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For example, suppose you're writing an article about triangles, and you want to include a short proof of Pythagoras' theorem, but you can't quite remember how to derive it, so you pop over to: https://en.wikipedia.org/wiki/Pythagorean_theorem#Algebraic_proofs and check the proof there. It works mathematically, makes sense and is as far as you can tell, correct, so you include it. Now the proof on Wikipedia doesn't have a citation because probably someone has been taught it and copied it over to Wikipedia, but it's still correct. The only thing you could cite for the proof would be Wikipedia, would a citation be ok or should it just be copied down without a citation?

Edit: Ok, there have been many responses. Most with a firm "no", but some giving the reason: "Just get the proof from a book" since it's so common, but suppose then it wasn't a common proof of something. Maybe it's not very well known or something but suppose there is a small Wikipedia page with the correct mathematical proof. How much effort are people going to go to to find a proof in a book when there's a (correct (which we know, becuase it's maths and we can check it)) proof on Wikipedia? Why is it so bad to say: "I found this proof on Wikipedia, and the maths checks out so it doesn't matter who wrote it, it is correct, but that's where I found it." Or if you do find it somewhere else why not say: "Proof taken from Wikipedia and verified by the proof shown in "Triangles and their properties, Nature, 2014, p113 etc..."

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What is the context? Is this a class paper or an academic paper? –  badroit Apr 8 at 17:58
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I cited wikipedia once, and my advisor told me that the first thing referees look at is your references, and if they see wikipedia cited, they will reject the paper without reading it. –  Akavall Apr 8 at 18:17
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I think you've created a catch-22. If the proof is so obvious that a wikipedia entry is reasonable, then you don't need to cite it - anyone with basic education will accept Pythagorean theorem without a reference. If the information, however, is rare or cannot be found elsewhere other than wikipedia, then wikipedia itself cannot possibly be accepted as a valid citation. There is no reason to cite wikipedia for the trivial stuff, and your audience will not take a complex idea at face value with a wikipedia citation. –  Adam Davis Apr 9 at 17:30
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Whenever possible, cite primary sources -- or at least closer to primary. A good Wikipedia article will cite its sources, so you could follow those pointers and cite those. (It might be polite to add a footnote saying that you found Wikipedia a surprisingly useful tool in tracking down those sources, but I wouldn't cite it per se... not least because citing something that's subject to change and may show something different next week is bad practice independent of how authoritative it is or isn't.) –  keshlam Apr 9 at 22:32
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It's a bit silly, but I know that people sometimes get information from Wikipedia (or from colleagues, lecture notes, etc.) which is perfectly correct, but they can't properly cite it, so they cite a book or review (that they didn't necessarily read) pro-forma. It goes against everything proper attribution is about, but its just one of those silly things you have to do in academic writing, because that's how it is... –  jdm Apr 11 at 13:10

10 Answers 10

up vote 29 down vote accepted

Are there instances where citing Wikipedia is allowed?

I'm not going to try to answer the question of "is allowed" or "isn't allowed" but instead I'm going to try and answer if citing Wikipedia is, in general, a good idea or not for research papers.

Here's five points I can think of for and five points against.

Good idea:

  • If Wikipedia is your source, and you learn something from what Wikipedia's editors have provided, then citing Wikipedia is the Nice Thing To Do™.
  • Wikipedia is a convenient, well-known, easily and freely accessible source (vs. final-copy published papers that are pay-per-view if not out of your wallet, then indirectly out of your university's).
  • Content aims to be written in an accessible manner targeted at a wide audience (vs. arguably the bulk of technical articles published in journals and conferences). Plus there's clickable links for jargon! Sweet!
  • Notable or Featured Articles will probably have undergone more scrutiny from experts (w.r.t. bias, technical correctness, sources cited, etc.) than your average peer-reviewed article on a similar topic.
  • At least with Wikipedia, readers should know where they stand with such a citation. Compare this with the artifice of citing papers for claims made in poor-quality journals or conferences that can be considered authoritative solely on the basis of being "peer-reviewed".

