for one object. This would be an interesting discovery after the fact, but no one sets forth an interpretation intending for two names to designate one object. That is what this article is supposed to be talking about designating the various aspects of the interpretation. There is a big difference between what we designate, and what we discover happens to be identical.Pontiff Greg Bard (talk) 02:31, 2 May 2008 (UTC)


 * As someone else pointed out above, there is an interpretation of the language of rings in which both the constant symbol 0 and the constant symbol 1 are assigned to the same object. There is no other way to make a ring with only one object, when there are two constant symbols in the language. Here I am using interpretation in the sense of structure (mathematical logic). It is possible that some other meaning of interpretation is being confused with this meaning. &mdash; Carl (CBM · talk) 02:44, 2 May 2008 (UTC)

Cokaban has added a reference from Benson Mates that supports my formulation (although it does not specify unique names), and Cokaban who was entirely right while I was either entirely wrong or didn't make sense has accepted that formulation as have I. So I would appreciate at least some concilliation from all the harsh criticism of myself here. If I had listened to Marc there would have been NO progress at all. Stay cool. Pontiff Greg Bard (talk) 19:55, 2 May 2008 (UTC)


 * I agree I was harsh, and I'm happy to provide some concilliation. In fact I just wanted to be clear, and did not intend personal critcism, although I was not so naive to ignore that I could hurt your feelings. In any case I did not make any judgement of your intentions, I just said that in this particular discussion you were (in my opinion) wrong. And in saying you did not make any sense at all was certainly sloppy, I just meant that the arguments you supplied did not seem to support the point you were defending; therefore saying you were wrong was somewhat missing the point. In my opinion the main issue of the discussion was whether an interpretation maps names (in the language) to objects (in the domain of discourse) or objects to names, and you seemed to defend the latter point of view, but I could not see many arguments or sources that supported this. To me it would seem that in a natural interpretation of a language that formalises a sentence like "if all humans are mortal and Socrates is a human then Socarates is mortal" the domain of discourse could well be the set of all creatures, without any need for the language to have names for each and every one of them (in fact the language only needs the name "Socrates" to formulate the sentence; being human or and being mortal are predicates). That's all. By the way the reference from Benson Mates seems to be added by Djk3, not Cokaban, see this diff. I see Interpretation (logic) is improved since I posted my remarks above (even though some of it resembles a talk page); I'll leave it in the middle whether this was thanks to or in spite of the fact that anybody did or did not listen to what I said. Marc van Leeuwen (talk) 11:03, 3 May 2008 (UTC)


 * The rephrased writing has removed the comments about names, which were the part that was most problematic. On the one hand, I think Hans's question whether the names were meant to be formulas, objects in the domain, or something else, was never answered. On the other hand, Marc pointed out above that if names are part of the language, the original phrasing in the article was wrong, and I discussed on the article talk page how the text in the article had accidentally reversed the meaning of reference that it was drawing from. &mdash; Carl (CBM · talk) 11:40, 3 May 2008 (UTC)

Mathematics bias
Please have a look at WikiProject Countering systemic bias/Mathematics. Is this an apt analysis of a justified complaint? --Lambiam 12:38, 1 May 2008 (UTC)


 * Looks like a one-man movement, by the history. This WikiProject should probably be deleted, as it's clearly an attempt by one person to create an issue out of nothing. As far as I know, logicians between philosophy and math get along just fine - well, except for maybe this guy. Tparameter (talk) 12:54, 1 May 2008 (UTC)


 * Isn't it a bit late for April Fools pranks? --C S (talk) 13:38, 1 May 2008 (UTC)


 * Unfortunately I am sure that Gregbard is serious about this. But I think the worst thing we can do is to be confrontational about it. I suppose the systemic bias people will deal with this.
 * Actually I am not sure if the problem exists. Some philosophical sources on logic contain passages that look like they are intended to be mathematical definitions, but these sources rarely if ever use these definitions in any significant way. I don't know what that means. It could be anything from "I will show my students the mathematical definition to scare them" via some kind of metaphorical use to serious transgression of boundaries. If it is the former, it should be covered only by mathematics articles, because everything else would be a POV fork. If it is the latter, then Wikipedia shouldn't cover the philosophical part per WP:FRINGE.
 * If it's something solidly between these two extremes, then it may well be worth covering from a philosophical angle. The problem in this case would be that we don't seem to have anybody with the necessary qualification and interest to write such articles. That would in fact be a mild case of systemic bias. --Hans Adler (talk) 14:34, 1 May 2008 (UTC)
 * PS: Gregbard is doing some very dedicated work on logic articles; if anybody has an overview of that part of Wikipedia then it's him. Much of what he does is actually quite beneficial. --Hans Adler (talk) 14:43, 1 May 2008 (UTC)
 * I've noticed a systemic bias against gemology articles. Did you realize that the WP:PHILO talk page has ten times as many page views as the WP:GEM talk page?  Something should be done about this. CRGreathouse (t | c) 17:37, 1 May 2008 (UTC)


 * Thank you Hans, that was very kind and open minded of you to say. This effort certainly isn't personal. I think you guys (is it almost all guys btw?) here are sincere, of course. Nobody questions that. There is an interesting theorem that is described at doxastic logic, the one about the "inconsistency conceited reasoners" (not a slight). It says basically that 'If you live in a bubble, you can never really know that you live in a bubble.' I don't expect anyone in the Math department to either admit, recognize, or otherwise acknowledge the issue that I am trying to address. My effort is a sincere one, and yes so far it's just me. This seems to be the "work within the system" thing to do for me. I don't want to be a jerk about things anymore than you guys do when there's a flurry of edits dealing with some of my edits made to to a supposedly 'mathematical' article. I think this is a way to bring wider attention to the issue. I think WP:MATH will most likely benefit from the attention as well. In any case, I do not see that there is any threat of harm in it. It could turn out to be a big nothing, or a flash in the pan, or it may evolve into a project dealing with general anti-philosophical bias from whatever source, etc. You guys are certainly welcome to laugh about it if you like. Ha ha ha, Greathouse, an inductive argument doesn't get by on one claim you know. I will try to avoid anything too personal under the supporting evidence section, which I admit could use more specifics. Although the proposal to delete within 12 hours could qualify. Be well, Pontiff Greg Bard (talk) 19:05, 1 May 2008 (UTC)
 * May I ask what, specifically, is different between logic in philosophy and logic in mathematics? I've taken the logic course offered by the math department at my college as well as the one offered by the philosophy department.  The focus was different, but the logic was the same.  In the math course, we primarily covered meta-theorems and talked about model theory.  In the philosophy course, we mostly did derivations.  The philosophy course was less rigorous, but the logic was not different.  I understand that there are systems of logic that are studied by philosophers that are not generally studied by mathematicians (modal, relevant, paraconsistent, etc.), but in terms of classical logic, what constitutes the bias?  I'm sorry, but I don't even really understand how there can be a bias.  Please explain.  Djk3 (talk) 19:32, 1 May 2008 (UTC)


 * This is certainly a fair question. After all its MATH, what could be more unambiguous, objective, and rigorous? And this WikiProject...it's full of geniuses --no shortage at all. They aren't going to let anything inaccurate through. All of this is the truth --no sarcasm.


 * In the history of philosophy we have seen an evolution. Back in the day there were NO scientists, they were called "natural philosophers." As the knowledge they accumulated became greater, and more understood, specialized fields developed, and the idea that it was "philosophy" went by the wayside. These days science and philosophy only intersect (in an academically recognized way) where there is a frontier: theoretical physics, artificial intelligence, etc.


 * Well guess what? Math used to only be done by philosophers too. However, math is a little different from other "natural sciences." It deals with abstraction, and there is no limit to the frontier of abstraction. So math is still philosophy in certain areas especially in logic. Some here at WP:MATH will probably vehemently disagree with that statement. I have seen on a talk page more than once about "mathematical logic isn't logic," or "these are two different concepts we are talking about," or "the logicist project was a failure," or how about "I don't know much about philosophy, but I know x is not philosophy," etc. These sentiments, all of which have been seen here in some formulation, are more about personal identity with an academic group, than it is about the actual nature of the concepts being considered.


 * We have a very large group of mathematicians, some are introverted, some are very critical because of their appreciation of rigor, some are attracted to the idea of certainty, some are just left brained, etc. There are all kinds of generalizations that could be made, however in the aggregate we get a self selecting group of whatever stripe. Certain patterns have developed some of which I have noted under "supporting evidence" at this CSB/Math project.


 * For certain articles the issue is obvious: Consistency. There is almost no philosophical treatment even though it is obviously a very important concept for philosophy. This kind of issue is widespread, and it is basically the philosophy department's fault because we are so small, and not nearly as active as the math people. However, when efforts are made to provide the philosophical aspect, there is an intellectually hostile tendency due to this environment to either delete it as irrelevant, or unimportant (even if sourced as we are seeing at interpretation (logic)), or there is a proposal to disintegrate the article covering what really is one concept into two (see Theory and theory (mathematical logic), for instance). These are a few small examples, however the tendency behind them is solidly in place in this culture. Over time we get what we expect: a math department with very mathematically complete, rigorous articles, with almost no connection to any other areas. So is it really true that there are no connections or is it just the case that you aren't in a position to see all the connections? The tendency is a self-segregation into math and everybody else. That just doesn't make quality for a general use encyclopedia. Intelligence involves being able to make connections between ideas. If WP is to promote intelligence, we need to endeavor to make those connections.


 * So the way it manifests itself isn't necessarily in any particular statements in any particular article: they are all accurate just fine. The issue is about the organization of articles among each other, and the organization of the outline within some others, for some it is hostility to alternate terminology, for many others it's the omission of important aspects that mathematicians would never themselves see as important. The issue is real, the question is what do we do about it? Pontiff Greg Bard (talk) 21:00, 1 May 2008 (UTC)


 * So what exactly, then, is the difference between logic in philosophy and logic in mathematics? Djk3 (talk) 22:57, 1 May 2008 (UTC)


 * Greg, frankly, most of the time when you complain about an "anti-philosophy bias", my observation is that you really mean things that don't agree with your philosophy. Not all of us mathematicians are clueless about philosophy -- some of us know at least a little about it. Your views, at least if I've understood them correctly, are sharply at variance with most of the prevailing currents in philosophy of math. That doesn't mean they're wrong, of course, but casting the disputes as tensions between a "mathematical" and "philosophical" worldview is inaccurate. --Trovatore (talk) 19:56, 1 May 2008 (UTC)


 * I think that's a little 'very' unfair. I may be the only person really bringing up the issue, but that doesn't mean its all about me. You are trying portray me as some kind of radical or fringe, and that is very unfair. At some point I thought it was important that the article on set include the fact that a set is an abstract object. It was you guys who really are on the fringe making a big discussion of it and trying to say that this isn't actually quite important. FOR INSTANCE. My views and more importantly, my edits, are well within the academic mainstream. As usual I give examples, but when I am accused it's just rhetoric. Don't get me wrong Trov. I appreciate you quite a bit, but you are being unfair in that last paragraph.Pontiff Greg Bard (talk) 21:00, 1 May 2008 (UTC)


 * Naturally, you'd feel this way, being susceptible to the "living in a bubble" theorem that Greg Bard described above. Your photo on your user page even seems to show this bubble, although I wonder how you managed to get a realistic nature backdrop in there.   --C S (talk) 20:10, 1 May 2008 (UTC)
 * Yes the theorem applies to me too. Feel free to jab at it so as to make it pop, please. That would be doing me a favor. But I don't have any image on my user page?? To what are you referring? Pontiff Greg Bard (talk) 21:00, 1 May 2008 (UTC)
 * The comment was to Trovatore, as the indenting indicates. --C S (talk) 21:17, 1 May 2008 (UTC)
 * It all makes sense. Pontiff Greg Bard (talk) 21:35, 1 May 2008 (UTC)

Could this be part of the larger phenomenon: Wikipedia has covered the topic of mathematics more succesfully than it has philosophy? Michael Hardy (talk) 22:07, 1 May 2008 (UTC)
 * If you mean to say that there really isn't a bias issue, but rather the math articles are just more complete because of the sheer numbers, and the philosophy articles just need to catch up but are slow to do so because of the numbers, that's just not the whole story. For certain articles that really that need attention from both, there is intellectual hostility, and segregation. I am constantly watching things being deleted from articles: for example. Also, I pretty much go through hell just to add any logical or philosophical foundations/connections in these articles. For example the idea that a set is a abstract object. Where does the idea come from to fight about these things? Then there is the tendency to split an article into (math) and (everyone else). These are tendencies that hold back progress toward any eventual GA. So there is more to this issue than completeness or numbers. Be well, Pontiff Greg Bard (talk) 19:41, 2 May 2008 (UTC)


 * When I see a statement in an article that is incorrect, I tend to correct it. In mathematics, there is no such thing as "the notion of completeness". There are various uses of the term "complete", which are only marginally related, and are not instances of an embracing notion of "completeness". Therefore, a sentence making a claim about "the notion of completeness" in mathematics is in error and should be corrected. It is obvious that the notion of completeness in mathematical logic is a precisely defined version of that notion as used by logicians who are not mathematicians; I did not think that needed to be pointed out. For the rest: is the set of members of WikiProject Philosophy an abstract object? --Lambiam 21:39, 2 May 2008 (UTC)
 * You are really proving my point here Lambiam. Everything has to be within mathematics or it doesn't seem to exist under that view. It's a common view. However it is missing an opportunity to improve a great many of these articles to a much higher level. Yes, a set is an abstract object, so therefore the set of members of WP:PHILO is itself an abstract object, and yes the empty set is too. Pontiff Greg Bard (talk) 22:50, 2 May 2008 (UTC)


 * From personal experience - the mathematicians I know are very precise with their language and definitions. This makes it difficult for someone with a little training in logic to contribute substantive logical content on wikipedia without running into true logicians, who are very precise, and who tend to read every word in this manner. I suspect this is the nature of the aforementioned so-called "bias". Instead of a interpreting this as a problem, I would suggest that those of us lower on the totem pole should be humble and learn from the PhDs. (Not directed at Lambiam, obviously) Tparameter (talk) 22:10, 2 May 2008 (UTC)
 * I have no problem deferring to any PhD's. The problem is for the precious tiny little logic I do know about, which is being deleted or omitted as irrelevant or unimportant, that's not a rigor issue. That's pov. The links to meaning, name, and reference were all taken out of this article on interpretation. I'm pretty sure there are plenty of PhDs who understand that there are relevant connections to these concepts in an article on interpretation. Be well, Pontiff Greg Bard (talk) 22:50, 2 May 2008 (UTC)
 * Are you aware of WP:OVERLINK? In articles that use plenty of technical terms that people may not know the definition of, you have an inclination to make wiki links for words that are used in their natural language sense. These wiki links go to articles that sometimes give the correct definition for the context, sometimes a wrong and utterly misleading one (as in the case when you linked to consistency from a natural language use of "consistent" in a legal text). In both cases they are only helpful for people who don't want to understand the article and prefer surfing away on a random link. --Hans Adler (talk) 23:06, 2 May 2008 (UTC)


 * This isn't about the thing where a few weeks back, you indiscriminately added a wikilink to consistency to all wikipedia articles containing the word "consistent" in any vaguely mathematical sense, regardless of whether that sense had anything to do with logical consistency, is it? You were reverted, and rightly so. To inject some computer science / statistics terminology into a discussion about mathematics and logic, you might do to read Precision and recall — by introducing so many wikilinks, you increase the recall (the number of times a relevant wikilink is present where it should be) but at great expense in precision (the proportion of the present wikilinks that are relevant). The same seems to be true for the completeness example you're pushing above: the mathematical article about completeness says that it has many different meanings, but your edit pushed the logical meaning to the front and claimed that "the" mathematical meaning is related to it. That claim may sometimes be true, for some of the meanings of completeness, but is often not true. By being less pushy in your claims that everything is about philosophy you would be more likely to have your edits accepted. —David Eppstein (talk) 23:02, 2 May 2008 (UTC)


 * You guys all have a knack for exaggeration. I did not indiscriminately added a wikilink to consistency in all wikipedia articles containing the word "consistent." I had a list of a few hundred, I looked at each one to exclude things like consistency like oatmeal, consistency in performance, etc. I took a look at the article on precision and recall, and I found it interesting, so thank you for that. However, the key disagreement between us is the idea about how relevant these links are.


