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This question came up from a discussion on meta.MSE.

My question is:

Do we need to search MSE (or blogs, math forums, ...) to make sure someone hasn't already proven a result when writing a paper?

What if we are already aware of a them (so no need for searching)?

Is not citing such a post in these two cases considered plagiarism?

As I understand, the common practice is to check standard reviewed reputable publication venues (journals, conferences, maybe arXiv) and also with experts in the area to make sure a result is not already published nor a well-known folklore result. No one is going to search all over the internet and check every post that Google returns and citing other resources is very uncommon. I think checking MatheOverflow can be considered similar to the later (checking with experts) (also see this discussion on MO but that doesn't seem to apply to a site like MSE. I am not going to cite a discussion with some random person on the street (not a professional mathematician) who claimed to have a solution or an idea for a solution for a problem (which is not passed peer-review process and I might not want even want to spend time understanding or checking the correctness of the solution).

What are the accepted practice for checking originality of a result?

What is expected from authors regarding this before making a paper submission?

Some clarification since there seems to be a misinterpretation of the question about being academic honesty. The question is not about posts that

  • you are aware of,
  • contain a complete rigorousness solution (not just ideas), and
  • you are confident the solution is correct.
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As best I understand it, the clarified question is this: if you are writing a paper and find a posting on the internet that contains ideas on your problem (which may or may not be correct, may be difficult to understand, and in any case do not seem to constitute a complete solution), then should you cite it? Let's assume you are making no use of the ideas, since if you are then you obviously need to cite the posting (regardless of whether you developed the ideas independently).

In general, you must cite it anyway. Of course, there are exceptions. If it's obviously crackpot work, then you are free to dismiss it as worthless. (Andrew Wiles didn't need to cite thousands of crackpot "proofs" of Fermat's Last Theorem.) If it's really only tangentially related to the problem you are working on, then it may not be relevant enough to cite. However, it absolutely does not matter at all whether the work is peer reviewed or formally published, who wrote it or what their credentials are, whether it is complete, how easy it is to find, or whether it is difficult to understand.

You don't have to endorse it, and citing a paper does not in any way indicate that you feel it is correct. If you rely on the paper, then that's an endorsement, but mentioning it is not. For example, you could write "Several authors have studied this problem, including..." and give citations to them. Then readers can decide for themselves what to make of these contributions. They will understand from the form of your citation that you feel these works are closely enough related to be worth citing, but not important enough to your paper to discuss in detail. You can also say something more skeptical if warranted.

One reason you don't see these sorts of citations very often is that this situation doesn't often arise. (I've never seen a post on mathoverflow or math.stackexchange that I felt I should cite in one of my papers.) And even when it does arise, the citation may be as a personal communication rather than giving a URL. (It's much better to give a more detailed citation, so other people can find and learn from or evaluate the posting, but I guess an uninformative citation is better than none at all.)

As for due diligence in searching for prior work, there's no simple rule. You should search everywhere you feel there might plausibly be something to find, and you should consult with experts on anything you feel unsure of. It's certainly impossible to search the entire academic literature, let alone the entire internet, so you'll be forced to make compromises compared with an ideal world. For most purposes, non-academic internet sites will not be relevant enough to be worth searching carefully, but I guess it depends on the situation.

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    +1 for However, it absolutely does not matter at all whether the work is peer reviewed or formally published, who wrote it or what their credentials are, whether it is complete, how easy it is to find, or whether it is difficult to understand.
    – JeffE
    Jun 19 '12 at 4:07
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    In my opinion, "personal communication" belongs in the body of the paper or in the acknowledgments, not in the bibliography (where it is out of place and useless). It's just mean to make people flip to the end of the paper only to find out that there's no way for them to access the source in question.
    – Noah Snyder
    Jun 19 '12 at 5:16
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This is a question of academic honesty and due diligence.

If you did not arrive at the result yourself, but got it from someone else (either on SE or a homeless man on the street) then it is your responsibility to not claim credit for the result. Of course, in the case of the homeless man you can get away with claiming credit, and in most cases for SE, too. However, it is simply not honest.

If you arrived at the result by yourself, then as a research you should provide due diligence and check if the result is already known. This usually consists of checking the standard sources (i.e. published papers, books) and the communities which you are a part of. "Folklore" in mathematics is vast, and MO, math.SE, and cstheory are all becoming part of it. If you are aware that others arrived at a result before you then you should mention it in your paper (either with a full citation, if applicable, or with an acknowledgement).

However, just like you are not expected to search the back-log of every journal ever published, you don't have to scour the whole internet, either. If you want precedent of this: consider all the results that were published independently in the west and the soviet union during the Cold War. It would have been unreasonable of the scholars on both sides to be fully aware of the work of the others.