Bad idea:

  • A Wikipedia article is subject to frequent editing and the content you cite it for may not be there when the reader goes looking for it (adding a date-accessed only partly addresses the issue since it will be difficult for the reader to start going through versions edit but as per the comments below, you can use a citing service within Wikipedia to cite a specific version of a page).
  • Relatedly, the content may have been correct at the time of citing but errors may be edited into the content at a later point, making you look bad by association (edit, again, citing a specific version could work around that)
  • There is no minimal guarantee of the quality for most Wikipedia articles (which peer-review, at least in theory, should provide, depending perhaps on the venue).
  • Wikipedia is not a first-party source: in theory, no new knowledge is "created" in Wikipedia. Where feasible, you should try to attribute knowledge to those who create it (and optionally thereafter add a reference to those who report it or better describe it in a book or survey)
  • Attribution for the content of a Wikipedia article is difficult: multiple editors may be involved in a certain piece of content, many editors are anonymous, etc. This means that there is no culpability for information (unlike peer-reviewed papers where authors have something to lose by publishing crap). This opens up further possibilities, such as authors anonymously adding content to Wikipedia that they can cite to support the claims in their paper.

Okay, back to academic convention and "isn't alloweds" and "is alloweds" ...


Maybe it's not very well known or something but suppose there is a small Wikipedia page with the correct mathematical proof. How much effort are people going to go to to find a proof in a book when there's a (correct (which we know, because it's maths and we can check it)) proof on Wikipedia?

According to Wikipedia policies, it should have a reference to an original source. Cite that.

If it doesn't have a reference, or if you copy how the proof is expressed directly, I would recommend to add a footnote (rather than a formal citation) stating the Wikipedia article you found the proof on and how you verified it (and the CC-BY-SA licence if you copy the expression).

Generally avoid citing web-pages (unless they are normative online standards or something) if only to avoid getting your hand bitten off by a reviewer. Using footnotes is much safer in this regards and serves a similar-ish purpose (though it won't be counted as a formal citation).

In research, if enough reviewers believe something isn't allowed, then de facto it isn't allowed.

Or if you do find it somewhere else why not say: "Proof taken from Wikipedia and verified by the proof shown in "Triangles and their properties, Nature, 2014, p113 etc..."

Why not say "Proof sketched for me by Fred, the guy who sits next to me, who had previously read it in 'Triangles and their properties, Nature, 2014, p113 etc...'"?

In other words, what's important is the reference, not how you found.

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Wikipedia articles are subject to constant vandalism, as well as edits by ignorant people and those with a political ax to grind. It's OK for quickly surveying a field to see what's out there, but you don't want to use it as your final source, especially in academia. –  Phil Perry Apr 8 at 20:16
    
I agree and I think that's covered in the answer under "subject to frequent edits" and "lack of attribution". (I deliberately avoided the use of the word "vandalism" since I believe that this problem tends to be over-exaggerated based on a few famous anecdotes: in the general case, Wikipedia has plenty of tools to suppress/revert vandalism and I cannot remember the last time I inadvertently encountered a vandalised article on my travels through Wikipedia.) –  badroit Apr 8 at 20:30
    
I remember one of the first times I used Wikipedia. I wanted to look up the scientific (taxonomic) name of the House Cat. The article stated that science had found that cats were actually reptiles -- cold blooded, scaly tailed, etc. By the time I researched how to edit this misinformation, someone had reverted the article. The vandal then struck again, and I recall that there were literally dozens of updates/rollbacks logged until the vandal was either blocked or got tired of the game. So, even scientific material can be vandalized. –  Phil Perry Apr 8 at 20:35
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"adding a date-accessed only partly addresses the issue since it will be difficult for the reader to start going through versions" Isn't this addressed by permalinks/revision IDs that can be looked up without needing to search the history manually? –  hexafraction Apr 9 at 0:15
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@hexafraction Yes, if you go to Special:Cite or click "Cite this page" on any article it will give a link to a specific revision, along with example citations, and a lot of the warnings found in these answers too :) –  Colin Pickard Apr 9 at 9:23

You should never use something that isn't your own without a citation. "Copied down without a citation" is not an option.

However, you should also not cite Wikipedia as an authoritative source; you should track down a source that is authoritative and use that.

Why not use Wikipedia as a source?

