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Coming from the regular Stack Overflow, the high quality of discussion on Math Overflow is very noticeable. Questions are well presented and detailed, answers and comments are thorough and precise.

What specific steps or policy changes have been made that have led to or ensure this? Is this merely a byproduct of the nature of the profession?
What part, if any, does Math StackExchange have in this? Is there an unspoken threshold to meet when asking a question below which the discussion is directed to the aforementioned site instead?

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    $\begingroup$ Perhaps it is appropriate to link to mathoverflow.net/questions/74707/… $\endgroup$
    – Gerry Myerson
    Commented Feb 15, 2014 at 22:25
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    $\begingroup$ It's interesting to compare with physics.SE. Physics.SE tried to split itself into two pieces, a high-level one and a general one, like MO and math.SE. The high-level spin-off failed, and physics.SE has had trouble retaining members who are professional physicists. The lesson seems to be that you can't attract and retain professionals if participation on the site seems too much like work (i.e., teaching undergraduates). MO was high-level from the start, unlike physics.SE. $\endgroup$
    – user21349
    Commented Feb 16, 2014 at 21:18

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MO is aimed at questions from professional mathematicians (including PhD students), though we accept questions at a comparable level from amateurs and strong undergraduates. We don't allow questions at the undergraduate or lower levels. m.SE like SO accepts questions at all levels.

Note that MO predated m.SE by quite a bit, so the existence of m.SE isn't the direct causal factor here. Prior to the existence of m.SE we simply closed lower level questions, but now we will direct good lower level questions to m.SE.

The fact that MO is aimed at math professionals keeps the mathematical level of the questions high. But the fact that math professionals are a relatively small and community also keeps the quality of discussion high. Many of the top users know each other, and people have offline reputations to maintain.

