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As far as I can say, some users of math.stackexchange also participate in editing wikipedia articles.

E.g. here the summary says: corrected the statement of the "subring test"; the mistake was pointed out on math.stackexchange.com. The related question is The subring test

In comment to this MO question a user mentions editing a part of wikipedia article relevant to the question.

Questions of the type: Wikipedia claims this, I do not understand, can somebody help? are, in my opinion, perfectly valid mathematical questions, so there should be no problem with them.

What about questions, where the motivation of the OP is his effort to improve wikipedia article? Examples:

  • Wikipedia article on A contains the claim that B holds if and only if C. I believe that this is wrong for the following reasons..... However, I am not an expert in this area, could someone tell me whether I made a mistake or the wikipedia article is wrong?

  • Wikipedia article on A contained the claim that B holds if and only if C. I believe that this is wrong and I did my best to correct the article; namely that B holds if and only C and D. However, I am not an expert in this area, could anyone check my work?

  • User XYZ changed the wikipedia article about A in the following way.... I think this is not correct. Could someone confirm my suspicion?

  • Wikipedia article about A contains no references for the claim that B holds if and only if C. I was not able to locate such references myself. Is anyone aware of some references confirming this claim?

I believe that the primary place for asking such questions should be at wikipedia, probably somewhere in the scope of WikiProject Mathematics - although I am not exactly sure where, but I was wondering what the users of math.SE would think about posting such a question here.

If such questions are not recommended here, would it at least be appropriate to ask such a thing here after trying at wikipedia and not getting an answer after some longer period?


Perhaps I should add, that I am asking this because I intended to ask the question about an unreferenced definition in wikipedia article, i.e. the last example. (But I will do some more searching before.) I was am not sure, whether to ask it here or at wikipedia.

My motivation is that I would like to know this reference for my study - so it's not the case that the reason for asking is solely an effort to improve the wikipedia article. But if I would get a good answer here, I would probably go on and edit wikipedia article.


EDIT: Another question(s) of this kind:

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    $\begingroup$ What I don't understand is: What does Wikipedia really have to do with this? I mean the motivation of many questions here is often a bit unclear, so I'd say what counts is whether the question is of (at least marginal) mathematical interest. I would be opposed to too many questions asking to "referee" Wikipedia articles or providing sources, but as long as there is something that is on-topic on this site I don't really care if a claim on Wikipedia or a homework sheet is the reason for asking. $\endgroup$ – t.b. Aug 13 '11 at 13:47
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    $\begingroup$ The key word in @Theo's comment is "too many"; I would suppose a few questions of the form "I saw claim x on Wikipedia, but it seems dodgy because of blablabla... am I misunderstanding something?" Note that particular formulation; I would say that even with the free-for-all editing nature of the beast, the likelihood that you're the one misunderstanding is often higher. $\endgroup$ – J. M. is a poor mathematician Aug 13 '11 at 14:41
  • $\begingroup$ Otherwise, only the mathematical portion really matters for the purposes of this site, so you don't necessarily need to tip your hand that your endgame is editing the wiki-page... $\endgroup$ – J. M. is a poor mathematician Aug 13 '11 at 14:42
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    $\begingroup$ @J. M. so you don't necessarily need to tip your hand that your endgame is editing the wiki-page It would feel a little like cheating to me, if I were hiding the reasons for asking. Moreover, quite often people ask about motivation for questions, although usually it is when a question is poorly stated. $\endgroup$ – Martin Sleziak Aug 13 '11 at 14:56
  • $\begingroup$ I did say "not necessarily". But I would say "improving my understanding" is slightly better motivation than "editing a wiki-page"... $\endgroup$ – J. M. is a poor mathematician Aug 13 '11 at 14:59
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    $\begingroup$ @J.M. The source of a question plays no role in its topicality here - only the mathematics. $\endgroup$ – Bill Dubuque Aug 13 '11 at 15:31
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    $\begingroup$ ... that's what I said, @Bill. "only the mathematical portion really matters for the purposes of this site" and all that... $\endgroup$ – J. M. is a poor mathematician Aug 13 '11 at 15:35
  • $\begingroup$ @J.M. My comment refers to your remark about "too many" questions about Wikipedia articles. There can be no such thing since the source plays no role. Perhaps there can be too many questions posted by a user during some time frame, but that has nothing to do with the source. $\endgroup$ – Bill Dubuque Aug 13 '11 at 15:38
  • $\begingroup$ @J.M.: But it is also true that there are quite a few bad mistakes on wikipedia; it really isn't a reliable source for math yet. $\endgroup$ – Hendrik Vogt Aug 13 '11 at 15:46
  • $\begingroup$ I know @Hendrik, but it's always safe to have the initial assumption that you're the one misunderstanding... $\endgroup$ – J. M. is a poor mathematician Aug 13 '11 at 15:59
  • $\begingroup$ @J.M.: Yes, agreed, that's not a bad strategy. $\endgroup$ – Hendrik Vogt Aug 13 '11 at 17:15
  • $\begingroup$ Has there been any question posted on this site with improving a wikipedia article as the main motivation? $\endgroup$ – Srivatsan Sep 2 '11 at 1:56
  • $\begingroup$ Very few questions on stackexchange state a motivation for askin the question. Generally people don't want to know. $\endgroup$ – Michael Hardy Aug 6 '12 at 20:50
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It seems that I am the user referred to in both the second and third paragraphs of the question. If anyone was wondering, this is my wikipedia account. A few years ago I was a rather active wikipedian and rewrote about a dozen math articles from the ground up. More recently my edits have only been to make improvements / fix mistakes that have come to my attention in other ways.