One reason for not using Wikipedia as an authoritative source is that it is simply not reliable enough in many cases. Wikipedia's founder, Jimmy Wales, himself says

that he gets about 10 e-mail messages a week from students who complain that Wikipedia has gotten them into academic hot water. "They say, 'Please help me. I got an F on my paper because I cited Wikipedia'" and the information turned out to be wrong, he says. But he said he has no sympathy for their plight, noting that he thinks to himself: "For God sake, you’re in college; don’t cite the encyclopedia."

Even if you can verify that the Wikipedia article is correct, you should not use it as an authoritative source. You asked:

Why is it so bad to say: "I found this proof on Wikipedia, and the maths checks out so it doesn't matter who wrote it, it is correct, but that's where I found it."

Citing Wikipedia as a source for an idea that isn't original to Wikipedia does not give credit to the original author of the idea, which is a major reason for citing something in the first place. (The same applies to any tertiary source.)

The Wikipedia entry on Citing Wikipedia itself advises:

It will usually be more acceptable to cite those original sources rather than Wikipedia since it is, by nature, a secondary or tertiary source. At the same time, simple academic ethics require that you should actually read the work that you cite: if you do not actually have your hands on a book, you should not misleadingly cite it as your source.

When should you cite Wikipedia?

It is appropriate to cite Wikipedia if you are commenting on Wikipedia. For example: "The Wikipedia page on X shows that it is a controversial topic, with a large number of rollbacks indicating disagreement on the correct approach."

Similarly, Wikipedia can sometimes be a primary source on popular culture. In this case, you should use it and cite it accordingly. Update: I gave an example of this in another answer.

If you use Wikipedia as a source for finding other sources, then the question, Is there a problem with citing the original source instead of the source where the information was first found? applies.

Further reading

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Yes, "copied without citation" is bad. But/and also, "used without citation" is not so good, in my opinion. –  paul garrett Apr 8 at 18:29
    
@paulgarrett I agree: I think you should not use Wikipedia in such a way that it requires citation. –  ff524 Apr 8 at 18:36
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Well, that might entail never looking at Wiki, then, to be honest? After all, if someone learns something from some of my expository writing, and uses my document to find the primary source, I'd expect that this would be acknowledged. Otherwise one is keeping secrets. –  paul garrett Apr 8 at 18:41
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@paulgarrett Perhaps you could write as much on this question then. (The question asks whether you should cite the source which led you to other sources.) –  ff524 Apr 8 at 18:42
    
possibly, at least as counterpoint...? –  paul garrett Apr 8 at 18:43

In my opinion a lot of the answers are too negative about wikipedia, at least when applied to the part of wikipedia that applies to mathematics (my academic field, and the field the OP asked about).

I am a little surprised to hear people describe wikipedia as "unreliable", including links to university websites which say rather snootily to avoid it. This is how I felt about the mathematics on wikipedia circa 2006. It has gotten so much better in the intervening years, for the obvious reason: a lot of very mathematically experienced people (including at least one Fields Medalist, and also including me, for a period from about 2006 to 2008) put in a lot of time writing and vetting the articles. Where it stands now is that wikipedia is the best single repository of mathematical information in the world. It has been several years since I have seen anything that was wrong on a wikipedia math article. Some of these articles contain content that is difficult to find in other places, and some of the content is new: it is far from unheard of that someone just put in their own proof of a theorem. Many feel in principle that this sort of thing should not be done (I think I do; it's been a while since I've really thought about it), but in practice when someone writes a nice self-contained proof of a mathematical result, why delete it? So there is some really great stuff there: I think that most research mathematicians who are frequent users of the internet have by now learned mathematics from wikipedia.

As others have correctly pointed out, the question of "when to cite" is more complicated. Let me consider several of the alternatives:

1) Should you refer to wikipedia for standard proofs?