 * As far as completeness, I didn't push anything to the front as you describe... it was there by some mathematician's hand believe it or not, originally. It was removed by one too and has remained out. So stop with the exaggerating and all that "pushing" baloney. I'm just bringing the issue up, and if you view that as pushy, well then that also supports my thesis about the math-centric view: Just bringing up the logical and philosophical aspects of these things alone is viewed as pushy. You should see this as an opportunity to improve a lot of articles in a way that isn't being covered. It seems to me that that should be a wonderful thing for WP:MATH. The fact that it isn't seen that way is why there is the whole CSB/Math thing. Be well, Pontiff Greg Bard (talk) 23:32, 2 May 2008 (UTC)
 * When there is something like "syntax (structure)" and "semantics (meaning)" in an article, then it seems bleedingly obvious that "syntax" and "semantics" must be linked at the first occurrence because they are technical words that many people don't understand, and that even those who do might want to look up in connection with the article where they occur, and "structure" and "meaning" must not be linked because they are just vague natural language explanations of the technical terms. I really don't understand what's the problem with that. And it's exactly the same for mathematical technical terms.
 * The problem with your overlinking is that people no longer know which are the technical terms they need to look up to understand the article. That was the problem with the abstract object link in set, for example. It's hard enough to learn what sets are about if you are explained the basics, and only the basics, in a systematic fashion. But when your teacher starts with digressions about abstract objects, formal languages, meaning, and giraffes, without making it clear that these are digressions rather than essential for the subject, then you will be so confused that you never learn it. I am talking about teaching mathematics. Teaching philosophy is probably the other side of the coin. The point is that they need to be taught separately, because it's almost impossible to learn both aspects at the same time. --Hans Adler (talk) 00:06, 3 May 2008 (UTC)

GregBard, I wanted to address your complaint about the segregation of mathematics and non-mathematics content. I sympathize with your point of view that there are advantages to a broader perspective. However, there are very good reasons to insist on a clear separation between math and non math in WP. There are plenty of people who are often confused by mathematics (in fact, perhaps that’s true of every person exposed to mathematics, including mathematicians). If you mix mathematics and non-mathematics in a way which is not clear, that is likely to add to the confusion. A very important aspect of mathematical education is in the learning of what constitutes a mathematical argument, a mathematical statement and a mathematical definition. Exposure to mixed content is likely to result in some unlearning. This is less of a problem for fluent mathematicians, and much more of a problem for the lay person. For this reason, we are very reluctant to mix in some philosophy within a mathematics article. Oded (talk) 06:54, 3 May 2008 (UTC) P.S. I now notice that essentially the same point was raised earlier by Hans Adler above. Sorry about the repeat. Oded (talk) 18:05, 3 May 2008 (UTC)


 * To be fair, most of the articles that Gregbard is referring to are the mathematical logic articles. I don't think anyone is proposing that we should add philosophical stuff to articles like fibre bundle or even group (mathematics).
 * The articles where this issue arises tend to be those where a single word has several meanings. For example, there is a concept of atomic sentence in predicate logic, and another concept of atomic sentence in natural-language philosophy. These are (distantly) related, and my initial guess is that the terminology in predicate logic was chosen exactly because of the similarity between the them. My impression of Gregbard's argument is that he would like to see articles that cover both aspects of the terminology, and I agree with that. But I view the two terms as substantially different, although similar, rather than the same. Another example is theory: I don't view theories in mathematical logic (which are sets of formal expressions) as identical to scientific theories (which are natural language things, typically not formalized).
 * Unfortunately, a few editors who are interested in these philosophical aspects have not added the philosophical stuff to the articles, they have instead been duplicating the mathematical material that appears in other articles. One example of this is atomic sentence, which in predicate logic is a trivial intersection of two definitions and not interesting enough for more than a couple sentences. Its real interest is in the context of philosophy. &mdash; Carl (CBM · talk) 11:36, 3 May 2008 (UTC)

"List of mathematics articles (A)" is badly misalphabetized
List of mathematics articles (A) is not in alphabetical order. I've done enough nitpicking for today; can someone help. Michael Hardy (talk) 18:25, 2 May 2008 (UTC)


 * Mostly it looks fine? It is sorted in the "C" locale way, with upper case letters coming before lower case letters.  I think the list is mostly machine made, so this makes some sense.  Probably the machine could be asked to sort case insensitively, and just fix the list on the next update. Are there (m)any that are not explained by the case sensitive issue? JackSchmidt (talk) 18:46, 2 May 2008 (UTC)


 * If that's true, then it should say "ANO" where it says "Ano". It is absurd to put "Ano" before "Abh". Michael Hardy (talk) 21:27, 2 May 2008 (UTC)


 * When Mathbot generates the heading, it replaces an all-caps title by one in which only the first letter is capitalized. The same happened for RTC. It's smarter than it looks, perhaps being too smart here; perhaps its trainer can dumb it down a bit. --Lambiam 22:38, 2 May 2008 (UTC)
 * Good points. I made sorting case-insensitive. Oleg Alexandrov (talk) 20:07, 3 May 2008 (UTC)

Exterior algebra for peer review
I've nominated Exterior algebra for peer review. Perhaps this article can be brought up to GA status. silly rabbit (  talk  ) 20:58, 3 May 2008 (UTC)

10-millionth Bernoulli number computed
Someone's just added to the Bernoulli number article an external link to an article on Wolfram's web site reporting that a new algorithm as made it possible to compute the first 10,000,000 Bernoulli numbers (the denominator in the last one is 9601480183016524970884020224910 and the numerator has a very large number of digits). Michael Hardy (talk) 22:24, 1 May 2008 (UTC)


 * The algorithm is not new, just running it for longer than anyone has attempted before. Still, it's a nice achievement. Fredrik Johansson 18:23, 2 May 2008 (UTC)
 * It's the 10,000,000th Bernouilli number only. The algorithm in principle goes back to Euler; its advantage is that it's not recursive. Septentrionalis PMAnderson 23:40, 6 May 2008 (UTC)

template:logic
Someone is requesting comment on the philosophy of logic section of the logic template. Pontiff Greg Bard (talk) 23:16, 6 May 2008 (UTC)

Problem of Apollonius
The problem of Apollonius is gradually oozing towards its Featured Article candidacy. If any of you wanted to contribute or offer suggestions on how to improve it, I'd be most grateful! :) Willow (talk) 00:09, 7 May 2008 (UTC)

Compact Spaces *
What shall we do with the new article titled Compact Spaces *? Does its creator know that Wikipedia article titles are not usually supposed to be plural or that the capitalization of the initial s is against Wikipedia conventions? What's the asterisk for? And then there's the question of the article's content. Take a look. Michael Hardy (talk) 13:17, 30 April 2008 (UTC)


 * It is User:Topology Expert (of Induced homomorphism fame). Nearly every one of this editor's edits has been problematic, but I'm not sure what to do about it.  Invariably I would inadvertently bite the newbie.  I do feel that some kind of intervention is needed.   silly rabbit  (  talk  ) 13:21, 30 April 2008 (UTC)


 * Induced homomorphism though revised, is still of questionable accuracy. Though the case discussed there (fundamental group) currently is an example of an induced homomorphism it's far too restrictive. For example given an invertible linear map S on a vector space V
 * $$T \mapsto S T S^{-1}$$
 * is an induced homomorphism on algebra of linear operators.--CSTAR (talk) 13:30, 30 April 2008 (UTC)


 * I revised it this morning to take a more general point of view. Please take a look at it again. —David Eppstein (talk) 19:54, 30 April 2008 (UTC)
 * Back to the original question, I suggestion undoing the recent move: i.e., moving the article back to supercompact space. Though I see you have already done that.  silly rabbit  (  talk  ) 14:21, 30 April 2008 (UTC)


 * Can someone please check out some of these other edits. To my mind, almost all of them degrade the articles.
 * Special:Contributions/58.161.137.66
 * Special:Contributions/58.161.138.218
 * Special:Contributions/58.161.139.34
 * Special:Contributions/Topology Expert
 * JackSchmidt (talk) 21:03, 30 April 2008 (UTC)


 * I agree with your assessment. If these are all the same person (is WP:RFCU called for?), then someone clearly needs to have a heart-to-heart with User:Topology Expert.  silly rabbit  (  talk  ) 21:17, 30 April 2008 (UTC)


 * someone might wanna check out those links again. Mct mht (talk) 13:24, 4 May 2008 (UTC)


 * Call me an optimist, but I think that this editor will be fine after some guidance. Silly rabbit, please do not let WP:BITE stop you from talking to Topology Expert. People won't learn unless their mistakes are pointed out to them. -- Jitse Niesen (talk) 14:17, 4 May 2008 (UTC)


 * You optimist! But seriously, although I have no doubt that User:Topology Expert will eventually be able to contribute constructively to the encyclopedia, the problems continue.  Now he or she keeps adding (inexplicably) the db-repost template to the Supercompact space article.  I explained that the correct procedure is AfD, as have other editors, but this doesn't seem to have made an impression.     silly rabbit  (  talk  ) 14:30, 7 May 2008 (UTC)

Moving the math section from WP:Words to avoid to WP:Manual of Style (mathematics)
WP:Words to avoid talks about different meanings in mathematics for the word "natural". Does anyone here know a reason why this shouldn't this be in WP:Manual of Style (mathematics)? WP:WORDS is one of just 6 pages in the "Wikipedia style guidelines" category that's a requirement at Good article nominations, so this guideline should be just as short and non-subject-specific as possible. Why should we make people learn about mathematical terms as preparation for writing any Good Article? Full disclosure: my degree is in math, and if I have a bias, it's pro math/sci/tech. - Dan Dank55 (talk)(mistakes) 15:55, 7 May 2008 (UTC)


 * That section would serve no function in WP:Manual of Style (mathematics). Mathematicians already know that it is not evil to claim that some numbers are more natural than others. They do not need to be lectured that the words "natural" or "naturally" may have precise technical meanings.
 * However f that section is removed, then, when a maths article is up for Good Article review, the reviewers will naturally balk at occurrences of the words "natural" and "naturally". --Lambiam 21:44, 7 May 2008 (UTC)


 * Exactly. The whole point of that section is to inform those who don't already know, not those who do. Michael Hardy (talk) 02:32, 8 May 2008 (UTC)


 * If a reviewer says "I can't pass this article, you're using the wrong word", which is extremely unlikely anyway, then you could just point them to this section in WP:Manual of Style (mathematics). Why is it that everyone on Wikipedia who wants to learn about Good Article criteria needs to read about mathematical definitions?  Would you want to have to study terms from medieval art or biophysics as part of your WP:GAN process? - Dan Dank55 (talk)(mistakes) 03:41, 8 May 2008 (UTC)


 * Why the repeated emphasis on GA? This has nothing directly to do with GA; it is a Wikipedia style guide that applies to all articles.  Using your argument, does it make sense to have every Wikipedian read this style guideline before editing articles?  I think not.  In fact, I think this page's purpose is to be a reference to point people towards, rather than something one is supposed to read before editing Wikipedia articles.  Many dedicated, thoughtful Wikipedians don't need most of the advice in the guideline.  But some need to be gently guided to a relevant passage should something arise.  So your questions presuppose an argument that nobody is advocating.  The passage could be improved to be a more general statement about technical writing, if that would make you happier.  That is really the content there; it is not aimed at only mathematics.  --C S (talk) 04:41, 8 May 2008 (UTC)

List of scientific publications of Albert Einstein
Hi all,

I'm about to nominate List of scientific publications of Albert Einstein as a Featured List candidate, but if any of you had any suggestions, I'd be happy to incorporate them. I know this falls somewhat outside the scope of the Math WikiProject, but many of you might be interested, so I thought it couldn't hurt to mention it here. :) Willow (talk) 19:50, 6 May 2008 (UTC)


 * I've now nominated it as a Featured List.  Your input there would be welcome; follow the link! :) Willow (talk) 20:23, 8 May 2008 (UTC)

No new math articles for several days
If we can believe WikiProject Mathematics/Current activity, then no new math article have been created for several days. Is this just a case of someone who takes care of that page being on vacation? Michael Hardy (talk) 02:31, 8 May 2008 (UTC)


 * User:Oleg Alexandrov's bot maintains the lists of mathematical articles, and has not made any recent changes to the mathlists. JackSchmidt (talk) 02:52, 8 May 2008 (UTC)
 * Oleg says it is fixed now and will work as normal tomorrow. JackSchmidt (talk) 04:16, 8 May 2008 (UTC)
 * Sorry, the computer on which the bot ran had issues. Working now. Oleg Alexandrov (talk) 15:13, 8 May 2008 (UTC)

Request for comment on Linear least squares
I am having a big disagreement at the linear least squares article with another editor. I believe it is very important to state early on in the article that a linear least squares problem amounts to solving an overdetermined linear system of equations. The other editor disagrees, claiming that the article in question is not about mathematics, that its primary readership is people in experimental data fitting, and that matrix notation is an advanced topic. Other editors views on this are very welcome, at Talk:Linear least squares. Thanks. Oleg Alexandrov (talk) 15:13, 8 May 2008 (UTC)

Disambiguation help at Quasilinear?
Hello wonderful Math-smart editors!

