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I asked the question "Averaging $2^{\omega(n)}$ over a region" because this is a necessary step in a research paper I am writing. The answer is detailed and does exactly what I need, and it would be convenient to directly cite the result. However, the author of the answer is anonymous... how would one deal with such a situation? I could of course very easily just reproduce the argument in my paper, but that would be academically dishonest.

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    $\begingroup$ Once, I left a comment indicating I would like to give the author proper credit, and asked them to contact me (they did). Another time, I asked the moderators to contact the author and ask them to contact me so proper credit could be given (they did). $\endgroup$ – Andrés E. Caicedo Nov 4 '17 at 12:55
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    $\begingroup$ If you want the member to "out" themselves to you, while still preserving their anonymity, you should not tell us what question title is involved. I might be curious enough to read all your answered questions and corresponding papers to find out, but probably not, whereas you make it too easy by specifying which question. While Chris Godsil has a good suggestion, you should still give the poster the opportunity (ask them in a comment or through moderators) to unmask for this paper. Gerhard "Maybe 'Reveal' Is The Word" Paseman, 2017.11.04. $\endgroup$ – Gerhard Paseman Nov 4 '17 at 17:11
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    $\begingroup$ Just to add minor clarification to @AndrésE.Caicedo comment, moderators might have access to more personal information about a user than regular users do. But they are bound by moderator agreement not to disclose this information to other users. (Of course, this is different from what Andrés E. Caicedo describes in his comment.) $\endgroup$ – Martin Sleziak Nov 5 '17 at 7:15
  • $\begingroup$ One perfectly ethical way is to simply give credit in the prose of the paper, just as you would for an unpublished result that someone told you out loud at a conference. $\endgroup$ – Carl Mummert Nov 12 '17 at 20:10
  • $\begingroup$ Did you try to email the user? There is an email address at the user page. $\endgroup$ – მამუკა ჯიბლაძე Nov 30 '17 at 19:30
  • $\begingroup$ A related (recent) post on Academia Stack Exchange: How to acknowledge a MathOverflow user? $\endgroup$ – Martin Sleziak Apr 12 '18 at 13:35
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I think you should just reproduce the argument in your paper while attributing it to the user in question (with a link to the question). As long as you give the correct attribution, there is nothing academically dishonest about this.

I had to do this in one of my papers; see the top of page 20 of this.

I don't think it is any different from including an argument that a non-anonymous person told you. People do this all the time, and there is nothing wrong with it as long as you indicate who told you the argument (assuming it isn't really standard, in which case you can just thank them in the acknowledgements). For example, I did this in the "Proof of Theorem B" on page 3 of the paper I linked to above (which was explained to me by Eduard Looijenga).

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    $\begingroup$ Well -- imagine the pseudonymous user changes their pseudonym, or even chooses to switch to their real name at some point. -- How does a citation by pseudonym look like then? $\endgroup$ – Stefan Kohl Nov 4 '17 at 23:21
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    $\begingroup$ @StefanKohl: Not sure that is such a big deal. I think that readers of my papers are sophisticated enough to realize that the internet is not a static thing. The important things are that 1. the argument is correct, and 2. it is given in my paper (in case it is deleted from the internet at some future date), and 3. I did the best job I could at attributing it to the right person. $\endgroup$ – Andy Putman Nov 4 '17 at 23:24
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    $\begingroup$ @StefanKohl the citation could/should list their MO user page, which is identified by a unique number. There are a lot of "what ifs" that prevent readers down the track looking up stuff; but maths is a lot better than subjects where an unjustified statement is made with a citation to "Private communication". $\endgroup$ – David Roberts Nov 6 '17 at 22:40
  • $\begingroup$ Reproducing is always better than just referencing, but I'm not sure if this answers the question about the citation format :) $\endgroup$ – darij grinberg Nov 8 '17 at 9:29
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    $\begingroup$ It has probably something to do with versions, but it is the bottom page 22 now instead of the top of page 20 $\endgroup$ – Vincent Dec 27 '17 at 13:14
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    $\begingroup$ It would be helpful to update the online PDF to add proper links to the text. Thanks to a ligature, the link to the relevant answer doesn't copy/paste properly. $\endgroup$ – dfeuer Apr 12 '18 at 16:38
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You seem to view a nickname in the bibliography as embarrassing or unprofessional. There is no reason this should be the case. If you use the built-in "cite" feature of the stackexchange network, the author's nickname will immediately be followed by the URL of their profile, which should allay any doubts about what kind of name it is:

@MISC {496728,
    TITLE = {Decomposition of a tensor product of Lie algebra representations into irreducibles},
    AUTHOR = {Balerion_the_black (https://math.stackexchange.com/users/88863/balerion-the-black)},
    HOWPUBLISHED = {Mathematics Stack Exchange},
    NOTE = {URL:https://math.stackexchange.com/q/496728 (version: 2013-09-17)},
    EPRINT = {https://math.stackexchange.com/q/496728},
    URL = {https://math.stackexchange.com/q/496728}
}

The profile link also survives name changes and is a unique identifier (and in this case, also a disambiguator).

In the unlikely case the editors object to such a reference, let them suggest an alternative. It is ultimately not your fault if they mutilate your bibliography; this is what arXiv is for :)

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You attribute it to an anonymous author and give the link. So you are not claiming credit and your readers can check the source.

I would see no harm in reproducing the argument as well, especially if it’s short.

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  • $\begingroup$ I don't think the link is needed; this is not really different than a personal communication. $\endgroup$ – Carl Mummert Nov 12 '17 at 20:07
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    $\begingroup$ It’s extra information, and it’s no effort. $\endgroup$ – Chris Godsil Nov 12 '17 at 21:00
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This blog posting by me was cited in this article on page 12, footnote 2.

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    $\begingroup$ This is nice, but it's an URL in a footnote, not a proper citation. I think the OP wants the latter, as he wants to rely on the proof. $\endgroup$ – darij grinberg Nov 8 '17 at 9:27
  • $\begingroup$ @darij grinberg: for something that is not published in a permanent format, a footnote may indeed be the most appropriate citation. I would generally not put ephemeral things like emails, letters, or anonymous website comments in the references section. They can be acknowledged in the prose of the article. The same would go if someone told you the result orally at a departmental tea - MO is not really different than that, in my opinion. $\endgroup$ – Carl Mummert Nov 12 '17 at 20:08
  • $\begingroup$ @CarlMummert: MO is not ephemeral; it is archived on the Internet Archive under a license that makes mirroring easy. More likely that various currently existing journals will disappear. $\endgroup$ – darij grinberg Nov 12 '17 at 21:47
  • $\begingroup$ @darij grinberg: I suppose it depends on what we mean by ephemeral. For printed journals on paper, we have a good sense that they should be readable in thousands of years. For MO, I'm not sure we have that sense; I do view it more as the equivalent of a letter than the equivalent of a paper. (Of course, I doubt people will want to read most current math papers in thousands of years... ) $\endgroup$ – Carl Mummert Nov 12 '17 at 21:57
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    $\begingroup$ @CarlMummert: Modern paper isn't like that. But even for the more immediate future, the survival of paper journals is far from guaranteed. When I was at MIT, it was in a process of throwing away journals that had been scanned by the publishers (e.g., Elsevier journals). Even barring this, nowadays most universities only subscribe electronically. When I publish in a "paper" journal, I cannot rule out that my paper never ends up seeing a printer. $\endgroup$ – darij grinberg Nov 12 '17 at 22:15

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