I think I believe that sometimes you should but I have never actually done it in a "serious research paper", in part because of exactly the sort of internet-phobic practices that Paul Garrett refers to in his answer. Recently I was writing a broad-audience article, and I wanted to say that a certain aspect of a classical construction -- the Galois connection between ideals of a polynomial ring over an algebraically closed field k and subsets of affine n-space over k -- worked verbatim with k replaced by an arbitrary integral domain. I ended up referring to Lang's Algebra for this. That is really not (ahem) ideal: this is one of the most "standard texts" in the sense that a large percentage of professional mathematicians have a copy in their office. On the other hand it is not free and even more mathematicians and math students don't have it. But billions of people have internet access, and surely wikipedia (for instance) does a perfectly good job of explaining the point. I wussed out and didn't give an explicit electronic reference, and I rarely do in formal writing. (In fact I have myself written many, many pages of mathematical writing -- as has Paul Garrett, by the way -- and I usually wuss out and do not refer to it in my formal writing either, even though I know exactly where I would like to point and a student would understand my research paper much more easily with that reference included.) At this point, when I say that something is "well known" I assume that students will look for it on the internet, and as a code between me and myself, at least, I try never to say that in papers except in cases where a student who looked for it on the internet would quickly and easily find it (and when that happens I don't worry so much about tracking down a print reference).

In the above case, the big advantage of wikipedia is its ease and convenience: it has almost exactly what any text would have but is much quicker, easier and freer to access.

2) Should you refer to wikipedia for non-standard proofs?

In other words, if a wikipedia article has a proof which is different from the one that you would find in any expensive math text, should you refer to that? If you want the reader to read that proof, I think you have to do refer to it or try to track down the source of the proof that made it into the wikipedia article. However, the latter brings me to my biggest complaint about the math articles on wikipedia: they're great for mathematical content. They can be really bad as references: e.g. they can be taken out of some standard source without referring back to that source. Or an article on the X-Y Theorem will have a statement of the theorem, motivation for the statement, the proof of the theorem, and then talk about further work and generalizations. That would make for a great lecture about the X-Y Theorem, but for an encyclopedia article there's a lot missing: who are X and Y? (Sometimes they don't even try to tell you, even when there are wikipedia articles on X and Y.) Where was the X-Y Theorem first published? (I'm sorry to tell you that many mathematically rock-solid articles don't contain this kind of primary source material.) Is the proof included in the article the original proof of X-Y? If not, where does it come from?

When I was involved with it, the culture of mathematical wikipedians was not good at addressing the above issues: if I asked for this information about an article, someone would usually nicely tell me that I was more than welcome to add it myself. I would mention that unfortunately I didn't know the source material that led to most of what other people included in the article...and there the matter usually got dropped.

So it may very well be the case that wikipedia has a proof of something for which it is not trivial to discern where the proof comes from. As an example, wikipedia has a really nice proof of the Schwartz-Zippel Lemma. It is not the original proof, I think -- it's slicker. Where does it come from? I couldn't tell from the article itself. This is not a hypothetical example: I wrote a brief expository note including this proof. As you can see, I did refer to the wikipedia article. However, I should say that this is an article in the informal sense of the term: I wrote it up for myself, spoke in a colleague's seminar about it, and kept the document for myself. I have not tried to publish it anywhere, nor would I, since it is "just an exposition" of a proof of Zeev Dvir's resolution of the Finite Field Kakeya Problem. This brings me to my last point:

3) When should you include proofs from wikipedia in your articles?

If you use a wikipedia proof in your article in a critical way, then you should include a reference to it (or where it comes from, if possible). However, if you are using a wikipedia proof in a critical way in your article, is your article a research article or even a "serious expository" article? Why would a journal want to republish something that is available in a standard source?

In the OP's example he mentions including a proof of the Pythagorean Theorem. No math journal I know is going to allow you to include (any one of; I'm sure it gives several) wikipedia's proof of the Pythagorean Theorem, but not because it comes from wikipedia: they're just not going to want you to rehash such old-hat stuff. To be honest, the introductory passage "For example, suppose you're writing an article about triangles..." raises some eyebrows in this regard: are you trying to formally publish an article about triangles? Good luck with that: it's going to be tough. Such articles are published, but for every one that is, probably a hundred are rejected.

I also think that in a formal article -- even, perhaps even especially, if it's an expository article -- the burden falls more highly on you to investigate primary source material. If you're teaching a class or something, then it's helpful to say exactly where you got the material from. But if you're writing an article, it becomes more important to track down the provenance of the intellectual content itself: that is a much more challenging thing to do. Still though I think there are cases where the answer really will be that the argument appeared for the first time on wikipedia, in which case you should cite it there.

4) What about the "unreliability" of wikipedia articles?