I'm trying to clean up the disambiguation page Quasilinear, and in that, the best thing that I could figure to do would find the most relevent article for each fo the three terms there, in order to clean up the page. For the middle item, it seems like Big_O_notation could provide the necessary information, but I've become lost trying to find related articles for the other two entries. I was hoping there might be some good ideas here, at least for the first one (I know the third is economics related). On a similar note, are all of these topics close enough to make this not a disambiguation page, but actually an article? If only I understood the concepts enough to know... but since I do not, I defer to you all. Many thanks, -- Nataly a 20:35, 9 May 2008 (UTC)
 * Wow, that dab page does need clean up! I think the meanings are very close, but perhaps not close enough for a single article.  Basically "quasilinear" means "linear is easy, here is something that superficially resembles linear and still happens to be somewhat easy".  However, the definition of "linear" is different in each of three cases, and the way it resembles it differs as well, making a single article very hard to write.
 * For the first meaning, differential equations might be the best link. I don't know if you want to make quasilinear differential equations a section redirect (until someone can write an article on it, it is the name of a chapter in my intro pde book, so probably easily its own article).
 * For the second, I think you are good, and I've no idea on the third. Thanks for taking on such a difficult dab, and asking here rather than just deleting it. JackSchmidt (talk) 21:34, 9 May 2008 (UTC)
 * Thanks for the help! That first link seems like it will be good for the first entry - thank you!  Two down, one to go.  :)  I'll see if I can get any ideas out of some economics folks.  Thanks again, -- Nataly a  12:11, 10 May 2008 (UTC)

New number articles
What do people think about these number articles? &mdash; Carl (CBM · talk) 02:30, 10 May 2008 (UTC)
 * 314 (number) and 3141 (number)
 * 12765 (number)
 * 1033 (number)


 * 314 and 3141 are obvious deletion candidates per Notability (numbers), particularly given Articles for deletion/3.14. I would just prod these and cite the precedents.  Best play it safe and AfD the other two.  My own vote is delete both as non-notable.   silly rabbit  (  talk  ) 02:46, 10 May 2008 (UTC)


 * I don't think they need to be deleted; we can always redirect them to the nearest round integer instead. But I'm not well-versed in esoteric number properties the way some people are. &mdash; Carl (CBM · talk) 02:56, 10 May 2008 (UTC)


 * Well, 1033 (number) contains only one section 1033 in computing, and apparently it refers to the numerical encoding of a certain locale on some operating systems. This is really rather a silly thing to have an encyclopedia article on.  It would be better to have one like Numerical encodings of locales on Windows XP, and I'm not even sure that deserves an article (per WP:INDISCRIMINATE).  As for 12765 (number), this may be more significant: it is (apparently) an internet meme in Finland.  But the article does a rather poor job of establishing notability.  Of all four, this is the one I could be most persuaded to keep.  As for 314 and 3141, the only notable feature the articles establish is that they are a power of 10 multiplied by &pi; with the trailing decimal then truncated.  Plenty of articles involving digits of &pi; have already been deleted.  I see no particular reason these should be kept.   silly rabbit  (  talk  ) 13:43, 10 May 2008 (UTC)

Notations for Cartesian products
This appears in copula (statistics):
 * $$B=\times_{i=1}^{n}[x_i,y_i]\subseteq [0,1]^n;$$
 * $$B=\times_{i=1}^{n}[x_i,y_i]\subseteq [0,1]^n;$$

I'm wondering if there are particular views on advantages and disadvantages of this particular notation for Cartesian products, as contrasted with this:
 * $$ B=\prod_{i=1}^{n}[x_i,y_i]\subseteq [0,1]^n; $$
 * $$ B=\prod_{i=1}^{n}[x_i,y_i]\subseteq [0,1]^n; $$

Michael Hardy (talk) 18:17, 9 May 2008 (UTC)
 * I use capital Pi myself; but this may well be one of those things on which we can afford to differ. We will never have a Bourbakian uniformity of notation; the only functional difference is that one may be more familiar than the other. Septentrionalis PMAnderson 19:16, 9 May 2008 (UTC)


 * A slightly more important question, though, is if the former notation is used at all. (I have not seen it myself, which is not to say that there isn't some reference out there for it.)  It isn't Bourbakian to choose standard notation over nonstandard notation.  But like I said, it's entirely possible that the first notation is commonly used.  VectorPosse (talk) 05:54, 10 May 2008 (UTC)


 * I have seen $$\times_{i=1}^{n}$$ a few times, but in my experience it is not nearly as common as $$\prod_{i=1}^n$$. Oded (talk) 05:57, 10 May 2008 (UTC)
 * I've seen it in collections of algebraic topology papers; my memory suggests it was one of the large Springer paperbacks, but I have no idea which. Bringing it up on the article talk page, and seeing if anybody minds switching, may be best. Septentrionalis PMAnderson 16:42, 10 May 2008 (UTC)
 * For cartesian products, I would have thought that
 * $$B=\otimes_{i=1}^{n}[x_i,y_i]\subseteq [0,1]^n;$$
 * was most common.
 * I would think use of capital pi (Π) should be kept to just the case of arithmetical products. Jheald (talk) 19:43, 11 May 2008 (UTC)


 * One should not use $$\otimes$$ for Cartesian product because, in my experience at least, it is always used for the tensor product which is quite a different thing. Personally, I prefer to use $$\Pi$$ or $$\prod$$ when taking the Cartesian product of a sequence of spaces, but an infixed $$\times$$ for the Cartesian product of just two spaces. JRSpriggs (talk) 20:16, 11 May 2008 (UTC)
 * I whole heartedly agree (don't use ⊗), but my experience has been a bit more disturbing. I have seen ⊗ used for the direct product of abelian groups (I think Fulton, I'll have to check at the office), and × used for the tensor products of algebras (A.A. Albert). At any rate, the world is crazy, we do not need to fix it, but I think we should stick to whatever notation is common in the community.  Has someone considered simply:
 * B = [x1,y1] × ⋯ × [xn,yn] ⊆ [0,1]n
 * which might be easier on everyone. JackSchmidt (talk) 22:52, 11 May 2008 (UTC)

Just to add to the notational confusion, Cartesian product of graphs uses a box symbol, while in graph theory the &times; symbol instead refers to the tensor product of graphs. The symbols have some visual resemblance to the graph products they create. —David Eppstein (talk) 22:59, 11 May 2008 (UTC)

Linear algebra for algebraists
I was trying to help cleanup symplectic group, but I noticed I would need to counter a very real systematic bias in our linear algebra articles. That is, most articles assume the field is the real numbers, but a few particularly enlightened articles also allow the complex numbers. Some claim to allow any field, but actually mean any field of characteristic 0.

What is the right way to handle this?


 * 1) Should I go around breaking all sort of physicists articles so that they apply to all fields (in the sense of algebra), but maybe not fields with a riemannian metric on them?
 * 2) Should I create parallel articles that handle the algebraist's idea of linear algebra?
 * 3) Should I create "Over arbitrary fields" sections of every article?

I don't personally have the expertise to simultaneously address the analytical / physicist audience and the algebraist audience. In fact, I don't even have the number theory or topology expertise to handle linear algebra over complete DVRs. My main references are Kaplansky's textbook for a Second Course in Linear Algebra, and Grove's textbook on Classical Groups. I don't think I can give a complete, broad perspective, just a different perspective, and I am not sure how to use that to help out. JackSchmidt (talk) 16:40, 10 May 2008 (UTC)


 * In your situation, I would go through the articles, remove all spurious mention of the field, and put a note at the top of the articles that the field can be arbitrary. Then, if something isn't true over an arbitrary field, you can go and put back in R, C, or "characteristic zero" wherever necessary.  Sometimes, of course, an "in arbitrary fields" section is necessary, especially to balance a discussion of a theorem which requires special fields but has a limited generalization to others (for example, the Jordan canonical form).  If it's an interdisciplinary article (i.e., a "physicists' article"), you can instead put at the top of the article "these results are true for any field; for illustration, this article will use R as an example", thus satisfying everyone.  You could save yourself work and do that even for the pure math articles, if you wanted to sacrifice absolute correctness (but also avoid a lot of arguments). Ryan Reich (talk) 16:35, 11 May 2008 (UTC)
 * We don't get much feedback from people actually trying to learn from our articles, but what there is suggests that we do best beginning from a well-known, comprehensible, case, and increasing in generality as we go down the article. This would mean beginning over R or C (which is usually what the physicists will be using and linking to), and expanding first to characteristic zero and then to arbitrary fields.  Septentrionalis PMAnderson 18:09, 11 May 2008 (UTC)
 * This approach is very reasonable in many circumstances. However, I think that WP will be increasingly useful for mathematicians to look up a concept that is outside their experties and to refresh their memory with regards to a definition, find a reference, etc. Depending on the subject of the article, we can try to make an educated guess who the likely readers would be and write accordingly. Oded (talk) 18:51, 11 May 2008 (UTC)
 * If I'm looking for a particular fact about symplectic groups, the arrangement doesn't really hurt me; I'll search down until I find what I;m looking for. (And unless it's the dimension, or the homology group, I won't find it.) So we should accommodate the students for whom it does matter. Septentrionalis PMAnderson 19:44, 11 May 2008 (UTC)

Ok, to make sure Im summing this up right: we prefer keeping R, C, char 0, and all fields together in one article, but with a section nearer the bottom describing the general field case, while the top of the article pretends we are working in the one (or two) true field(s), R (or C). For the most part this bottom section will be "the previous holds with obvious modifications over all fields of characteristic not 2, and for char 2, we do the following non-obvious modification. We also have the following algebra-y facts that don't matter much over R or C, but that are important over more or less every other field." We will ignore linear algebra over non-fields for now, and assume it will mostly get put into articles about the functors measuring how weird that stuff is.

Assuming so, I'll go add *references*, transvections, perfection, centers, and orders to symplectic group, and have a go at adding the general field / char 2 stuff to all of the various symplectic/alternate articles. JackSchmidt (talk) 22:37, 11 May 2008 (UTC)

"Theorem"?
The initial sentence of the article titled theorem offended me and accordingly I did this edit. Opinions? Michael Hardy (talk) 20:21, 11 May 2008 (UTC)
 * has been proved, surely? Septentrionalis PMAnderson 20:22, 11 May 2008 (UTC)
 * The article originally mentioned the mathematical use of the word, until it was changed by (guess who): .  silly rabbit  (  talk  ) 20:27, 11 May 2008 (UTC)
 * .....sigh........ That whole culture needs to get some sense talked into them, not just that one Wikipedian. Michael Hardy (talk) 20:31, 11 May 2008 (UTC)

Not "surely" at all. Mathematical logicians speak of whether or not there is an algorithm that decides of statements in a formal language, whether of not they are theorems. In that context, "has been proved" is wrong. And the article seems biased toward that particular context, although I hope my recent edits have left it less so. Michael Hardy (talk) 20:30, 11 May 2008 (UTC)

This led me to notice Formula (mathematical logic), which is currently in extreme need of improvement (permanent link). I'm going to work on that, if someone else can work on the theorem article. &mdash; Carl (CBM · talk) 20:49, 11 May 2008 (UTC) h
 * I have no objection to your clarification at all, M Hardy. The distinction you make is correct. I don't understand the offense, however. Be well. Pontiff Greg Bard (talk) 20:55, 11 May 2008 (UTC)
 * The offense lies in replacing an understandable lede describing a concept used widely in both mathematics and mathematical logic, and turning them into unintelligible technicality focusing only on the usage in logic, as you did in these edits. Or, in other words, consider the audience: how many people reading the theorem article will find it helpful to have the second and third links of the article be to abstract object and type-token distinction? If they follow those links, will it help them to learn about what a theorem is? —David Eppstein (talk) 21:27, 11 May 2008 (UTC)

Both these articles will benefit from having a few more people participating on them, so that the editing pool has more breadth. &mdash; Carl (CBM · talk) 21:05, 11 May 2008 (UTC)


 * To Gregbard: You should not be defining words like "theorem" and "formula" in terms of "token" which, as far as I am concerned, is a meaningless noise. "Abstract object" is also nonsense. JRSpriggs (talk) 23:37, 11 May 2008 (UTC)


 * To be fair, they aren't really nonsense. It's more a question of weight, and presenting things in a way that conveys the correct sense of the field to others. Given that essentially no mathematical logic text will define a first-order formula as a token, I don't think the first sentence of our article should dwell on it. But it may be relevant to include lower down. &mdash; Carl (CBM · talk) 23:42, 11 May 2008 (UTC)


 * Basically, you guys place little to no priority on explicating the foundations of things. In my eye, that view is as inexplicable as how irrelevant you my edits appear to you. Here I am trying to tell what the thing is in some fundamental way. That clarifies it, and clarification is the main project of analytic philosophers. The audience to which I write is a reasoner in the spirit of the doxastic logic article. That means everybody: the average person, the logician, the mathematician (in so far as they follow reason). I take my cues from what an analytic philosopher would say x is for any article within the purview of logic. That is the perspective that should be in the first paragraph of all of the most important logic articles: template:logic. I am not worried about confusing your mathematical brethren. If that is a priority, then further clarifying language will be the way to handle it, rather than deleting, marginalizing, etc. Hopefully this type of knowledge will bridge the gap in the future. Be well, Pontiff Greg Bard (talk) 02:25, 12 May 2008 (UTC)
 * No, Greg, you take positions as to what the foundations of things are and present them as non-controversial, when they are anything but. Your insistence on conflating "theorem" with "formal theorem" cannot be left unchallenged. If they were the same thing, then no one would have proved any theorems before, maybe, Frege. --Trovatore (talk) 02:35, 12 May 2008 (UTC)


 * Could you provide any mathematics or mathematical logic text that defines a theorem as a token? It seems to me (and I am probably among the more accommodating people) that at best the articles abstract object and type-token distinction are tangential to the article on theorems. Everyone has things that they wish were done differently in the literature, but we generally try to avoid reconstructing foundations, and stick to the way that things are presented in mainstream textbooks. &mdash; Carl (CBM · talk) 02:31, 12 May 2008 (UTC)


 * I changed the wording from "can be proved" to "proven". If I say "the Riemann hypothesis is a theorem", it means I think someone has proved it, not that I simply accept the conjecture. CRGreathouse (t | c) 15:49, 12 May 2008 (UTC)
 * Well, a quibble: I think the conjecture is not really that RH can be proved in any particular fixed theory, but simply that it's true. So the example is not exactly on point the way you've worded it.
 * That said--you've given a pretty good example of the theorem-v-formal-theorem distinction. The collection of formal theorems of, say, ZFC, is a mathematical object that we can study in its own right (noting, say, that it's computably enumerable but not computable). If we code RH into a formal string in the language of set theory, then whether that string is an element of the collection of formal theorems of ZFC, is not a time-dependent question -- if it is, then it always has been and always will be, independently of whether some human mathematician has proved it. But whether it's a theorem in the more usual sense used in everyday mathematical discourse is a time-dependent question. Thus "theorem" and "formal theorem" are not the same thing. --Trovatore (talk) 21:09, 12 May 2008 (UTC)

Concerning the "offense". I am beginning to suspect that some people take this to mean that the person who wrote the words has sinned somehow, and that's why it alarms them to read that someone was offended. That, however, is not what I intended.

Mathematical logicians sometimes distinguish between "theorems" and "meta-theorems". But the things they call "meta-theorems" are really theorems, and the things they call "theorems" are really mathematical models of theorems in the same way that one might use a mathematical model of a bridge over a river, and the model isn't really a bridge. Michael Hardy (talk) 00:21, 13 May 2008 (UTC)

discourse, interpretation, model
I'm afraid a lot of articles are in a shambles right now. I am not a professional mathematician - though, I have a hard-earned degree, and am working toward another. I believe that these terms describe different things, though lately there has been a ton of work done to blur, if not eliminate, this distinction. Here is what I believe is the difference, simplified, between these terms:

The discourse contains primitive terms, like elements, relations, operations, and so forth. It also contains a set of unproved statements about the primitives, which we can call 'axioms' or 'postulates'. All other definitions and statements in the discourse come from the primitives and axioms. 'Theorems' are logically deduced from previous statements.

