What references must be acknowledged in a paper?

Question

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?

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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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.