This is really "weak sauce" for math articles, because unlike most encyclopedia articles, mathematics articles are self verifying by any sufficiently qualified reader. So saying "Don't include this proof from wikipedia because wikipedia is full of errors" sounds silly to me: on the one hand lots of published books have a higher density of errors than wikipedia math articles; on the other hand, every proof you read you're supposed to check anyway. So don't worry about whether it's correct: see whether it's correct. Most proofs in wikipedia articles are no more than a page or so in length, so they can be checked in a relatively short time. If it's not correct, fix it or tell someone about it!

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Indeed. Good points. In particular, the rapid improvement of quality since not-so-many years ago. In my answer I did forget to mention the point that Wiki articles seem less obliged to "make the reader pay a price", unlike many standard textbooks, which work hard to "do things the orthodox way, no short-cuts". And I do wonder whether the nearly-anonymous editor policy is optimal long-term... –  paul garrett Apr 8 at 21:56
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I like this answer. Any answer that says "wikipedia is unreliable" isn't quite right. It is generally unreliable for fields where the research is highly political (i.e. climate change, nutrition, medicine, conservation etc.) or a subject that non scientists care a lot about (sports, entertainment etc.) but not for highly technical fields. The general public does not feel compelled to to edit the article titled "Enriched category". That said, it probably shouldn't be used in serious research papers for the practical reason of getting the paper accepted. –  MHH Apr 9 at 1:25
    
Thank you for your answer Pete, it was a very interesting read. I'd like to clarify that I'm not actually planning on writing an article about triangles, I just thought it was an example that anyone would understand, whether they were mathematicians or not. –  captainjamie Apr 9 at 10:12
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My only experience with citing Wikipedia in a math research paper was positive (I had another reference challenged by a reviewer, but not the Wiki one). I had a reason that I thought a special one, though. I was investigating very weak set theories and I needed to reference "standard" formulations of basic set theoretic axioms. Unfortunately, because of the variable absence of their sister axioms, the various "typical" formulations of the same axiom were no longer equivalent, or at least no longer obviously equivalent. I needed a very accessible and generic source. I chose Wikipedia. –  Jirka Hanika Apr 9 at 20:05
    
There is one other aspect of mathematical research papers in particular (less relevant to expository papers). In a research paper in math, many basic results just go uncited - the author is usually able to just make a bare claim, or say "the following proof is well known", and as long as the referee agrees there will be no problem. I have never found what I thought was a good and accurate description of mathematical citation practices, but any such article would have to menton this common avoidance of citing "well known" results. –  Oswald Veblen Jul 21 at 23:20

If you got your information from Wiki, or used the Wiki article to find a more authoritative source, it would be honest and proper to cite it. Cite what you use, at the very least! Acknowledge your sources.

I know this is not universally approved, and, as in one comment, many people will react negatively if Wiki appears in the references... and this could have in impact on a referee's reaction to your paper, yes.

And, yes, Wiki's context for technical matters is a roller coaster... Best to see what Wiki says, maybe use Wiki as a pointer to key-words, to external/traditional sources. Then, if you are being honest, cite Wiki and the/an-other more conventional/traditional/orthodox (authoritative?) source.

In mathematics, sometimes Wiki comes up with connections or sources or people I'd not been aware of previously, as well as often mentioning historical sources that many standard sources do not. Also, it is ... available!

If you find yourself in the (unfortunate) situation of needing to conform to a retro standard of "what's legal" to cite, not only can you not cite Wiki, but probably shouldn't give URLs in your bibliography, either? Can't cite arXiv, either? Can't cite anything that was not refereed and "published" (in a now-archaic sense) in one of the known journals? Probably...

But, looking forward, it is happier to be in a situation where you can be honest about sources! Obviously!

EDIT: It seems that people react variously to two aspects (at least) of Wiki, namely, issues about authoritativeness, and issues about primariness of sources, which segues into giving credit where credit is due.

The bad scenario is, as in @ff524's quote from Jimmy Wales, that someone uses Wiki uncritically, and gets burned because something's wrong. This potential is arguably greater in Wiki than in other sources, but it's only a matter of degree. Everything needs corroboration, if it really matters.