If for the primitives we substitute definite terms that convert all of the postulates into true statements, then this set of substituted terms are called an interpretation of this particular discourse. If all deductions are correct, then the theorems are now true statements as well. The result of such an interpretation is called a model of this particular discourse.

There.

Now, can some experts please, please, please clarify the above for any non-experts who are drastically modifying (if not vandalizing) these articles so that we can start to repair the related articles? Tparameter (talk) 14:13, 12 May 2008 (UTC)


 * In contemporary math logic, the terms are used somewhat differently than that. The term discourse isn't used at all. An interpretation gives semantic meaning to the symbols of a language; in first-order logic an interpretation is also called a structure. So for example, if the language has a single binary function symbol, +, an interpretation is a set together with a concrete function that interprets the + symbol. A model of a set of axioms is an interpretation that also makes the axioms true. So for example, the interpretation above might be a model of the group axioms, or it might not. &mdash; Carl (CBM · talk) 14:19, 12 May 2008 (UTC)


 * Look at interpretation (logic) and Formal interpretation, and see how these various terms are at times combined and confused. Search each for "discourse", "interpretation", and "model", and you'll see that they are at times used as synonyms. In fact, various model articles and interpretation articles have recently experienced various degrees of combining/inter-meshing.


 * I was taught the type of meaning I noted above, though I'm not sure that I've summarized it well enough - but, I'll defer to PhDs, and hope for the best. Tparameter (talk) 14:30, 12 May 2008 (UTC)


 * Yes, there is a lot of confusion about interpretation (logic) and formal interpretation. I was hoping you would be able to shed some light on the philosophical use of the terminology. &mdash; Carl (CBM · talk) 14:32, 12 May 2008 (UTC)


 * First, let me clarify that your definition of model is consistent with what I believe to be true, which distinguishes it from the definition of interpretation. In fact, I'm not sure how what you said really differs from what I said, other that being more specific to logic.


 * I took a formal course in math logic (taught in the Philosophy department) not that long ago, so I'll dig the Boolos text out and refer to it specifically - but, I'm not a logician. I'm sure several logicians here could attack this with much more accuracy than me. I really just wanted to bring attention to the ambiguity that has recently arisen. Tparameter (talk) 14:36, 12 May 2008 (UTC)

Is ugly duckling hocus pocus?
The article Ugly duckling theorem which is in Category:Set theory seems to me to be a bogus article. What do you think? JRSpriggs (talk) 18:58, 3 May 2008 (UTC)
 * On first sight, I would say the "theorem" is probably a meme rather than a theorem, and it seems to have been around for some time. Google Books confirms that the PDF file linked from the article is not a hoax either.  I would say the real question is whether it's notable, but that's probably not a mathematical question. --Hans Adler (talk) 19:18, 3 May 2008 (UTC)


 * (e/c) It appears legitimate to me (see Scholar). The article is poorly expressed, and poorly categorized as well (Category:Set theory is pretty obviously inappropriate).  This may be an actual theorem, although a proper statement and reference would obviously be need to establish this.   silly rabbit  (  talk  ) 19:24, 3 May 2008 (UTC)


 * I have run into this article before. My impression is that this is an interesting issue for artificial intelligence; the argument given in the article is enough to imply that artificial intelligence software may need to be programmed to value some relationships more than others if it is going to simulate human judgment. But the topic is unrelated to set theory. I changed the categories some. &mdash; Carl (CBM · talk) 20:00, 3 May 2008 (UTC)


 * Update: has PRODed this article. JRSpriggs (talk) 12:17, 4 May 2008 (UTC)


 * I have de-PRODed it, and provided an additional reference. There are about 60 links to this theorem on Google Scholar, so Arthur's PROD reason doesn't hold up.  More references are available, but I don't have time to sort through all of them to find those which will enhance a reader's understanding of the article: many of them are technical reports and papers, which only mention the theorem in passing.  At any rate, the theorem is notable, and more references establishing notability can be given if needed.  I think this article should be kept (but cleaned up significantly).   silly rabbit  (  talk  ) 12:55, 4 May 2008 (UTC)
 * I think if we frame it right that is the important part. I knocked it down a bit, myself. Pontiff Greg Bard (talk) 23:16, 6 May 2008 (UTC)


 * What a profound theorem. If we discard all information about objects, we cannot systematically classify them. Has this ever surprised anyone, expect perhaps by its hocus-pocus (pseudo)mathematical explanation? CRGreathouse (t | c) 16:09, 13 May 2008 (UTC)

mathscinet bibliography format
Hello,

I noticed that bibliographical references in math articles tend to follow the format usually used for physics papers. This is a bit odd. I suggest the mathscinet format. I have used it in all the articles I have written. There are a number of differences. For example, the year, instead of appearing in parentheses at the beginning of the entry, appears toward the end (before page numbers). Katzmik (talk) 14:25, 7 May 2008 (UTC)


 * I think you mean the format that Mathscinet uses for search results, e.g.:
 * Wiles, Andrew Modular elliptic curves and Fermat's last theorem. Ann. of Math. (2)  141  (1995),  no. 3, 443--551.
 * I prefer the year near the beginning when I use author-date referencing such as (Wiles 1995), since the year is needed to look up the reference. This is the format produced by Template:citation as well:
 * &mdash; Carl (CBM · talk) 14:38, 7 May 2008 (UTC)
 * &mdash; Carl (CBM · talk) 14:38, 7 May 2008 (UTC)


 * (edit conflict) I think the best is to use citation or similar citation templates, which has various advantages over un- or manually formatted reference information. These templates show the year after the authors. Seeing the year in front is usually good, I believe, because in a list of references you immediately see whether it is a historical or modern text etc. Jakob.scholbach (talk) 14:40, 7 May 2008 (UTC)


 * It would be hard to figure out from first principles which bibliography style is preferable. I don't think it can be done, in fact.  I do believe that most mathematics publications use the mathscinet format.  My guess would be that most mathematicians would find it more convenient because they are used to it, since most math journals do follow some variation of what one sees in mathscinet.  I personally find the format author (year) confusing, but again only because I am used to it, not because I think it is better from first principles.  I don't know whether it can be reasonably argued that a majority of people reading wiki math articles are, in fact, mathematicians.  If this is the case, a reasonable argument can be made that the articles should follow the format that they are used to.  Katzmik (talk) 14:50, 7 May 2008 (UTC)


 * I believe the benefits of a standardized non-hand-formatted citation from citation outweigh the possible slight unfamiliarity to mathematicians of having the citations in a different format than MathSciNet's. —David Eppstein (talk) 15:02, 7 May 2008 (UTC)


 * Katzmik may not be familiar with things like harv, which uses the citation template, but it makes inline citations much nicer in my opinion. The usefulness far outweighs any issues of compatibility with mathscinet.  Another point is that Wikipedia tries as much as possible to maintain a consistent consistent style and appearance across all articles, regardless of the discipline.  So I think it would break this consistency to insist on a different style for math references.  Finally, to enforce a new style of reference would require a change to tens (hundreds?) of thousands of articles.  "If it aint broke, don't fix it."   silly rabbit  (  talk  ) 15:15, 7 May 2008 (UTC)

I certainly agree with the famous "if it ain't broke" principle. Actually wiki should have a page on it. Unfortunately, in this case, it is indeed broke. For example, the mathematics article contains a bibliography that's half in mathscinet style, half in physics style. Also, I believe that one of the people who commented above may have misunderstood me. I don't think hand-made references are preferable. Obviously it would be preferable to have an automated system, whichever style is used for math articles. I am not sure which hundreds of thousands of articles you are referring to. I believe the total number of math articles is below 20000. Katzmik (talk) 16:00, 7 May 2008 (UTC)


 * You can use the website http://zeteo.info/ to import bibtex (say from MathSciNet) and have it nicely formated using the citation template. It even include the MR template linking back to the MathSciNet entry for the article.  Zeteo is setup to recognize authors and publishers, and for already known authors the citation template will be used so that the author's name is wikilinked to their wikipedia article. JackSchmidt (talk) 15:21, 7 May 2008 (UTC)

I do prefer hand-made citations in general. There are references (particularly historical references, and citations of articles and chapters in books) which citation does not handle particularly well; it also tends to muck up "ed.". Where its format is useful, more power to it; but may I request that it be used all in one line? The format {{citation
 * author= Ish Kabibble
 * publisher = Nonesuch Press
 * publication date = 19000
 * title= A short list of even primes

takes up a lot of space, and makes bibliographies very hard to maintain. Septentrionalis PMAnderson 22:25, 7 May 2008 (UTC)


 * Problem with the one-line format is that it's unreadable. Compare

{{Citation | last1 = Beilinson | first1 = A.A. | last2 = Bernstein | first2 = J. | last3 = Deligne | first3 = P. | author1-link = Alexander Beilinson | author2-link = Joseph Bernstein | author3-link = Pierre Deligne | title = Faisceaux pervers | year = 1982 | journal = Astérisque | volume = 100 | publisher = Société Mathématique de France, Paris | language = French }}
 * to (apologies; it doesn't wrap when displayed)

{{Citation|last1=Beilinson|first1=A.A.|last2=Bernstein|first2=J.|last3=Deligne|first3=P.|author1-link=Alexander Beilinson|author2-link=Joseph Bernstein|author3-link=Pierre Deligne|title=Faisceaux pervers|year=1982|journal=Astérisque|volume=100|publisher=Société Mathématique de France, Paris|language=French}}
 * Sure it takes up a lot of space, but it's precisely because of this that it's easy to maintain. Second author link is wrong?  Scan down the page until you see the author2-link tag.  In the one-line format, you would have to read the entire citation.  If the vertical length makes bibliographies hard to maintain, you can always increase your edit box. Ryan Reich (talk) 23:12, 7 May 2008 (UTC)


 * The multiline format does make it easier to read and maintain the citation, but when used inline it makes the article itself harder to edit -- following the train of thought of a sentence across a gigantic citation is difficult. If they're going to be used that way I'd prefer to see them used at the end of the article and cited by name. CRGreathouse (t | c) 16:05, 13 May 2008 (UTC)


 * As an aside, in zeteo it is possible to switch between the multi-line mode and the one-line mode (in the options page). There is still a slight bug, not separating all fields, but I will shortly fix this. Jakob.scholbach (talk) 12:01, 8 May 2008 (UTC)


 * Between zeteo and citation, would it be possible to equip one of them with a flag that could be set either to yes or a no, so that an article could be switched to the mathscinet format if this is found to be appropriate? The idea of imposing a straightjacket of a uniform style all all of wiki's billion articles seems a bit totalitarian to me.  Katzmik (talk) 09:03, 11 May 2008 (UTC)


 * I don't want to let zeteo output some data in a non-template form. If you want to format the references your way, nobody prevents you from doing so, but it seems that the {{tl|Citation}} template does a good job. You might ask for another citation template featuring the scheme you have in mind, but I think taking into consideration all possible ways (journal papers, books, web citation etc.) is quite demanding. Anyway, what is actually way more important is to have complete and correct information. Jakob.scholbach (talk) 08:59, 13 May 2008 (UTC)

Two new illustrations
I just uploaded these two new illustrations and put them into the article titled trigonometric functions. For several years the absence of pictures to this effect has irritated me and I finally got around to doing something about it. Comments? Criticisms? Proposed improvements? Michael Hardy (talk) 22:17, 11 May 2008 (UTC)


 * I think they will be helpful for the articles, no doubt. In the sin one, could you move the arc for &theta; closer to the angle, inside the small triangle, so that the arc and vertical line don't intersect? In the cosine one, could you move the horizontal ine segment with arrows for cosine below the corresponding side of the triangle, so it doesn't intersect the circle? &mdash; Carl (CBM · talk) 22:25, 11 May 2008 (UTC)


 * These are gorgeous pictures, Michael. However, they are a little "busy" because of the collision of all your double-headed arrows.  My suggestion:
 * In the "vertical" picture, the only big collision is between &theta; and the tangent line; I think it would look better if you simply placed &theta; at the angle itself, rather than making a (well-intentioned) effort to illustrate radian measure as well as the trig functions. Since the geometric definitions don't actually require any particular standard of angular measure, the picture might even be better that way.
 * In the "horizontal" picture, you have more problems. If you take my suggestion above, you'll have to (for consistency) put the &theta; at the angle here as well, which will pretty much require that you move the csc &theta; label (or at least, the two-headed arrow next to it).  Unfortunately, there's nowhere it can go.  The only solution that comes to my mind is that you should use color: give each trig function a (distinguishable) color, and label "their" segments with the same color.  That eliminates the need for the arrows altogether, and basically solves the real estate problem.  My thoughts for colors:
 * sin in dark red, cos in light red;
 * sec in dark blue, csc in light blue;
 * tan in dark green, cot in light green;
 * Maybe others will see this issue more clearly and express themselves more eloquently. Ryan Reich (talk) 22:39, 11 May 2008 (UTC)

Thank you, Ryan.