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    $\begingroup$ The last sentence is in my opinion a myth, or at least cuts both ways, in that I cannot help but feel that sometimes, although rarely, (off-line) reputation (for lack of a better words) is used as a substitute for a proper argument (or correct behavior). $\endgroup$
    – user9072
    Commented Feb 15, 2014 at 20:29
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    $\begingroup$ @quid: I think it's become less true, but certainly for the first year or so of MO people really did all know each other, and I think that made a big difference in how the tone got set. At a bare minimum the fact that all the early moderators knew each other made a huge difference in terms of the MO team functioning well. $\endgroup$
    – Noah Snyder
    Commented Feb 15, 2014 at 20:36
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    $\begingroup$ Perhaps I misunderstood what you mean by "did all know each other" I agree the site was and is still small enough so that on the site most the regular user somehow know each other (and this has some effect). For claims beyond that I highly doubt it. You might have known quite a lot of people, but first after a year the site was already quite developped and second I would be curious what happens if you go through the list of users by rep, and reflect to what extent you really know them other then on/via the site. Did you really know (in a meaningful sense) most all of the first two pages? $\endgroup$
    – user9072
    Commented Feb 15, 2014 at 23:44
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    $\begingroup$ From this snapshot of the top 35, 11 were offline friends or colleagues. Another few are friends of friends, and another few are people who I was "internet friends" with through the math blogosphere before MO. $\endgroup$
    – Noah Snyder
    Commented Feb 16, 2014 at 2:09
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    $\begingroup$ First, thanks for the effort. I did not really mean the old list but still. Second, this is not a year but six month after the creation. Third, while this is impressive, all knew each other feels still like an overstatement for the situation you describe. In addition to various of these now seeming virtually gone (what you acknowledged too). But let us leave this side subject. My actual issue is with the second part. The q is mainly about content and detail, not tone. I do not buy this is due to people being worried about maintaining their offline reputation. $\endgroup$
    – user9072
    Commented Feb 16, 2014 at 2:30
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    $\begingroup$ @quid: For those of us who edit under our own name, of course there is a desire not to embarrass ourselves. I just now clicked on "users" on the main site, and 31 of the 36 users shown on the first page appear to edit under an identifiable name (of course this is just one sample). My belief is that a significant part of the quality of this site is that users view it as an extension of their professional interaction with other professionals whom they already know, rather than as a mere diversion with anonymous strangers. $\endgroup$
    – Carl Mummert
    Commented Feb 17, 2014 at 13:20
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    $\begingroup$ @CarlMummert did it occur to you that for those that do not edit under their own name but use the site regularly, there is also a desire not to embarass themselves on this site. As a pseudonymous user you have nothing but what you contribute here to establish some credibility, and thus it is more important that this is rather consistently solid. And actually above all I would assume that any mathematician that deserves to be called one will make an effort to write correct mathematics no matter what, out of respect for the subject itself. (cont.) $\endgroup$
    – user9072
    Commented Feb 17, 2014 at 13:34
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    $\begingroup$ Yes, I realize that for users who use pseudonyms, the only source of real "reputation" is a pattern of good contributions. However, I think the role of real identities on this site cannot be ignored. Under the list of "top lo.logic users / last 30 days", I know at least 9 of 19 personally (not counting myself), and 19/20 appear to use their real name or at least first name and initial. The final one uses three initials. Of course, again, this is just one sample, and the debate of using real names versus pseudonyms can't be answered here. But I do feel that real names encourage civility. @quid $\endgroup$
    – Carl Mummert
    Commented Feb 17, 2014 at 13:40
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    $\begingroup$ (cont.) It does not affect me personally but if I would be here under my own name and would be told I only (or mainly or also just significantly) try to be coherent and correct out of some kind of fear for consequences elsewhere I would find this ever so slightly offensive. But, also, if you want to actually establish what you claim shouldn't you at least compare the quality of the contributions of the regular contributors posting under a real name and not? Rather than just claim it is relevant. [Written in parallel to @CarlMummert second comment but seems still relevant.] $\endgroup$
    – user9072
    Commented Feb 17, 2014 at 13:42
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    $\begingroup$ Sorry for one more comment @CarlMummert Re 'civility' This likely depends on what one means by 'civility'. Some likely are not as openly confrontational as they otherwise would be, perhaps, but then some seem, as a substitute, to engage in some not so easy to spot bullying and related activity. It is not clear which of the two is more of a problem. (But we are getting a bit off-topic now, I agree.) [To be clear the "some" does not refer to anybody in thsi thread.] $\endgroup$
    – user9072
    Commented Feb 17, 2014 at 13:48
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There was related discussion at What is needed to succeed in keeping up the level of the site and retaining the good contributors?, which you might be interested in.

I don't think it's merely the nature of the profession (although it helps: it's in the nature of mathematics that a very high level of precision, and broad consensus on what it means for an answer to be correct, is possible).

Roughly speaking, the norm from the beginning in 2009 has been to keep the level of question roughly at a level expected from someone who has passed PhD qualifying examinations and who is undertaking some research. Moderation from the community on this score is quite active, and the added benefit of being able to redirect questions which don't meet this threshold to M.SE has also helped a lot, as Noah explained.

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  • $\begingroup$ Thank you very much for the link, it has a lot of good discussion and references to similar threads. Should this question perhaps be closed as a duplicate? $\endgroup$
    – Etheryte
    Commented Feb 15, 2014 at 19:16
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    $\begingroup$ As meta functions a little differently from MO main, I'm not too fussed about possible duplication. Ongoing discussion of community norms is probably a healthy thing -- reasonable people can and do disagree on them at various points. $\endgroup$
    – Todd Trimble Mod
    Commented Feb 15, 2014 at 21:56
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In addition to what was said already, another aspect is in my opinion that the site is relatively low volume, at least "per user," yet also globally. Very few people post (q&a) more than, say, every three days. This is in starck contrast to SO and math.SE where many regular users post a lot more (multiple posts almost every day).

Put differently, the site is in the fortunate situation to have since a long time a very good size. It is small enough not to be hectic and it is large enough not to feel static even if one visits frequently.

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