Similarly, pretending that Wiki is somehow a primary source probably is never correct, just as no old-timey paper encyclopedia was every primary. But I recall, quite honestly, being exposed to ideas accidentally in encyclopedias that I would not have known to look for at all otherwise, ... and a good encyclopedia, and the better articles in Wiki, do give external pointers of various sorts.

For that matter, how many mathematics textbooks manage to come anywhere close to citing primary sources? :) It's not easy, I agree! Not a good argument for not trying. I was amazed to observe, some years ago, that L. Ahlfors' "Complex Analsis" has no bibliography whatsoever, although there're many named-after theorems.

The near-universal accessibility of Wiki means that many, many people will turn to it first, rightly or wrongly. Again, I use it often to get clues about aspects of mathematics distant from my prior experience, although I certainly do seek corroboration! To pretend that Wiki wasn't used when it was used is a bit dishonest, as well as not giving credit to its utility, if not to its primariness as source.

There can be different reasons for acknowledgements, I think.

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"Don't use Wikipedia as an authoritative source" does not at all imply "Can't give URLs in bibliography" or "Can't cite arXiv" or "Can't cite anything that isn't peer-reviewed." –  ff524 Apr 8 at 18:45
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@ff524 I think Paul is trying to say that blanket statements such as "Can't cite URLs" are usually not very well thought out now that the internet is so widely used. (And by extension, a blanket "Can't cite Wiki" is also poorly thought out) –  captainjamie Apr 8 at 18:48
    
@ff524, I didn't mean to suggest that "not using Wiki" literally implies "don't cite unrefereed things", but, in fact, the same reasons given to support the one support the other, to my perception. –  paul garrett Apr 8 at 18:58
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@paulgarrett My argument against Wikipedia is not "Don't cite unrefereed things." It's find and cite the original source of an idea (thus giving credit to the actual author), not a tertiary source. –  ff524 Apr 8 at 19:02
    
@ff524, I agree that one should often give credit to the original innovator, yes, but I think also to a source that one used to find the original thing. (And, of course, many people do criticize the "lack of authoritativeness" of Wiki, and of non-refereed documents, as a fatal flaw.) –  paul garrett Apr 8 at 19:05

For the title question, it is almost always No!

Although you may be able to find a venue in which you could 'get away' with citing Wikipedia for something like that, it is almost never a good idea. If I see Wikipedia cited as a source (for anything except a comment on Wikipedia, as @ff524 mentioned), it will raise a huge red flag. My immediate thought is that this writer is too lazy to search for and find a better source! Don't do this to yourself. For something very common like this, you should be able to go to your local physical university library and -- without much effort -- find a book that references the needed theorem.

For your second question in the body, copying without citation, even from a Wikipedia page, is plagiarism. Again, don't do this to yourself!

Find a better source if at all possible, and no matter what, cite your source!

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-1 for an authoritative "No!". In some cases Wikipedia is the most comprehensive source on a given subject (see a Wikipedia reference in my paper). Surely, I used it only to provide social context and motivation, not to support any scientific claims. But it's not binary - one should always be aware of trustworthiness of a given source in a given context. –  Piotr Migdal Apr 8 at 18:42
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@PiotrMigdal, I did qualify my statement by saying "almost always". You are right that in some cases Wikipedia may be the best source available, but (and I may be old-school here) to me a Wiki citation is still a red flag. –  J. Zimmerman Apr 8 at 19:02

What is "allowed" and "not allowed"?

But there's almost no reason to ever cite Wikipedia. If Wikipedia states something without citing a source, then you're basically citing "Some random guy on the internet told me that..." If Wikipedia states something and does cite a source, check the source yourself, to make sure it says what Wikipedia says it says; then cite that.