I object to moving the arc for &theta; into the small triangle because the idea is that &theta; actually is the length of curve. Michael Hardy (talk) 22:49, 11 May 2008 (UTC)


 * If you adopt the coloring scheme, you won't have to move &theta; after all (as you can tell, I wrote my comment off the top of my head, and the end contradicts the beginning). Ryan Reich (talk) 22:59, 11 May 2008 (UTC)
 * I agree with Ryan, use color instead of arrows. JRSpriggs (talk) 23:42, 11 May 2008 (UTC)
 * Come to think of it, &theta; isn't a length, it's a ratio of lengths, of which the denominator is, in this case, 1. The way you draw it, an observant reader who isn't very confident in their understanding of radians might pick up on the distinction and wonder if it's important (this is, of course, a learning experience; also, however, a distracting one.  And there is the real estate issue to deal with).  My original assessment, that the geometric definition is agnostic of how you choose to formalize the notion of angle, I think makes for a more focused diagram. Ryan Reich (talk) 03:09, 12 May 2008 (UTC)

I'm actually thinking of using directed arrows. These could be thought of as corresponding to positive numbers if they point away from 0 and negative if toward 0. Michael Hardy (talk) 01:16, 12 May 2008 (UTC)


 * Nice drawings! Tparameter (talk) 02:06, 12 May 2008 (UTC)


 * That's a nice idea. You could incorporate the arrowheads into the line segments in the diagram, rather than placing auxiliary arrows beside them.  That also saves space. Ryan Reich (talk) 03:09, 12 May 2008 (UTC)


 * The same comment I just made below applies to this thread, too: please use article talk pages for talking about specific articles. It is nice to get attention of many, but this very attention is a precious good. Thanks. Jakob.scholbach (talk) 20:13, 13 May 2008 (UTC)

Vital articles
Any editor with a broad knowledge of mathematics is invited to take a look at Vital articles and offer suggestions on how to improve the list of 1000 vital Wikipedia articles, as well as on the process of choosing them. It suffers from a severe lack of attention and POV editing. &mdash; goethean &#2384; 01:48, 12 May 2008 (UTC)


 * There is a nice list of mathematicians and math articles here. They do seem reasonably "vital", and probably some here are interested in looking at them.  Most of the "top level" articles (algebra, statistics, topology, etc.) are on the list, and some mathematician articles on the list clearly are important and yet need work (Euclid, Hilbert, Poincare are all B-class).
 * We might want to check our rating of Euclid -- we rate it as a start class article, but 4 or 5 other projects as B-class. JackSchmidt (talk) 03:10, 12 May 2008 (UTC)
 * I am not sure I am qualified to as having broad enough knowledge, but a few things seem out of place to me. For example, Game theory and Chaos theory seem a bit less fundamental then other things listed.  It doesn't seem to me that Probability and statistics be underneath Combinatorics.  It is also interesting that Square root and logarithm are the only two functions listed, but I am not especially troubled by that. Thenub314 (talk) 04:04, 12 May 2008 (UTC)


 * I would like to make a comment concerning the overall structure of vital articles page in math. It has entries for Algebra, Analysis, Geometry, and Topology, among others.  The single-word headings are catchy and make for a nice index.  However, the index is a bit misleading as it does not include fields that are just as important as the ones listed, but happen to have two-word names.  I am thinking in particular of fields such as differential geometry and algebraic geometry, which are no less important than topology for instance, but occupy a tiny portion of the Geometry entry.  Since I myself am a geometer, I should justify the above claim beyond personal preference.  Indeed, I think it can be easily justified in terms of the number of publications, how old the field is, etc.  For instance, a hundred years ago topology did not even exist yet (and was called analysis situs), while both differential geometry and algebraic geometry were by then established subjects with huge bibliographies. Katzmik (talk) 13:19, 12 May 2008 (UTC)


 * What about Real analysis, Complex analysis, and Functional analysis? Each of these fields is at least as significant a development in modern mathematics as topology or chaos theory as well.  The current list spends far too much time, in my opinion, on geometrical shapes: Point, Line, Plane, Circle, Shape, Square, Triangle, Cube, Sphere.  This is really overkill.  silly rabbit  (  talk  ) 13:33, 12 May 2008 (UTC)


 * It's a question of what "vital" means. I interpret it as "vital to a classical encyclopedia". So I think it should be tilted towards classical, elementary topics. The list of vital articles begins, "This is a list of basic subjects for which Wikipedia should have a corresponding high-quality article, and ideally a featured article." &mdash; Carl (CBM · talk) 13:37, 12 May 2008 (UTC)
 * (&larr;) Right now, I don't think it is of much importance if their list of vital articles is exactly "right". If it has *any* vital articles on it that are not up to snuff (and still fit on a page, which it easily does), then it serves a very important purpose to remind us of some articles that definitely need work. Surely we can agree that the fathers of geometry Euclid, Poincare, and Hilbert deserve more than a B?  It also nicely points out that most of the "index" articles need work as well.  Many of us concentrate on subjects that didn't exist a thousand years ago, when a fundamental subject like Geometry is still B class.  Once we have good articles to offer the editorial team, then we can nitpick over which of our good articles are vital.
 * Part of our wikiproject's job is to organize the experts, so that we can work together to bring together cutting edge research into encyclopedic form, but probably we should also remember a little of our duty to the "service courses". WP Math should probably ensure that a student in school can find a reasonable encyclopedia article on basic subjects such as Number, Geometry, and Algebra.  Things like Game Theory and Chaos Theory are vital because they captured popular attention (actually, I think game theory is reasonably vital on its own), and WP math should ensure they get expert coverage, not just rehashes of new york times articles (or IMDB summaries of Jurassic Park!). JackSchmidt (talk) 13:46, 12 May 2008 (UTC)
 * I agree 100% with Jack's statement. I'd also like to take this opportunity to expand on his comment about game theory. I think that it is extremely important for our society that people be better educated about game theory. Game theory can offer insight into so many of our social and economic interactions. Many current laws (for example, tax laws) are flawed because the public and its representatives do not benefit from this perspective. So while game theory is not so central in mathematics, it is very important for human society, and as such can also help us promote math. (I am not a game theorist myself.) Oded (talk) 14:47, 12 May 2008 (UTC)


 * I did not mean to put down game theory or chaos theory. Anything to improve tax laws is great.  But given the context of the rest of the list those subjects seemed to stand out to me.  If they should be there I would only suggest that perhaps many other things are missing that also capture the publics attention. In the end I did not know exactly what was meant by a vital article so I was going by the context of what was listed.Thenub314 (talk) 16:16, 13 May 2008 (UTC)

sine_cosine_plot.svg
On the trigonometric functions page, I just noticed that one of the illustrations could be improved. There is a nice color picture of the graphs of the sine and cosine functions at sine_cosine_plot.svg. However, the slope of the graph of the sine function as it appears in the picture is definitely not 1! The whole point of introducing radians is to get rid of the constants arising in differentiating these trig functions. The picture definitely uses radians as the x-axis is marked with &pi;, 2&pi;, etc all over. Yet the slope is wrong! Katzmik (talk) 14:11, 12 May 2008 (UTC)

P.S. The same goes for Img:Tan.svg later on on the page. Katzmik (talk) 14:12, 12 May 2008 (UTC)


 * Messages concerning specific articles (like this one) should be posted on the corresponding article talk pages. Jakob.scholbach (talk) 20:10, 13 May 2008 (UTC)

The obnoxious word "where"
Can anyone who can, respond to my comments at Talk:Titchmarsh theorem? Michael Hardy (talk) 04:47, 14 May 2008 (UTC)

Geometries vs. Spaces
An interesting question has been raised at Talk:Geometry. --Lambiam 21:41, 16 May 2008 (UTC)

Emmy Noether update
Hello maths people. As many of you know, I have been working over the past several weeks to bring Emmy Noether to FA status. and others have provided some invaluable assistance, providing crucial context and detail on the mathematics sections. We'd like to invite you to drop in and have a look, just to check that all the info is accurate and sensible before we move ahead in the process. Thanks in advance! – Scartol  •  Tok  22:04, 16 May 2008 (UTC)

knot theory for FA?
Jkasd, who is off to a good start on Wikipedia (including adding a nice knot table to the knot theory article), has suggested putting up knot theory for FA status. I think some (maybe even many) people are happy with math articles being A-class (rather than FA), and there have been issues in the past with math FA nominations. Nonetheless, I think this ought to be discussed as Jkasd has wisely asked for comments before starting the nomination. Personally, one thing I'm a bit afraid of is the FA reviewers coming in and mucking up the article. Comments, such as objections or reasons why this might be good, are welcome! [I've notified Jkasd of this thread]--C S (talk) 20:34, 1 May 2008 (UTC)
 * The lead would need to be fixed for FA, which might be good or bad. It reads well, but it is at least double if not triple the standard post-FAR length.  The lead has some unsourceable claims in it, and that will force a hundred little footnotes into the lead as well.  Certainly these need to be fixed, but we might want to have some experienced, patient, and understanding editors ready to handle the subtle changes to the article and to respond to the FAR.  It might be even better to have some experienced editors go in before the FAR request to preemptively fix a few of them (though its always wise to leave a few things for a reviewer to complain about). JackSchmidt (talk) 21:15, 1 May 2008 (UTC)


 * By "FAR" I believe you mean FAC (FAR refers to FA review which is for FAs that are revisited). By "unsourceable" I believe you mean "unsourced".  I'm curious as to what you think is unsourced and would require so many footnotes.  Citations would only be required for items which are not already sourced in the body (as the lede is meant to summary the body of the article).  I can see a handful of sourcing for some of the historical claims, but not much else as far as the lede goes.


 * The lede length is a bit worrisome, although I note that actually from a random sampling, most are well within 50-75% length of knot theory's lede, and some like action potential are substantially longer. I think it shouldn't be too difficult to shorten it to about 80% of the current length.  --C S (talk) 21:36, 1 May 2008 (UTC)
 * Yes, FAC not FAR, I've mostly watched the FAR process. I definitely mean unsourceable, though there are plenty of things that might want footnotes.  The majority of "This was investigated most actively..." to "wide variety of background and goals." cannot be adequately sourced.  If you can find a knot theorist's recent state of the union address, then some of it can be sourced, but this is making huge claims about a huge number of people in the present day.  It of course can easily be altered to make sourceable claims, but perhaps they no longer convey the same simple message ("this used to be done, then this was done." really, does it say more than that?).  Most of the FA articles I've looked at are littered with citations, and I don't think this one would be an exception.  I don't feel footnotes in a lead improve an article, but I also believe in the three paragraph lead that doesn't need any. JackSchmidt (talk) 23:21, 1 May 2008 (UTC)
 * Actually, checking some more FAs, it looks like 0-20 footnotes in the 3-5 paragraph lead without much pattern as to which articles have 0 and which have 20. At any rate, I only mention the problems in the lead as an example of *good* writing that might have to be altered, doctored, cited, etc. as a result.  The FAC (or at least the FARs I've seen) creates a sense of urgency to fix those teensy problems, rather than correcting fairly egregious problems in the stub and start class articles, or just generally improving articles to B class.  In other words, I was just trying to agree with you about A- being generally good enough, with a specific example of good enough from this article. JackSchmidt (talk) 23:29, 1 May 2008 (UTC)


 * Regarding your comment about having editors ready to shepherd the article through the process, yes, I definitely think that is necessary. In the few math FA nominations I've observed closely, it was definitely necessary to have math editors at hand to make sure everything went smoothly.  That's another reason for starting this discussion here.  Unless there are several people willing to do this, I don't think FA status will happen.  I have nothing against the FA system (not that I'm particularly enthusiastic about it), so if it came up for nomination, I'd help out a bit.  But I think the nomination will require a lot more than that.  --C S (talk) 23:37, 1 May 2008 (UTC)

Thank you, C S. I can see how making this into a featured article might involve "dumbing it down", in an attempt to make it more accessible to the layman. However, I believe we should still try to find definitions that our both mathematically rigorous and easily understandable. Maybe we can receive some new insights on how to find this delicate balance, but in the case that they do start to mess up the article, I say we pull out and content ourselves with an A-class article.  J kasd  22:13, 1 May 2008 (UTC)


 * Who said anything about "dumbing down"? --C S (talk) 22:47, 1 May 2008 (UTC)


 * Ok I see you think "mucking up" = "dumbing it down", but that's hardly my concern. If only what we had to worry about was FA reviewers carefully reading the article and trying to make it more accessible!  Typically, the "battle" is the other way.  Math editors trying to make it accessible while a reviewer argues that it is original research or not supported by a citation (because the source may use more weighty notation, etc.), and trying to make it more complicated. --C S (talk) 22:53, 1 May 2008 (UTC)
 * Sorry about the confusion. This is one of the reasons I didn't just nominate it myself, I've never had experience with FA reviews, and I apparently don't understand the dynamics of the situation.  J kasd  22:56, 1 May 2008 (UTC)

In my opinion it doesn't look like a featured article yet, but it should. When I thought about possible mathematics articles that should be featured, a while ago, I found four obvious candidates: Srinivasa Ramanujan, four colour theorem, fractal and knot theory. These topics have an exceptionally strong appeal to a general audience. I have no experience with FAC, but I doubt that I would consider it as bad as it has been described above. If this article is proposed, count me in. --Hans Adler (talk) 20:39, 2 May 2008 (UTC)

FAC is horribly variable. There are a half-dozen editors who read for clarity and content; but if you don't get reviewed by one of them, you will get reviews like Featured article candidates/Émile Lemoine, which should be read at length; it is what may be expected in a review by people who know nothing about a subject and most of whom will not do research: much quibbling about punctuation (some of it sound) and a superficial review of grammar and sources. (For example, Mathworld is attacked because it's a website, and G-guy had to come along and reassure them about its connections with Wolfram; no mention of its real defects.) Septentrionalis PMAnderson 23:31, 6 May 2008 (UTC)

So, no, at least not yet?  J kasd  17:25, 12 May 2008 (UTC)


 * I think there is no point unless someone is willing to go through the article and make sure all the formatting and punctuation and so forth is done correctly. If you looked at the examples I gave you on my talk page, you will see the majority of issues are of that type.  If too many of those issues are not taken care of before the nomination, some of the reviewers are liable to be annoyed.  --C S (talk) 03:20, 13 May 2008 (UTC)


 * I would recommend anyone thinking about taking an article to FAC participate in reviews for other articles (or at least watch) for a while. There are certainly some folks who may focus on more or less superficial cosmetics.  The article may end up better.  It may not.  The current referencing "standard" is at least one reference per paragraph, which is one reason footnote referencing is more or less standard.  I've kept Monty Hall problem (currently under its second WP:FAR!) using Harvard referencing partly so that there's at least one FA not using footnotes.  I would further recommend anyone taking any article to FAC possess a near Zen-like ability to absorb criticism without becoming defensive.  Taking an article to FAC is to some extent an act of hubris, but succeeding requires putting aside any pride you might have and responding (one way or another) to any actionable suggestion anyone makes.  I suspect a FAC nomination from a newbie would be particularly scrutinized.  I'm distinctly not saying don't do it, just be aware of what you're in for.  Oh, and BTW, if you do nominate it and it does pass, then realize that if you don't babysit it in perpetuity it will eventually degrade to the point that it will be nominated for an FA review and will be de-featured if you don't go through the whole process again.  -- Rick Block (talk) 04:25, 13 May 2008 (UTC)

I think it would be wise to hold off for about a month or so. I created a sandbox version to work on and while going through it, realized I am dissatisfied with various aspects of it. So taking some time before the actual nomination to improve it (a la Willow) seems to be a good idea. Here's a couple things that bother me: 1) previously I had not realized (or perhaps forgotten) that there is a well-respected historian, Moritz Epple, that has written several articles (in English) and a book about the history of knot theory (which is unfortunately in German, which I cannot read). From reading one of these articles, it's clear that Listing's role needs to be amplified and clarified, and the interaction between Tait, Thomson, and Maxwell needs to be straightened out.  The material on the Tait conjectures could be fruitfully expanded.  Some of the knot tabulation history could be improved too (for example, besides the Perko pair someone wrote a paper detailing several mistakes in Conway's knot tables, currently not mentioned in the article).  2) reading the stuff on hyperbolic invariants (which I wrote), I conclude that nobody will understand it. 3) more material could be fruitfully added; for example, a simple Khovanov homology calculation for the trefoil (or hopf link) would go a long way toward showing the historical connection from Conway to one of the currently hottest topics in low-dimensional topology. --C S (talk) 08:53, 18 May 2008 (UTC)


 * I share other's trepidation about the FA process. Note that action potential has 138 footnotes. Regardless, there are some improvements I'd like to see in any case. I think the lede needs to be reworked so it does not put off lay readers with jargon. The reason why the ends of a string need to be joined deserve a paragraph with illustration. I'd also suggest moving the present history section into a separate History of knot theory article and making  paragraphs 4, 5 and 6 of the lede into a history section for the main article (with appropriate rebalancing, of course).  I think a long history section also puts off lay readers. The history article might include photos of key contributer and perhaps some diagrams as well. I also wonder if knot (mathematics) should be merged with the Knot theory article. --agr (talk) 11:26, 18 May 2008 (UTC)


 * these are good suggestions. Since people are now aware of this possible FAC and discussion is now turning to more specific details of editing the article, I recommend switching over discussion to the knot theory talk page.  I will start a discussion thread there.  I also suggest creating workshop subpages there for some of these things Arnold suggested.  --C S (talk)

This is your last chance...
...to review the problem of Apollonius before it heads off to its Featured Article candidacy. If you have anything to comment on or contribute, to improve or reprove, please let us know — thank you! :) Willow (talk) 22:50, 13 May 2008 (UTC)

PS. This will be the first FA for a geometry topic! :)


 * This article looks very well written on my first read. To reiterate things said earlier: it is very important for this wikiproject to support articles on such classical topics.  This article brings together different areas of mathematics from the last couple hundred years, and presents a beautiful problem from a couple thousand years ago.  The WP:Vital articles places a heavy emphasis on geometry, yet we have no geometry FA's.  This is a beautiful article to fix that discrepancy. JackSchmidt (talk) 23:08, 13 May 2008 (UTC)


 * I've done some copyediting, but I've got a few specific questions at Talk:Problem_of_Apollonius that I'd really appreciate some feedback on from WP:Mathematics people. - Dan Dank55 (talk)(mistakes) 17:47, 17 May 2008 (UTC)

WT:MATH versus article talk
Howdy, there has been a lot of article specific traffic here lately, and in some ways that is very good. However, it is important to have article specific discussions archived with the article (on its talk page). Also, large discussions here make it harder for people to watchlist this page.

