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So, MathOverflow is mainly used for posting research problems. Assume I have a research idea on which I want to write a paper. I developed it to some extent, but I am stuck somewhere and I post the current state of my problem asking for help here. Let's say that several nice and clever people help my research problem to be completely solved. Is it fine to publish the results, if they have actually done most of the work(at least as you did).

One option is to ask them whether they want to join you in writing this publication, but this makes the things complicated and sometimes you know in advance that the answer would be "No"(e.g. you're just a student, the people that answered your MO questions are some big names in math and the obtained results are far from good enough for them to accept putting their name there).

On the other hand, you have done some substantial work and waste significant amount of time, but you end up with nothing, if you don't publish. Of course you could and will cite all the MO questions in the paper, but is this enough in this case?

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    $\begingroup$ If the answerers "have actually done most of the work", I think it is up to them to publish their results. Of course, usually they should cite your question in the paper. If "the obtained results are far from good enough for them to accept putting their name there", then however it is likely that the results won't be publishable in a reasonable journal anyway. $\endgroup$ – Stefan Kohl Oct 31 '16 at 10:20
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    $\begingroup$ though the term "reasonable journal" here is subjective, would you say that if the contributors are not interested in publishing the results, this allows you to try to do it by yourself(with proper citing, of course) $\endgroup$ – sdd Oct 31 '16 at 16:07
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    $\begingroup$ Having identified a problem is already an important contribution. $\endgroup$ – kjetil b halvorsen Oct 31 '16 at 17:03
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    $\begingroup$ Are you asking whether or not you should invite MO contributors in as coauthors when writing up (the answer is a very clear "yes," if you want to stay ethical, at least that's my 2c), or if you should write something up at all (that's your decision entirely)? $\endgroup$ – Christian Remling Oct 31 '16 at 18:42
  • $\begingroup$ Where is the information actually found? MathOverflow Q&A's, as well as on all other SE sites, contain a "cite" link, and are publicly available and searchable records. You can use their contributions by citing the appropriate Q&A's, just as you would cite anything else in more traditional sources. More than one published paper has done so. Comments and chat conversations are also public records, but there may not be as convenient a citation mechanism. Also comments are impermanent, and even Q&A's can be deleted under certain circumstances. $\endgroup$ – zibadawa timmy Nov 4 '16 at 6:57
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    $\begingroup$ The situation is no different from asking questions in person or via email. The only complication is with anonymous posts. $\endgroup$ – Igor Belegradek Nov 4 '16 at 15:41
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    $\begingroup$ @Igor I think it is different, because MO is public, answers even have their own links $\endgroup$ – domotorp Nov 12 '16 at 21:13
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On my opinion, no general rule can be stated. But I can share my experience.

  1. I answered a MO question which was needed in someone's research. The result was two separate papers. My paper where the question was answered, and the paper of the person who asked using my result as a lemma, with a reference to my paper and to the MO answer:

Zeros of polynomials with real positive coefficients

  1. I asked something I needed, the person who answered published a paper. By that time my own paper on the subject was already published, so I could not make a reference, neither on MO nor on the published paper, and the question was stated in my paper as an open question:

Circles and rational functions

  1. There were several cases when I helped and was proposed a joint publication. I declined and people who used these results just cited the MO answer in their papers. MO is a sort of publication, and can be included in the reference list as a normal paper or preprint.

  2. In other cases, people do not offer a co-authorship, and just cite the MO answer in their publications. I think this is fine. Publications in MO should be treated as usual publications.

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It depends on your goal. If that goal Is to earn a degree or promote your career in academia or industry, then there are political and social obstacles and concerns, and one forum that can help with such issues is academia.stackexchange. Of course, you should have a boss, advisor, and/or mentor guiding you as you work towards such goals, and they should be consulted before considering such publishing.

If your goal is to disseminate information (and showcase your abilities in writing, communicating results, and working with the scientific community), there are few if any who would object to a well written article which is academically honest (cites well, draws connections, allows for verification and repeatability) and gives due credit, and is posted to ArXiv (assuming the article meets the intended standards). While some might say that posting your interpretation does not need permission, I think it is at minimum good etiquette to ask the people who contributed if you might use their names in the article. I'm not sure what you mean by "enough".

Gerhard "Could Use More Well Writings" Paseman, 2016.10.30.

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    $\begingroup$ I agree with you, but I think that it's important to add an echo of @ChristianRemling's comment above. I take the opportunity to summarise and editorialise as: if you ever need to ask yourself whether you should offer someone else the opportunity to be a co-author, then the answer is almost certainly 'yes'. $\endgroup$ – LSpice Oct 31 '16 at 19:46
  • $\begingroup$ In an academic context, I think you are right, especially if you have something worth publishing and are forming relationships. If the context is getting something out (either on ArXiv or on a personal page), I think authorship is a secondary consideration. I am quite willing to disregard issues of priority or credit in favor of perspective and understanding as I read someone's take on a result. Of course, if you want your take given due respect, you should respect and list sources and exercise due diligence. Gerhard "Give Respect To Get Respect" Paseman, 2016.10.31. $\endgroup$ – Gerhard Paseman Oct 31 '16 at 19:58

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