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  • +1 If you got the result from someone else it is definitely expected that you mention them in the acknowledgements section.
    – scientifics
    Jun 18 '12 at 20:02
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    @Kaveh I don't understand what kind of evidence you would expect. From consulting the top user list Math.SE has a number of practicing mathematicians (albeit less then MO), it is a community devoted to mathematics (although not necessarily at the research level), and it is a community your participate in and (I assume) know to provide good answers, occasionally. Communities don't have hard boundaries, and it is better to be more inclusive than less for something as important as giving credit where credit is due.
    – Artem Kaznatcheev
    Jun 18 '12 at 20:56
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    @Kaveh I think you are getting caught up in the mechanics of procedure and beauracracy to the point that you are losing the point. If you are aware of a result or did not arrive it at by yourself then cite it to be honest it doesn't matter where it came from. If the result is wrong, then don't cite it. I have no interest in having a long comment discussion with you though, since I see you already had an equivalent one on math.SE.
    – Artem Kaznatcheev
    Jun 18 '12 at 21:06
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    @Kaveh -- I happily cite arXiv all the time. When I search, I usually use Google, and all sorts of stuff comes up. Anything that's helpful (and otherwise meets standards for citation), from personal communications to non peer-reviewed drafts, I cite. I think the reason that random websites aren't cited isn't because they shouldn't be, but because they're rarely helpful, as Anonymous Mathematician points out in a separate answer.
    – Lev Reyzin
    Jun 19 '12 at 1:50
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    Certainly this question touches on some topics that are controversial. However, there should be absolutely nothing controversial at all about citing papers on the ArXiv.
    – Noah Snyder
    Jun 19 '12 at 5:06
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I think due diligence in searching the literature includes:

  • Talking to at least one expert in the field
  • Looking through the bibliographies of any major papers closely related to your paper to see if any of the titles look relevant.
  • Searching on google scholar or something similar for papers which cite any papers closely related to your paper.
  • Searching on google for some of the key terms in your paper.

The last of these would pick up math.SE, but also often picks up lecture notes, slides, wikis, and other things which would not come up through more traditional academic sources. If you find something clearly relevant then you should cite it. Furthermore, you should do these things before getting too far into a project.

That said, no matter how much due diligence you do, you're going to miss stuff sometimes. 5 years after my first paper was published, it was pointed out to me that Osterle gave the same argument in Seminaire Bourbaki (1987/8:165–186). More recently, one of the 3 main results in this paper follows from a 15 year old result of Popa. Searching what's known is incredibly hard even if you try your best. But that's no reason not to try your best.

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    The result in your first published paper, An alternate view of Mason's theorem, 2000 is essentially an observation I made 20 years prior about Wronskian estimates. In fact it shows up (then and now) on the first page of web searches for "Mason abc", because it is excerpted on the MathWorld page for Mason's theorem. So I was perplexed when I saw it published with no citation. Did you never google it?
    – Bill Dubuque
    Jun 19 '12 at 14:07
  • In 1998 Google had just been founded, was unknown and certainly didn't include newsgroups.
    – Noah Snyder
    Jun 19 '12 at 15:53
  • Of course "google" is generic for "web search". Such web searches circa 2000 (and much earlier) returned links to said MathWorld page on the first page of search results. Anyone who did a web search on "Mason's Thoerem" or "Mason abc", etc. cannot help but have stumbled upon said MathWorld page on Mason's Theorem.
    – Bill Dubuque
    Jun 19 '12 at 15:58
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    Anyway, I think this situation actually illustrates the point reasonable well. You weren't aware of Osterle's prior argument (even though it's in the mathworld bibliography for ABC), and Serge Lang and I weren't aware of your post or Osterle's talk. Nonetheless had any of us been aware of the others we should have cited them even though one is on a newsgroup, one is published lecture notes, and neither was a peer reviewed journal article.
    – Noah Snyder
    Jun 19 '12 at 16:37
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    In case you don't know the history, MathWorld started out as Eric Weisstein's Treasure trove. He included (without citation) many results from around the Web, including the math-fun mailing list. Said MathWorld entry on Mason's Theorem is excerpted almost verbatim from one of my 1996 math-fun posts. The references are probably all from my post. Later he started adding (some) attributions when it was commercialized.
    – Bill Dubuque
    Jun 19 '12 at 16:45
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In my experience I think the accepted practice is searching the peer-reviewed literature in your field. I'm not saying results published on websites/MSE, etc. aren't valid, they just aren't part of the expected search. Anyways, I don't think peer-reviewed journals would react well to web citations.

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  • Two exceptions may be in didactics (referencing good learning platforms) and in citing a particular implementation of a software. Another point: in my Diplom thesis I did cite e.g. the AI-FAQ (in addition to proper papers, and in a non-computer science field), and my supervisor emphasized this as positive.
    – cbeleites unhappy with SX
    Jun 18 '12 at 22:36
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    In my experience referees have no objections to citations to websites. I've linked to MO in a paper and put wikipedia in a bibliography in published papers (and of course the arxiv dozens of times in every paper). Indeed, referees would be committing academic misconduct to ask that a genuinely relevant citation be removed solely because of medium.
    – Noah Snyder
    Jun 19 '12 at 4:52

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