Does this sound like a reasonable compromise:
 * Discussions about specific articles should mostly be carried out on the article talk pages (rather than on user talk, or WT:MATH)
 * Editors are encouraged to post a short note here asking for comments
 * The comments should predominantly be on the article talk page
 * New or non-member requests might benefit from one or two short "endorsements", so we know which "advertisements" are worth checking out
 * Editors are encouraged to post notes on user talks, if those users are mentioned here
 * Editors are encouraged to have discussions here about broader issues affecting multiple articles

This should still encourage the project to collaborate on individual articles, but keeps article discussions with articles, and project discussion with the project. JackSchmidt (talk) 18:54, 15 May 2008 (UTC)


 * Rigorously speaking, you are right. In practice, it is sometimes simpler to get the discussion started here, then move it/continue it at individual articles. I think a laissez-faire approach works best, especially if there are not too many threads here at the same time. Oleg Alexandrov (talk) 02:46, 16 May 2008 (UTC)


 * The current project talk page is more of a noticeboard than a talkpage devoted to the interests of the project. Perhaps a WikiProject Mathematics/Noticeboard might help take some of the load off this page.   silly rabbit  (  talk  ) 15:51, 18 May 2008 (UTC)

24 hours in a day
Over on WP:AN someone pointed to 24 hours in a day as a page that needed attention. People from here might want to look too. It's packed with unsourced numerology involving Ancient Egyptians, the existence of certain spatial tesselations and the specialness of the number 24. Prod, maybe? I don't see a speedy candidate that fits. —David Eppstein (talk) 15:57, 17 May 2008 (UTC)


 * The prod was contested by the article's creator. I have listed it at AfD: Articles for deletion/24 hours in a day‎.  silly rabbit  (  talk  ) 17:56, 17 May 2008 (UTC)
 * Speedied after author !voted delete. Algebraist 09:44, 18 May 2008 (UTC)

Wikipedia Academy associated with Mathematics Year in Berlin
In case anyone hasn't yet seen it: I'm not sure exactly what this is about (I don't read German) but it's obviously something to do with both Wikipedia and Mathematics. There's a program of talks this June 20 and 21 listed on one of the tabs from this page; it's not clear to me whether they'll be in English or German, but any Wikipedians in the area might find it of interest.


 * Here's my translation. Note in what follows: "Science Year" has been a program from 2000 to 2008 of Germany's National Ministry for Education and Research.  "Science Year 2008" focuses on math.


 * Wikipedia Academy 2008.
 * Mathematics. Knowledge.  Wikipedia.


 * In Science Year 2008, "Mathematics: everything that counts", Wikimedia Deutschland is organizing this year's Wikipedia Academy in cooperation with the Berlin-Brandenburg Academy of Science, and supported by the National Ministry for Education and Research.


 * In lectures, discussions and workshops, the participants will deal comprehensively with Wikipedia and its potential for the (global, reaching a broad audience..."breitenwirksam" is a modern word) presentation of mathematical themes...Information on the Year of Mathematics can be found at jahr-der-mathematik.de.
 * - Dan Dank55 (talk)(mistakes) 21:01, 18 May 2008 (UTC)

In a way I'm amazed. In about November of 2002 when hardly anyone had heard of Wikipedia, then less than two years old, Axel Boldt was the author of most of the several hundred mathematics articles on Wikipedia, and I did some of my first edits. At that time I still had a computer account in the math department at MIT, having had an appointment there that had ended in the middle of August, and I sent an email to all professors, postdocs, and graduate students (I think?) in mathematics there (more than 100 people, maybe?), informing them that such a thing as Wikipedia exists. I think it may have been not long after that that Steven Johnson started editing here, and he was then a graduate student in physics at MIT if I recall correctly, and I think now he's a professor of applied mathematics there. Not long after that, lots of mathematicians became involved. But as recently as 2005, whenever Wikipedia was mentioned in the press, it was accompanied by an explanation of what it is. After Wikipedia's founder Jimbo Wales was named one of Time magazine's 100 most influential people in the world in 2006, the media generally assumed everybody knew what Wikipedia is. And today they do, and an older professor recently informed me, apparently assuming I didn't know, that Wikipedia is a very useful thing "even in mathematics" (that's verbatim). And now Academies of Science and National Ministries of Whatever seek Wikipedia's partnership in organizing conferences. This comes not long after I decided to start trying to reacquire my deficient grasp of German after I'd let it atrophy for a long long time. If some wealthy patron were to pay for the trip, maybe I'd want to go to this thing. Michael Hardy (talk) 04:07, 19 May 2008 (UTC)
 * The list of presenters is available here. All the titles of the talks are in German except for one, in English, to be given by Bill Casselman. The meeting, in Berlin on June 20 and 21, is free but needs advance registration. EdJohnston (talk) 04:37, 19 May 2008 (UTC)

Templates for numbered equations
Does anyone know if there is a template to facilitate the generation of numbered equations in a Wiki document? A pair of templates with roughly the same functionality as the LaTeX \label and \eqref commands would be ideal, but I think I would settle for anything which keeps the numbering consistent within a given document. Does anyone know if such a thing has been tried? If not, is it possible? silly rabbit (  talk  ) 13:23, 19 May 2008 (UTC)


 * I don't think this is possible with the present MediaWiki software. I believe that MediaWiki processes each &lt;math&gt; tag separately; since LaTeX needs at least two runs over the whole input to number equations properly, it's impossible to use standard LaTeX formula numbering. It should be possible to change this with enough work on MediaWiki and texvc, but that's not an easy solution.  If you really have to label an important equation, you're probably best off calling it (*).  Ozob (talk) 22:03, 19 May 2008 (UTC)


 * Sorry, I meant something like a numbering system that works outside the math environment (where ordinary templates have free reign). I guess the question boils down to whether it is possible to increment a counter each time a template is called in a page, and then to affix a label so that the value of the counter at a particular position of the text can be referenced.   silly rabbit  (  talk  ) 00:40, 20 May 2008 (UTC)


 * Footnotes are possible, so this should be as well -- but I doubt it's easy. CRGreathouse (t | c) 05:30, 20 May 2008 (UTC)
 * I'm not sure if this is what your looking for, but I have something in my sandbox that might work.  J kasd  14:36, 20 May 2008 (UTC)


 * Thanks. That's not quite what I had in mind, so I copied your templates over to Eqref and Eqlabel.  Here is an example:
 * $$\int_{\mathbb{R}} e^{-x^2}\,dx=\sqrt{\pi}.$$
 * The main thing is to be able to label an equation, and then be able to refer to the equation later in a way that will be stable under revision. I hadn't thought of using the external-link counter to generate the numbers attached to the equations, but that does seem to work.  Now it would be nice if I could have the back-link display the equation number as well.  Right now all I can get is a little carat symbol: .  silly rabbit  (  talk  ) 15:46, 20 May 2008 (UTC)
 * Ok, I see what you mean, I tried fixing this it, but I couldn't come up with anything that worked, so I added a request here. I'm glad you like the EquationRef template, and I agree that it it looks better that way.  J kasd  16:50, 20 May 2008 (UTC)

Martingale central limit theorem
Some things are unclear in this article. See Talk:Martingale central limit theorem. Can someone help? Michael Hardy (talk) 19:04, 20 May 2008 (UTC)

Edward Wright (mathematician): Peer review
Hi, in an effort to get the article "Edward Wright (mathematician)" to Good Article status at some stage, I've requested that it be peer-reviewed. In particular, comments on the article's general readability are welcome. If you would like to comment on how the article may be improved, please visit "Peer review/Edward Wright (mathematician)/archive1" or leave your comments on the article's talk page. Thanks. — Cheers, Jack Lee  –talk– 01:10, 21 May 2008 (UTC)

Pascal's triangle

 * Originally posted at User talk:Oleg Alexandrov.

Recently, you deleted me edit to pascal's triangle: Below are rows zero to sixteen of Pascal's triangle in table form (even numbers highlighted): Why? how is it not an improvement from the old one: Below are rows zero to sixteen of Pascal's triangle:

1                                             1     1                                           1     2     1                                        1     3     3     1                                     1     4     6     4     1                                  1     5    10    10     5     1                               1     6    15    20    15     6     1                            1     7    21    35    35    21     7     1                         1     8    28    56    70    56    28     8     1                      1     9    36    84    126   126   84    36     9     1                   1    10    45    120   210   252   210   120   45    10     1                1    11    55    165   330   462   462   330   165   55    11     1             1    12    66    220   495   792   924   792   495   220   66    12     1          1    13    78    286   715  1287  1716  1716  1287   715   286   78    13     1       1    14    91    364  1001  2002  3003  3432  3003  2002  1001   364   91    14     1    1    15    105  455   1365  3003  5005  6435  6435  5005  3003  1365   455   105   15     1 1    16    120   560  1820  4368  8008  11440 12870 11440 8008  4368  1820   560   120  16     1 ? Please give me a good reason why the new one should not replace the old one. And I do not think that memory and/or space is an issue. &mdash; Supuhstar  *  § 18:44, 14 May 2008 (UTC)


 * I find the plain text triangle easier on the eyes than the table with cells and colors. I don't think it is relevant to color the even terms. I don't think adding the cells makes things align better. Oleg Alexandrov (talk) 20:17, 14 May 2008 (UTC)
 * On the contratry,
 * the coloring of the evens is mentioned further down the article
 * I cannot see how it is not easier on the eyes, as it is easier to read, the rows are labeled, and the numbers are clearly separated.
 * How does it not make thing align better if they are, in fact, perfectly alingned?
 * Finally, these are all opinions, and that is quite bias, which I believe is against one if not a few Wikipedian policies to remove something based on the fact that you simply "find the plain text triangle easier on the eyes" or "don't think adding the cells makes things align better," when many more people might say the exact opposite.
 * These are facts, not oppinions, and I would like them to be seen as such. &mdash; Supuhstar  *  § 21:09, 14 May 2008 (UTC)
 * Comments here? Oleg Alexandrov (talk) 21:15, 14 May 2008 (UTC)
 * Rows 14, 15, 16 are not "perfectly aligned" as I see them in my browser. JRSpriggs (talk) 21:21, 14 May 2008 (UTC)


 * I agree that the alignment with out tables is better. The bottom rows do not disply correctly here. Thenub314 (talk) 21:27, 14 May 2008 (UTC)
 * I don't see what you are talking about. What browser are you using? I am using IE nd it looks perfect to me. &mdash; Supuhstar  *  § 22:30, 14 May 2008 (UTC)
 * I used MS Paint to judge it, and it has a perfect 45° slope frome each corner to the next. &mdash; Supuhstar  *  § 22:32, 14 May 2008 (UTC)

An advantage of the new table is that the rows are clearly labeled. The alignment is strange; no matter how I adjust the width of my browser I can clearly see irregular staggering along the edges. I don't believe the coloring is an advantage. Not only is it a garish yellow, but the property it is supposed to highlight (approx to sierpinski gasket) isn't particularly important so I would question why the main illustration of Pascal's triangle would need it. This is more aesthetics, but I don't like the boxes and left-centering. I think it shouldn't be difficult to produce an illustration using some illustrator program; it would be neat to have hexagons like a lot of pascal triangle illustrations do. --C S (talk) 22:50, 14 May 2008 (UTC)
 * Alright. I can either fix all those thing you mentioned or make the image you mentioned. which do you think would be best? &mdash; Supuhstar  *  § 22:56, 14 May 2008 (UTC)

(edit conflict) Addendum: I suppose one reason for the ASCII and not having hexagons, fancy boxes, etc., is that it is much more compact. My suggestion of hexagon probably wouldn't be able to clearly show the bottom rows without being incredibly large, but perhaps there is some way of doing it. Supustar's table is already too wide. It would look terrible on a low res system. --C S (talk) 23:01, 14 May 2008 (UTC)


 * I don't think it is necessary to label the rows. You can easily see the row number based on the second binomial coefficient in each row. The cells are also ugly. The ASCII table does a much better job. Oleg Alexandrov (talk) 23:02, 14 May 2008 (UTC)
 * The beauty of a table is that it can be shrunk! I can make it approx. 2/3 or less of the original size! &mdash; Supuhstar  *  § 23:09, 14 May 2008 (UTC)
 * (P.S. It is very necessary to label the rows. This also bring out the fact that you stated. "ugly" is another oppinion.)
 * Even if you shrink the table, the lines delimiting the cells will still be there. They make the table look very busy, which is why I prefer the ASCII version. Ozob (talk) 23:10, 14 May 2008 (UTC)
 * I can take the lines away, too. I love tables because they are amazingly versitile and flexible! &mdash; Supuhstar  *  § 23:13, 14 May 2008 (UTC)

Please make yourself familiar with tables before adding any more comments on what it can or can't do. —Preceding unsigned comment added by Supuhstar (talk • contribs) 23:17, 14 May 2008 (UTC)


 * I've tried it on multiple browsers and the table is uniformly badly aligned — the numbers are left-aligned within each rectangular cell rather than centered and then the cells themselves are placed a little off-center: the top single cell is a bit to the right of the dividing line between the next two cells, etc. But more to the point, it's ugly and hard to read. I much prefer the simpler textual version. —David Eppstein (talk) 23:37, 14 May 2008 (UTC)
 * Okay, I don't know WHAT you guys are seeing, or if you don't have the latest browsers, or what, but this is what I see:


 * &mdash; Supuhstar  *  § 23:49, 14 May 2008 (UTC)