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Some random guy on the internet answered a math question of mine, and we wrote a paper together: math.uga.edu/~pete/Clark-Diepeveen14.pdf. (It was accepted by the American Mathematical Monthly.) Other random guys (and gals) on the internet have directly helped with my mathematical research as well. Of course some random guys tell me incorrect things as well, so naturally I check what people tell me, probably especially so if I don't know them. If what they say pans out, of course one should cite accordingly. –  Pete L. Clark Apr 9 at 4:38
    
@PeteL.Clark Sure but mathematics is verifiable essentially just by looking at it hard enough. For just about anything else, verifying something on Wikipedia involves finding a reliable, independent source. If you found such a source, you'd cite that, instead of Wikipedia. (And add the source to Wikipedia, please!) –  David Richerby Apr 9 at 7:23
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@DavidRicherby but that was exactly the point of the question. Is it ok if what you've found is "verifiable essentially just by looking at it hard enough"? –  captainjamie Apr 9 at 10:05
    
Wrong, Watson beat humans using Wikipedia therefor Wikipedia is FACT. en.wikipedia.org/wiki/Reliability_of_Wikipedia –  Exitos Apr 9 at 17:52

I will not speak to the direct topic of your questions, which is proofs, because, to be blunt, that's not my field. I will say that there are some edge case where it's acceptable, in my mind, to cite Wikipedia - namely, where said Wiki has become the de facto repository of information for a given topic. These are rare, and usually pop culture focused, but they do exist.

For example, I have a paper which cites the Wiki for a game (which is even less authoritative as a source than Wikipedia), and it was cited without issue from reviewers, etc.

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One issue the other answers don't mention is the possibility of circular reporting: http://en.wikipedia.org/wiki/Circular_reporting

As other answers have said, if there's a citation then you should follow it. If there's not a citation, and you use the result in your published paper, the article may then be edited to use your paper as its citation.

This is dangerous, since referenced results will not be scrutinised as much as novel results. In this situation, it would be prudent to cite Wikipedia explicitly, so that such a circular arguments would become clear by looking at both sets of references.

The examples in the link above are false information about the real-world, which are difficult to verify and hence should be avoided outright. The situation isn't as bad for mathematical proofs, since you can verify them before including them, but you should make sure to present the proof in a way that shows it's novel (and hence needs review), but also cites Wikipedia as the source (or else it's plagiarism). A footnote like those mentioned above would work for this.

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Are there instances where citing Wikipedia is allowed? Yes, when appropriate. It is appropriate to cite Wikipedia in a case study or literary scrutiny of Wikipedia.

For scholarly articles, jurored sources are often mandated. For literary articles, source citation is based upon the origin.

For example, a literary examination of Xenophon's Cyropaedia or Wikipedia's page on Cyrus the Great, may cite the origin text to draw conclusions regarding (inclusive of, but not limited to) erroneous statistics or accurate accounting.

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In the case of your example, the wikipedia entry is a plagiarized source. A mathematical proof is a copyrighted thing, and wikipedia editors should be including proper citations, otherwise you are continuing the plagiarism.

Otherwise, I believe in the pragma of the intellectual commons. As long as there's some traceable link to the origin of an idea somewhere, one can link from the place where they found it, rather than the original source.

If Wikipedia is your source, and they continue to uphold their policies on giving citations, then wikipedia is a fine source. But, like with all Internet citations, give the date and time also.

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"A mathematical proof is a copyrighted thing." That is absolutely false. It is equally false that anyone who quotes wikipedia with attribution is committing plagiarism. Please do not spread misinformation. –  Pete L. Clark Jul 21 at 22:27
    
A proof represents original work in a published form (in the case of wikipedia, e.g.), in what possible way do you imagine that it is not copyrighted? And the issue with plagiarism is with an *un*attributed source, not with attribution. –  Mark J Jul 21 at 22:31
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Publication is not part of the definition of a mathematical proof. "In what possible way do you imagine that it is not copyrighted?" It is not a matter of imagination: I am a professional mathematician. If you would like to clear up your misconceptions about the nature of mathematical proof, you can ask questions at math.stackexchange.com. I'm not going to further debate you here, no more than a chemist would debate someone who claimed that the periodic table is a copyrighted thing. –  Pete L. Clark Jul 21 at 22:42
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As another professional mathematician I vouch for Pete L. Clark's comments, and also encourage asking this issue as a question on mathematics.stackexchange.com rather than continuing the discussion in comment here. –  Oswald Veblen Jul 21 at 23:25
    
This question has been locked due to off-topic comments and ad hominem attacks. As suggested by @OswaldVeblen, if you want to pursue the discussion regarding copyright on mathematical proofs, please visit mathematics.stackexchange.com. –  eykanal Jul 22 at 2:08

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