Let me say that by now I do think wikipedia is a reliable source for mathematics. Not perfectly reliable, but e.g. the density of errors is lower than that of many published mathematical texts.

In fact I am disappointed with (many of) wikipedia's math articles in a very different way: I find their non-mathematical scholarship to be lacking. Most of the articles are written in what I think of as "textbook" style: the reader is given the definitions, told some of the important theorems and sometimes given their proofs. The best of these articles are well-sourced in the sense of a good textbook: i.e., when they do not prove a result, they tell the reader where a proof can be found. For many of the articles, there is still room for improvement here: last week I was trying to look up some basic facts about Cantor cubes. In one of the wikipedia articles I found a statement of the theorem I wanted but with no attribution whatsoever. (And of course, as soon as wikipedia articles consistently source their statements to standard texts, they become at least as reliable as these texts....)

Relatively few math articles on wikipedia contain references to primary source material, in particular to the works where the theorems were first proven. (Exactly why math textbooks at almost all levels do so little of this is also something I've begun to find strange in recent years.) There is often no historical material of any kind. When historical material does appear, it is usually not directly sourced.

(For instance see the article on Wedderburn's Little Theorem. This article does describe some of the history, as related in a relatively recent article by K.H. Parshall. However it does not include direct references to any of the papers of Dickson, Wedderburn or Witt that it discusses.)

Apologies for what was something of a digression. My point though is that I view improving wikipedia articles as a worthy goal -- perhaps even worthier than answering the typical question that gets asked on this site. So for me at least, questions of the form "Here is what I think is a mistake / missing reference / clear, specific room for improvement in the following wikipedia article" are valuable ones on this site, to be encouraged rather than discouraged. Not every expert is active on every internet site: as a place where a lot of knowledge changes hands rapidly, math.SE seems like a pretty good place for wikipedians who want to improve an article but lack some specific expertise to come.

In particular I think the first, second and fourth bulleted hypothetical questions in the OP's post could be valuable ones. (I don't really see the point of the third question: it doesn't matter who most recently edited a wikipedia article; what matters is whether its content is correct.) Of course, as others have said, good questions also make for good questions: if every single person who reads a math wikipedia article and doesn't understand it comes here to ask, we'll see a lot of not so good questions on this site. But of course we see a lot of not so good questions on this site already, and we make do.

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    $\begingroup$ One thing that sometimes works for me when it comes to original sources is switching between languages. If a result was proven by a French mathematician, it is likely that the French page is better than the English one. $\endgroup$ – t.b. Aug 15 '11 at 10:59
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    $\begingroup$ One thing that really bothers me is that some of the sources are just links to claims in books that are completely unjustified there. For instance, I'm very willing to believe that Willard is right when saying that paracompact spaces are completely uniformizable. However, citing a remark in Willard's book that lacks a reference for this is completely worthless. Here's the page I have in mind: en.wikipedia.org/wiki/Completely_uniformizable_space $\endgroup$ – t.b. Aug 15 '11 at 11:02
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    $\begingroup$ It is certainly not true in general, but sometimes finding the original source might be a little tricky, or even speculative. Let me quote a paragraph from the introduction of Borceux's Handbook of categorical algebra. $\endgroup$ – Martin Sleziak Oct 23 '11 at 13:39
  • $\begingroup$ It was in July, I don't remember the year. I was participating in a summer meeting on category theory at the Isles of Thorns, in Sussex. Somebody was actually giving a talk on the history of Eilenberg and Mac Lane's collaboration in the forties, making clear what the exact contribution of the two authors was. At some point, somebody in the audience started to complain about the speaker giving credit to Eilenberg and Mac Lane for some basic aspect of their work which - he claimed - they borrowed from somebody else. $\endgroup$ – Martin Sleziak Oct 23 '11 at 13:39
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    $\begingroup$ A very sophisticated and animated discussion followed, which I was too ignorant to follow properly. The only things I can remember are the names of the two opponents: the speaker was Saunders Mac Lane and his opponent was Samuel Eilenberg. I was not born when they invented category theory. With my little story in mind, maybe you will forgive me for not having tried to give credit to anybody for the notions and results presented in this Handbook. $\endgroup$ – Martin Sleziak Oct 23 '11 at 13:39
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    $\begingroup$ Somehow I stumbled upon this question again. I think I should have clarified my point 3 back then: It was intended to mean, that I would give a link to particular edit or revision of Wikipedia article. I should have used better wording; I've left a comment instead of editing the question, since I wanted to avoid bumping this question unnecessarily. $\endgroup$ – Martin Sleziak Jan 8 '12 at 8:44
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    $\begingroup$ Secondary sources are valued more than primary sources on Wikipedia by explicit policy, because they establish notability. Riemann's original eight-page paper that stated his famous hypothesis does not establish that mathematicians generally consider that hypothesis a noteworthy topic, worthy of an encyclopedia article about it. $\endgroup$ – Michael Hardy Aug 6 '12 at 21:42
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    $\begingroup$ @Michael: I didn't see this comment for a long time. Thanks for it; it explains some things. I agree that secondary sources are better than primary sources for establishing notability. However, this is sort of meta-encyclopedic: i.e., it goes to the reason for inclusion in an encyclopedia rather than itself providing encyclopedic information. In cases like the one you cite the primary source is the more meaningful encyclopedic information (especially since the noteworthiness of Riemann's hypothesis is not in doubt!). Anyway, we should certainly have both! $\endgroup$ – Pete L. Clark Dec 13 '12 at 17:23

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