 * This last one looks much better than the first one. But maybe even it is a bit too cluttered. Michael Hardy (talk) 23:51, 14 May 2008 (UTC)
 * I'm sorry, but, could you type that differently? I don't understand. &mdash; Supuhstar  *  § 23:53, 14 May 2008 (UTC)
 * He means that image doesn't look the same as what the rest of us see; it's better, but still not great. here's a screenshot of what I see of your initial post here when I view it in Camino; it's not significantly different when I use Safari instead. —David Eppstein (talk) 00:08, 15 May 2008 (UTC)
 * I use the latest versions of Firefox and Safari and I see basically what David does. It's worse actually if I don't open my browser fullscreen.  Shrinking the table would obviously help with that, but I wonder if shrinking may create its own problems.  I imagine the cell divisions would make the table look pretty cluttered on a small sized table.  --C S (talk) 01:11, 15 May 2008 (UTC)
 * Oops, I see Supuhstar already suggested removing the lines above. Well, doesn't it seem like shrinking and removing the cell dividers, and the color, just brings us back to the ASCII table?  Or does it really look that different?  --C S (talk) 01:19, 15 May 2008 (UTC)
 * I note that, among some of our other articles in Category:Triangles of numbers, Floyd's triangle uses a lightly-formatted table (but a much smaller one), Lozanić's triangle uses ASCII, Rencontres numbers uses TeX, and Stirling numbers of the first kind uses a table without any background colors or dividing lines. I'm not sure there's any great need for making these more uniform, just throwing them out as examples. I think the ASCII in the current Pascal's triangle article is fine, and that redoing it in any of these other ways might end up being as good but is unlikely to be better. —David Eppstein (talk) 01:47, 15 May 2008 (UTC)
 * I haven't followed the discussion, but the plain text triangle looks much better to me. The yellow highlights are distracting and the table formatting reminds me of the bad old days of HTML 3.2. CRGreathouse (t | c) 00:59, 15 May 2008 (UTC)


 * Using tables purely for formatting purposes is discouraged by WP:accessibility and using color alone is even worse, since we actually have blind users who access our articles with screen readers. I'm not sure, but I suspect some of the appearance differences for the table version are due to font size which would affect not just blind users but users with visual impairments who have to use what you might consider to be ridiculously large font sizes.  WP:MOS recommends using minimal markup.  IMO the question that should be answered here is not what's wrong with the table version, but what's the compelling reason it needs to be a table. -- Rick Block (talk) 02:08, 15 May 2008 (UTC)


 * I believe my display problems were due to the fact the computer lab where I work ha a very low screen resolution (800x600) at most. From home or my laptop it looks fine.  The table of plain text always looks good.  Thenub314 (talk) 13:44, 15 May 2008 (UTC)


 * Actually I don't think even the plain text version is particularly accessible to blind users, though the text is still easier than the table. But even for those of us not using screen readers, I don't see any reason to use the table version. CRGreathouse (t | c) 14:54, 15 May 2008 (UTC)


 * Please be so kind to use article talk pages for questions which are about such specific questions as the layout of a single table! I can see that some people are a bit heated, but moving the discussion here doesn't help anybody. I may be wrong but I think this page is for discussions concerning the WP math community as a whole. Unless there are 5 articles where the same discussion about coloring tables is going one, this one is not of that kind. Thanks and good luck resolving the dispute. Jakob.scholbach (talk) 18:31, 15 May 2008 (UTC)


 * Personally, I think it's important to have a place to ask questions like this. Once the conversation is established, then moving it to an article talk page makes perfect sense, and I agree that this thread is ready to move. But I don't want to discourage anyone from posting here to get opinions on a disagreement. &mdash; Carl (CBM · talk) 18:37, 15 May 2008 (UTC)


 * Yes. I didn't mean to discourage anybody to post here, but something like "There is a dispute about ... at ..." should more or less suffice to draw the attention of people willing to dive in. (As for the above, btw, instead of coloring, a bold font type may settle the issue). Jakob.scholbach (talk) 19:33, 15 May 2008 (UTC)

Okay, I think I've made a table to satisfy everybody's wants and needs: Below are rows zero to sixteen of Pascal's triangle in table form: If that isn't reaching the middle ground, I don't know what is. &mdash; Supuhstar  *  § 19:42, 15 May 2008 (UTC)


 * I just thought I'd comment that I appreciate Supuhstar putting this effort in. It's not so easy to take criticism and regardless of whether the table is used, I hope Supuhstar understands we are not disparaging his/her contributions.  At this stage I'm pretty ambivalent about the table; the major issues have been resolved at least to some extend.  I wonder about the accessibility issues mentioned above however, but perhaps they are not so serious; I note that Supuhstar's latest table actually renders better on my mobile device than the ASCII table.  --C S (talk) 04:01, 16 May 2008 (UTC)


 * This aligns very badly in my browser on the right edge. And there is no need to count the rows, just track the second binomial coefficient in each row to see its row number. Oleg Alexandrov (talk) 20:38, 15 May 2008 (UTC)
 * Since I brought up the issue of labeling rows, let me point out that the issue of whether or not to label them is not really a mathematical one, but a pedagogical one. Sure it is not mathematically necessary, but it depends on how much you expect the reader to already know or figure out. --C S (talk) 04:01, 16 May 2008 (UTC)

It aligns quite badly in the mozilla firefox browser I'm using now, on my home computer, which runs (some version of) MS Windows. Michael Hardy (talk) 20:55, 15 May 2008 (UTC)


 * None of the diagonals align in Safari 3.0.4. I like the design much better than your previous one, but I think it's much better with a full-size font instead of 75%&mdash;I tried it out in the preview and thought it looked very nice. Ozob (talk) 23:09, 15 May 2008 (UTC)

One configuration that exhibits the alignment issues people are talking about is Firefox on a Windows machine in a narrow (but far from ridiculously narrow) window width. I'll repeat the question I asked above. What is the compelling reason it needs to be a table rather than the far simpler ASCII version using a fixed width font? I've also asked a blind user to comment on this thread. -- Rick Block (talk) 12:30, 16 May 2008 (UTC)


 * The second table is a vast improvement (IMO) over the first, though I'm perhaps not sure why a table is needed. CRGreathouse (t | c) 12:59, 16 May 2008 (UTC)
 * I want to know what you guys are seeing, but not in these vague terms. If I have solid specific facts, I might be able to fix it. &mdash; Supuhstar  *  § 02:38, 17 May 2008 (UTC)


 * See Image:Pascalstriangle Firefox Mac.png (this is Firefox 2.0.0.14 on a Mac OS X 10.3.9 in Classic skin). You haven't responded to the question yet, though.  What's wrong with the ASCII version?  Every browser has a fixed width font so there aren't any rendering issues.  The HTML is far simpler.  The Wikisource is far simpler.  -- Rick Block (talk) 03:43, 17 May 2008 (UTC)

I prefer the ASCII version to either of the table versions so far. I don't see what the problem is with the ASCII version, that the table versions solve. I find the boxes and colored cells to be distracting and uninformative. So the second table version is better in that regard. However I don't think labeling the rows adds much if any value, and the alignment of the table version is significantly worse for me (Safari 3.1.1, Firefox 2.0.0.14), especially in narrow window widths. Paul August &#9742; 16:51, 18 May 2008 (UTC)

I also prefer the ASCII version to both the table versions ... it will work no matter which browser is used. Both the table versions are difficult to use with screen readers. The second is slightly easier, but it's still difficult because of the empty columns (which have to be there. The ASCII version would also be much easier to read on suitably large Refreshable Braille displays. Graham 87 01:48, 19 May 2008 (UTC)


 * I see now that a table won't do, but what about a hi-def image of the table, or a show/hide feature between ASCII and table (and image?) versions with ASCII as the standard? This would probably my best and last compromise. Could somebody please agree with me? &mdash; Supuhstar  *  § 17:00, 21 May 2008 (UTC)


 * If an image is to be used, I'm certain better images than that of an html table could be made. I also cannot see why people would want to switch between different versions.  As for your "compromise", is your goal to have your table used somehow no matter how inappropriate?  Or is it to improve the article?  --C S (talk) 18:58, 21 May 2008 (UTC)
 * I absolutely agree, which is why an image was one of my first improvement ideas:
 * :Alright. I can either fix all those thing you mentioned or make the image you mentioned. which do you think would be best? &mdash; Supuhstar  *  § 22:56, 14 May 2008 (UTC)


 * And, yes, my goal is to have your table used, therefore improving the article, and some people might want to see the table rather than the ASCII, perhaps for their visual attraction towards a table, or maybe for educational purposes. It certainly would look better in a classroom presentation (if viewed/printed from IE). I am willing to put my graphical talent to use here, so an image is probably best, as it has the potential to be better than both media of presenting the triangle. What do you say? &mdash; Supuhstar  *  § 03:29, 22 May 2008 (UTC)

Fequently viewed articles list
I came across WikiProject Mathematics/Wikipedia 1.0/Frequently viewed/List, and I'm impressed. I'm active in WikiProject Economics and I think a frequently viewed articles list would be very helpful. I imagine there's a good deal of scripting and automation involved. Can anyone who's involved in that let us know what it takes so we can set it up for WP:ECON? Thanks a lot. -FrankTobia (talk) 00:21, 23 May 2008 (UTC)

Composition Ring
This discussion has been moved to Talk:Composition ring. Marc van Leeuwen (talk) 09:26, 26 May 2008 (UTC)

Solving fractional equations
I'm not sure what to make of Solving fractional equations. It looks to me like a fairly flagrant case of WP:NOT. Moreover the article appears to be based on a book of Vedic mathematics, oddly enough. siℓℓy rabbit (  talk  ) 13:39, 23 May 2008 (UTC)
 * Merge with partial fraction? (Perhaps only the assertion that this is treated in the Indian tradition.) Septentrionalis PMAnderson 13:51, 23 May 2008 (UTC)
 * Vedic mathematics is already mentioned at partial fraction. How about just making solving fractional equations a redirect? Algebraist 14:03, 23 May 2008 (UTC)


 * Yes, definitely contravenes WP:NOTHOWTO. I don't think there is anything in there worth saving. Feeling bold, I went ahead and prodded it. Gandalf61 (talk) 14:16, 23 May 2008 (UTC)


 * This so-called Vedic mathematics is a 20th century text with sloppily formulated rules for mental algebraic calculation. The author claimed this went back on ancient lost Vedic texts. No one has been able to relate these rules to formulations found in the known Vedas. As far as I can see the notability of this Vedic mathematics, which has been promoted in many mathematics articles by a single-purpose account, is quite obscure. The whole thing is thoroughly debunked here. --Lambiam 17:48, 25 May 2008 (UTC)

drawing the (2,3,7) triangle group?
Can the graphic wizards around think of a good way to visualize (elements of) the 2,3,7 group? It would be a welcome addition to the group article. Thanks, Jakob.scholbach (talk) 22:09, 26 May 2008 (UTC)


 * Use http://www.plunk.org/~hatch/HyperbolicApplet/ to draw a hyperbolic-plane embedding of its Cayley graph? It's the one in which each vertex is adjacent to two hexagons and one heptagon, right? —David Eppstein (talk) 22:25, 26 May 2008 (UTC)


 * We have images of the order-7 triangular tiling of the hyperbolic plane, and the order-3 heptagonal tiling, both of which have symmetry group (2,3,7). See tiling by regular polygons for more images. Gandalf61 (talk) 10:12, 27 May 2008 (UTC)


 * Yes, but both of those are objects acted on by the group, rather than the group itself. —David Eppstein (talk) 14:38, 27 May 2008 (UTC)


 * At some point I rambled on Talk:Group (mathematics) that drawing the set upon which a group acts is the best that can be done. Basically, groups are verbs, not nouns, so drawing them can only be done somewhat abstractly.  Often times a group acts regularly, so that copies of the fundamental domain can be used to label the group elements by asserting that one such domain is the identity element, and then labeling every other domain by the unique group element taking the fixed domain to this one.  The choice of the fixed domain is arbitrary, reinforcing the idea that you are not drawing the group, but merely its footprints of its walking. However, such drawings are usually pretty and reasonably informative, so probably up to snuff for an encyclopedia article. JackSchmidt (talk) 14:45, 27 May 2008 (UTC)


 * Indeed. A Cayley graph is just another object acted upon by a group - the group action on a Cayley graph is only distinguished by the property that the action of a non-identity element must have no fixed points . But if it is a Cayley graph of (2,3,7), that you want, then we have order-3 truncated heptagonal tiling and order-7 truncated triangular tiling. Gandalf61 (talk) 15:08, 27 May 2008 (UTC)

Two mathematical pages need checking for vandalism
An anon editor has been blocked for vandalising several user pages. (See Special:Contributions/86.131.88.77.) In between the vandal edits, they have also edited Adelic algebraic group‎ and Class field theory‎. Although I did maths as part of my degree, I've forgotten too much algebra to be able to tell if these are valid edits. Could someone please check them? Thanks. Ps there has been more obvious vandalism to one of these pages sicne, I'm not meaning that.--Peter cohen (talk) 10:51, 28 May 2008 (UTC)
 * Done. Both additions were nonsensical in context. Thanks for mentioning it. JackSchmidt (talk) 12:03, 28 May 2008 (UTC)
 * Not at all. It's my normal practice when reverting to check what other edits vandals make. On occasion, I've found vandalism that has been left untouched for weeks.--Peter cohen (talk) 19:05, 28 May 2008 (UTC)

More help needed with logic articles
I need to ask again for more eyes on logic articles that are being edited by Gregbard, in particular Formal system, Formal language, and Formal interpretation. &mdash; Carl (CBM · talk) 21:15, 21 May 2008 (UTC)


 * Given all the time that has been spent arguing with Greg, usually to no one's edification but him, perhaps it's time to file an WP:RFC.  While that's a time consuming experience, can anyone convincingly argue that is a worse use of time than the alternative?  I'd be happy to make an outside comment Since Greg has put some effort at making a more system-wide effort to combat the "math cabal" (including complaints at ANI), I think it is only wise to get the wider community involved.   --C S (talk) 22:12, 21 May 2008 (UTC)


 * I would greatly appreciate any involvement by the wider community. &mdash; Carl (CBM · talk) 22:38, 21 May 2008 (UTC)


 * It seems like Greg is trying to learn, and is attempting to do so by contributing to main space articles, often by contributing what seems like original research. Not sure if RFC is justified, as Greg seems to respond well to requests to discuss and slow down. He is active, however, so a major time commitment is required for any editor working with him. I do see what I believe to be a lot of errors in his contribs. Also, he seems to think the "math people" are out to get him, for whatever reason. Really, it's just that math people are very picky about language and things of that sort - or, at least it seems that way to me. Whatever the case, he has potential to be a very good editor if he'd stop with the OR. Bona fide logicians would be very helpful in these discussions. I am not one. Tparameter (talk) 00:05, 22 May 2008 (UTC)
 * If we can focus on the content, that would be the most constructive. I am using reliable sources. I would be more than happy to participate in any wider discussion concerning myself or the content. In the final analysis, getting people upset is not a WP policy violation. It's not my intention either. You will find I am quite reasonable, and that I edit, and then discuss at length without a big edit war. I find the threats for RFC distasteful however. I have already recently filed one myself so as to stand as testimony that I work well within the system. The response: "Content disputes happen." Lets all get along. Be well, Pontiff Greg Bard (talk) 03:25, 22 May 2008 (UTC)
 * The issue here isn't that you never use sources. For example, the most recent issue was partially because you took a sketched footnote from an older text, in which the author (Carnap) explicitly says he is only giving indications of the correct definitions, and then attempted to paraphrase that with sentences such as


 * "If the class α consists of all of the logical and non-logical signs of a formal language \mathcal{L} and the class ℑ consists of all sentences of \mathcal{L} then a formal language \mathcal{L} can be defined as the ordered pair <α, ℑ>."


