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Lets say that I build up parts of a chain of reasoning leading to a publishable research discovery by posting one or more questions on http://math.stackexchange.com (or any other public Q/A-board), and collecting the answers; what is the "right thing" to do?

Is there a general convention (with accompanying conditions)?

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In all cases, if you use someone else's ideas you have an ethical obligation to make all reasonable good faith efforts to contact that person and ask their wishes. For a site like Math.SE, that means checking their profile info and contacting them via email (if available) or by chat (if not).

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    $\begingroup$ Or by leaving comments on the relevant answer. $\endgroup$
    – Asaf Karagila Mod
    Commented May 18, 2013 at 20:52
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    $\begingroup$ One should actually go beyond this. On a couple of cases where I wanted to quote a result I saw on MathOverflow, and saw no way of contacting the originator directly, I explained the issue to the moderators, and asked them to contact the user on my behalf, so they can contact me, and we can discuss quoting the result with proper attribution. $\endgroup$
    – Andrés E. Caicedo
    Commented May 18, 2013 at 22:56
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    $\begingroup$ @AndresCaicedo On MathOverflow there is a cite possibility which generates the information needed for a .bib document for the lecture list in LaTeX $\endgroup$
    – Dominic Michaelis
    Commented May 19, 2013 at 16:02
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    $\begingroup$ @DominicMichaelis Yes, I mean: Some users use pseudonyms, and I always try to double check their actual name before quoting them or citing their results. Plus, they may want to add a few comments off-site. Even if they decide to keep the pseudonym, the exchange tends to be fruitful. $\endgroup$
    – Andrés E. Caicedo
    Commented May 19, 2013 at 17:18
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There are two important things.

The first one is that, such a question will usually be a part of an original work. The person who answers your question will even not be aware of your work and his/her name therefore can not be included to your publishable work. However, if a following assistance is required and if the paper is read by the person who helps you, then you can include his/her name.

Second observation is that, he/she will have a contribution to your work anyways and any contribution (at least according to my understanding of an academical work) should be mentioned in the paper. I think perhaps acknowledging his/her help with a nice way of thanking would be really appreciated.

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    $\begingroup$ I do not get the first part. Just because someone is not aware of a piece of work does not mean they cannot be mentioned in that work as having contributed. $\endgroup$
    – Tobias Kildetoft
    Commented May 18, 2013 at 23:48
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    $\begingroup$ Read please the following of the post. You can not write anybodies name to your paper unless they are a part of the work and aware of the work done. However, you can thank them, at least. $\endgroup$
    – Seyhmus Güngören
    Commented May 19, 2013 at 0:03
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    $\begingroup$ You cannot include them as authors, but you should mention them, by name at the appropriate place, if you are using their results. Permission in this case would not be required, as in the usual standard, as the result was posted on a public forum, but proper attributions (including a link to the relevant answer) should be given. $\endgroup$
    – Andrés E. Caicedo
    Commented May 19, 2013 at 0:09
  • $\begingroup$ I agree that you need to mention about them and I also agree that you can not write their names. I think we are speaking the same language. About providing a link is something different. There are other conversations which are public, BUT under the "nick names". So something is still private and you might indent to keep it private. My personal idea would not be including the link but finding another suitable way, if possible. $\endgroup$
    – Seyhmus Güngören
    Commented May 19, 2013 at 0:14
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    $\begingroup$ It seems the misunderstanding I had is that you seem to be using the term "write their name" as meaning "include them as coauthor". $\endgroup$
    – Tobias Kildetoft
    Commented May 19, 2013 at 0:27
  • $\begingroup$ yes exactly, sorry, I was not clear enough. $\endgroup$
    – Seyhmus Güngören
    Commented May 19, 2013 at 1:07
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    $\begingroup$ I disagree about not including links. If there is a link, it should be provided; you always cite primary sources, if at all possible. About nicknames and such, my comment on the other answer explains how I've handled it. (In all cases I recall, the person has contacted me with their name, or has requested that the nickname be used in the citation.) $\endgroup$
    – Andrés E. Caicedo
    Commented May 19, 2013 at 1:30
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    $\begingroup$ I respect your idea. The reason of my objection should also be clear I think. For example you had a post here, say an answer to my question. Then we have quite many conversations here and in some of them perhaps I didnt have a good understanding of your answer. I was perhaps struggling at that time to solve many questions and only one of them was this one. So why should all the readers of my paper be aware of this process? $\endgroup$
    – Seyhmus Güngören
    Commented May 19, 2013 at 1:36
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    $\begingroup$ Because of intellectual integrity. $\endgroup$
    – Andrés E. Caicedo
    Commented May 19, 2013 at 1:41
  • $\begingroup$ It is subjective. $\endgroup$
    – Seyhmus Güngören
    Commented May 19, 2013 at 1:42
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    $\begingroup$ No, it is not. We are talking of publishing a paper, not of opinions. $\endgroup$
    – Andrés E. Caicedo
    Commented May 19, 2013 at 1:51
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    $\begingroup$ (To be clear: A paper that does as you suggest, and does not cite primary sources, effectively hiding the origin of some results, would most likely be rejected in very stern terms by just about all but the most disreputable journals.) $\endgroup$
    – Andrés E. Caicedo
    Commented May 19, 2013 at 1:55
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    $\begingroup$ I think we are talking about different things. I agree on citing, but this is a web-page of discussion and in many cases AWAY from the serious style of paper publishing. $\endgroup$
    – Seyhmus Güngören
    Commented May 19, 2013 at 1:56
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    $\begingroup$ Seyhmus, I urge you to reconsider your opinion here. Andres is entirely correct. A conversation that happens on the internet is no less serious and no less deserving of citation than one that happens in real life. There is no downside to including a link to it. The author whose work you are citing deserves to have their original ideas available. $\endgroup$
    – Potato
    Commented May 20, 2013 at 3:49
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    $\begingroup$ @potato I don't oppose the citation. It is your understanding that this or the other web-page is no less serious than a published paper and I mostly see this in most of your comments. However, without a need to urge me, I have my opinion that such forums are less serious and I make my comments and ask questions accordingly. For example I can make jokes here but not in a paper. Another difference is that all authors of the paper are fully aware of what happens in the paper. It might happen that a question is only about some details of a little question. $\endgroup$
    – Seyhmus Güngören
    Commented May 20, 2013 at 14:02

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