 * The better practice is to avoid using footnotes like that as references for basic definitions. If a topic is actually of widespread interest, there will be a text that treats it thoroughly and in detail. If the only source for an entire topic is a sketched footnote, that's evidence that the topic is not of widespread interest.


 * But this is just the latest in what is starting to become a pattern. Just a couple days ago, you were trying to add the claim to Logical consequence that it is synonymous with syntactic consequence (which is incorrect, for those who don't know). The reference you provided for that, Hunter's text, doesn't use the term logical consequence at all! This is another example where you misread or misused the source.


 * Before that, you moved the article model (abstract) to formal interpretation, with no prior discussion and no real evidence that "formal interpretation" is a term that has widespread use among the philosophical logic community. The result on the talk page is that there is still demand for the old article, but now someone will have to rewrite it.


 * Before that, you created an article interpretation (logic), but you have declined to explain what topic you intended for it to cover, leaving everyone else stumped on the talk page. You also spent a while promoting an apparently unsourced viewpoint about "names" in interpretations.


 * There is also the article Theorem, where you have also been adding some unusual claims without providing any sources for them, despite being presented with several sources supporting the article as it is currently phrased.


 * This pattern is what I am concerned about. Each individual page can be resolved through discussion, but there is a limit to the amount that be done at one time. &mdash; Carl (CBM · talk) 11:20, 22 May 2008 (UTC)


 * this is persistent crank behavior cloaked in ostensible "reasonablen-ess". Mct mht (talk) 23:47, 22 May 2008 (UTC)
 * Just to clarify, are you referring to Gregbard or CBM? Thanks. Zero sharp (talk) 23:54, 22 May 2008 (UTC)
 * seems pretty obvious CBM is a professional. Mct mht (talk) 23:57, 22 May 2008 (UTC)
 * Not only that, he is also one of the most patient people I have ever met. I am surprised to see him brought to the point where he seeks action against another editor. But I am not too surprised it was Gregbard who has achieved this. Psychologically it's so much harder to deal with a nice person who is genuinely interested in a topic he doesn't understand than with a troll or someone with a conflict of interest. I agree completely with CBM's evaluation of the situation. For another example of the disruption caused by Gregbard, see the changes initiated by him to formal language, and the expansive discussion at Talk:Formal language that is now necessary to bring the article back to a sane state. There will probably be a few slight improvements in the end that wouldn't have occurred otherwise, but what a waste of time! --Hans Adler (talk) 19:12, 25 May 2008 (UTC)


 * Here we have more attacks on myself. Hans, you have demonstrated to me that YOU do not understand these topics. The difference between me and you is that I am not so arrogant that I have to constantly point out your ignorance. First of all the link you provide is to a Philogo edit. Furthermore, Philogo and I agree (basically) on the focus of the topic, and its first sentence. We both agree that your formulation is terrible. As usual the issue is that any interdisciplinary coverage ruins it for the precious mathematicians who are apparently easily distracted, and not capable of working with others in different fields.


 * Hans, you are exactly the same thing of which you are accusing me: Ignorant, but interested in the topic. However, you certainly are not a nice person, given your constant swipes.


 * This is a formal written request to WP:MATH to please have a chat with your bretheren, Hans. I think he is biggest phillistine-math-segregationist among you. I don't believe that his extreme positions, his incivility, and quite frankly his writing style is representative of WP:MATH. It may need one of you to talk to him and get through. Pontiff Greg Bard (talk) 21:28, 25 May 2008 (UTC)


 * By "changes initiated by him" I meant not only your changes but also those by Philogo, who clearly has his own share of misconceptions about formal languages (probably due to his limited exposure to them only in a special case), and who presumably only editing the article because he agrees with the general sentiment that it is necessary to clean up after you. Of course you are not responsible for Philogo's edits, but you have caused them in this case. Sorry if that wasn't clear.
 * The one positive thing that has come out of this nonsense for me is the following knowledge: That "my" version of the article, which you didn't like, described the Chomskyan version of formal languages, which is remarkably interdisciplinary in that it is used in mathematics (including mathematical logic), computer science and linguistics.
 * The version that you and Philogo created describes a pre-Chomskyan definition of formal languages that is known only in philosophy. Apparently philosophers, as so often, are using obsolete terminology. In the process the two of you have introduced numerous grammatical errors, an absurd bias towards applications in logic (which are dramatically less notable than those in computer science which you have removed), and a passage full of pseudo-mathematical gibberish.
 * I invite all fellow mathematicians who read this to go through the diff and note here whether my claims in the previous paragraph are correct or not. --Hans Adler (talk) 22:02, 25 May 2008 (UTC)
 * As to my alleged incivility: So far I only said that you are wrong and that you are incompetent. These are verifiable facts. It is incivil of you that you ignore these facts and force others to point them out to you continuously. (Not just me, and initially I was much more indirect. By now I am blunt, but try to counter-balance this by also saying positive things about you that I sincerely think are true.) --Hans Adler (talk) 22:20, 25 May 2008 (UTC)


 * Greg Bard wrote: "Hans, you have demonstrated to me that YOU do not understand these topics. The difference between me and you is that I am not so arrogant that I have to constantly point out your ignorance." Greg, I think by now you've demonstrated your ignorance plenty of times.  You have arrogance in spades, and I expect the reason you aren't constantly pointing out mistakes to Hans has nothing to do with your lack of it.  --C S (talk) 02:25, 26 May 2008 (UTC)


 * More attacks. Let's be clear. I have never claimed omniscience where these articles are concerned. However, I do know the aspects of the subject that I am responsible for knowing. I had formal instruction, and I have studied thouroghly since then. If you all insist on playing up how ingnorant I am, that really tells us more about you than me. I have always been willing to defer to those more knowledgeable with no loss to my ego. Hans and yourself on the other hand are truly ignorant, and will remain so because you are committed to your position. You need to learn some respect --both of you. There are edits that Hans has made, which I have yet to respond to because of time more than anything else. You can presume that it's beacuase I'm a big dummy if you want to. You are being very presumptuous, and that is not a good quality for anyone editing logic articles. Pontiff Greg Bard (talk) 03:37, 26 May 2008 (UTC)


 * Your response is not surprising, but I find it remarkable nonetheless. "I have always been willing to defer to those more knowledgeable..."  Always?  Pardon my skepticism.  What happens when you are not willing to admit someone else is more knowledgeable?  Frequently the comments I've seen you make are of the type "You may know more about subject X but we are discussing subject Y".  But even in the cases when you do actually know about subject Y,  it turns out you were completely wrong about the discussion being about subject Y in the first place.  "You need to learn some respect..."  Respect is earned. Think about it this way: Hans, Carl, and I each have no trouble earning respect from others by making contributions to Wikipedia.  You have trouble doing so.  You have chosen to explain this lack of earned respect as the result of victimization by some cabal.  But there is another explanation that you have overlooked.  --C S (talk) 04:56, 26 May 2008 (UTC)


 * Excuse me do I even know you? If you have some constructive criticism concerning some actual wikipedia content that would be wonderful. If all you have is this crap, then leave me alone. More peanut gallery attacks. You presume to know so much! That is arrogance. You should be ashamed of yourself. This whole discussion is a shame on the whole math project. Pontiff Greg Bard (talk) 13:27, 26 May 2008 (UTC)


 * Greg, there are reams of discussion throughout various Talk pages articulating substantive, reasonable concerns and criticisms relating to many of your (and other editors') edits to mathematics and logic articles, which you see fit to arrogantly and summarily dismiss as 'attacks'. This is a pattern.  You are apparently either incapable or unwilling (comes to the same thing) to participate in the normative process of editing, discussion and consensus-building.  Now you are simply being disruptive. Please, stop it. And, before you ask, no, you don't know me, and I don't know you. But I don't have to, it's all there plain as day in your edit history. Zero sharp (talk) 21:34, 28 May 2008 (UTC)


 * Turnabout is fair play. Hans' original comment was mostly about your editing behavior except that he also suggested you were a "nice person".  Don't complain about the "peanut gallery" when you come here and respond to Hans Adler by calling him "arrogant", "extreme", "uncivil", "not a nice person", "biggest phillistine-math-segregationist" and then to top if off, ask us to lecture Hans on behaving and editing properly.  What I "presume to know" is self-evident from the diffs and article histories and talk pages.  The complaints about your editing behavior are clearly valid; however, it's not surprising you don't see your behavior as a problem.  --C S (talk) 16:28, 26 May 2008 (UTC)
 * No CS. You really should be ashamed of yourself. I don't deserve any of this. Certainly, your position and the others here is the position of arrogance. I would never claim that there's nothing I can learn from other editors, however you and everyone apparently has decided that you cannot learn anything from me. That's arrogance. I have made a substantial contribution to the WP, and I have earned more respect than that. Shame on you. Pontiff Greg Bard (talk) 22:22, 26 May 2008 (UTC)
 * You (Greg Bard) are very defensive, not only here but in general about your edits when they are criticized. That makes it difficult and tiresome to deal with you. It is frequently clear to me that you do not really understand the technical issues being raised, but you brush them aside and cling to some formulation in some text you have found as if it is a magical formula. When you replace clear mathematical definitions by vague seemingly self-contradictory prose, you should not be surprised that the mathematical editors are not standing at the sidelines yielding for and applauding this boldness perpetrated in the name of logic. --Lambiam 08:54, 29 May 2008 (UTC)

Limit of a function
An IP recently nominated Limit of a function for GA status; I failed it due to a very sore lack of sources. If anyone feels that the article can indeed be improved to GA status, you're welcome to it. Ten Pound Hammer and his otters • (Broken clamshells•Otter chirps) 17:08, 28 May 2008 (UTC)


 * It still needs a lot of work. It's not even GA by mathematicians' standards. :-P   siℓℓy rabbit  (  talk  ) 12:08, 29 May 2008 (UTC)

Mary Cartwright's proof that &pi; is irrational
I just added to the page titled Proof that π is irrational the proof that Harold Jeffeys attributed to Mary Cartwright. I'm going to wait until tomorrow to look at it closely enough to to decide whether it's really an anticipation of Niven's proof (or maybe more accurately, whether Niven's proof is really just a re-working or re-discovery of Cartwright's proof) or not. In the mean time, maybe someone will beat me to it? Niven's proof seems well known because it was published in a journal; Cartwright's proof, on the other hand, may have escaped publication except in an appendix to Jeffreys' book that got deleted in some of the later editions. Michael Hardy (talk) 14:40, 27 May 2008 (UTC)


 * This seems quite close to the "Niven's proof", so including it doesn't add much. On the other hand, the attribution "Cartwright's proof" is bordering on OR, and as the source noticed, the origin of the proof is unclear (There are several stories of the type "This was well known in Cambridge when I studied there in the 1930s, although it's hard to ascertain who was the first to discover it"). Arcfrk (talk) 21:39, 29 May 2008 (UTC)

The term "Cartwright's proof" is qualified and clarified in the succeeding text, so it doesn't look as if it can mislead anyone. But it is of interest that Mary Cartwright did this two years before the publication of Niven's paper.

(BTW, an elderly professor told me that an elementary proof of the irrationality of &pi; was published "about five years ago". It turned out he meant Niven's paper.  I said that wasn't about five years ago; that was in 1947.  He replied "That's what I said: about five years ago."  (This was not dementia; it was his jocular way of saying I was splitting hairs too fine for him.)) Michael Hardy (talk) 18:39, 30 May 2008 (UTC)

Group for peer review
I have nominated the group article for peer review. When reviewing, please note that there is another related article, group theory. The latter is (or shall be) devoted to advanced topics related to groups, whereas the article under review is to cover more basic facets. Merging the two articles has been proposed several times, but consensus was reached not to do so (see for example here).

The article has reached good article status some time ago and has since been expanded somewhat more, so as to include history and more material on applications. I'm also putting this to PR as to see whether there are significant hindrances to a possible FAC, so if you want to comment on that perspective too, please do so.

Thanks, Jakob.scholbach (talk) 19:27, 30 May 2008 (UTC)

Perfomance of WP:MATH as a whole
I have two ideas concerning the performance of the Wikiproject as a whole, and I'd like to hear what others think about them:


 * 1) The Mathematics Collaboration of the Month is in a more or less dormant state. What about the following idea: restructure the COTM such that it's aim is  to improve an article which is frequently viewed, and is about a bigger topic. Among the top-priority, most frequently viewed and "start"-rated (Abstract algebra, Gaussian elimination, Group theory, Differential equation, Vector calculus, Optimization (mathematics), 1 (number), Equation, Formula, Multiplication, Percentage, Sequence, Combinatorics, Discrete mathematics, Graph theory, Mathematical proof, Fields Medal, Applied mathematics, Fluid mechanics, Euclid, Probability, Random variable) there are a number of articles, which already contain promising material, but need restructuring and so on. I think, this range of articles might be more interesting for people to get into collaborating.
 * 2) What about "measuring" the overall quality of a subtopic? From a look at the rating table of all of mathematics, it appears that Analysis, for example, is overall in better shape than Algebra. If we had a formula (a kind of weighted average on the qualities of the articles in the subdomain in question) assessing the overall performance, we might be able more easily to see what needs to be done. Jakob.scholbach (talk) 10:20, 31 May 2008 (UTC)


 * Good ideas. Tparameter (talk) 12:49, 31 May 2008 (UTC)

"Improper integral" has deteriorated
Improper integral seems to be in a condition inferior to some of its former states. This is one of those topics where people who know little more than first-year calculus get heavily involved, and that's OK as long as they realize that first-year calculus is not everything. But sometimes they don't, perhaps. Michael Hardy (talk) 14:33, 1 June 2008 (UTC)

"Jackson's dimensional theorem"
Jackson's dimensional theorem is certainly not well written. The question is whether there might be something legitimate if it were re-written. It seems clear that if so, it's not understood by whoever wrote this. Michael Hardy (talk) 20:43, 1 June 2008 (UTC)


 * No ghits or scholar hits. I have prodded the article.   siℓℓy rabbit  (  talk  ) 21:02, 1 June 2008 (UTC)


 * I thought I added a db-context. There's nothing there to indicate what the "theorem" (or representation) is.  &mdash; Arthur Rubin  (talk) 21:27, 1 June 2008 (UTC)


 * I had thought about tagging it db-a1 myself, so when I saw your tag I acted on it. Now, what should be done about Ortsbogen theorem? —David Eppstein (talk) 22:10, 1 June 2008 (UTC)


 * According to Google, Ortsbogen is most likely a German term used only in the Swiss school curriculum. It's the set of all points from which a given line segment appears under a given angle; the special case for the right angle is known (at least in German) as the Thales circle, see Thales' theorem. So the big question is: What's the English word for this? --Hans Adler (talk) 23:10, 1 June 2008 (UTC)


 * The locus of points from which a given line segment subtends a given angle is an arc of a circle; this was known to Euclid. Circular arc is probably not the right place for a detailed treatment of this material, but I'd prefer to call it something like Euclid III.21 if we have to have a separate article for it. —David Eppstein (talk) 23:19, 1 June 2008 (UTC)