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"MathOverflow is a question and answer site for professional mathematicians."

May other professional researchers ask questions at MO? Should they check their credentials at the door?

If not, and they are not "professional mathematicians", how do they decide whether their questions are at research level?

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    $\begingroup$ to be honest, if people post questions in their own argot and assume that pure mathematicians will understand them, it does not generally go well. I just answered a question on MSE, it took me quite a while to look up the terms, and that was in something called convex analysis that would be familiar to many here. $\endgroup$
    – Will Jagy
    Commented Apr 22, 2014 at 4:45
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    $\begingroup$ If they have the mathematical sophistication of a professional mathematician and ask questions at the appropriate level (e.g. graduate school level mathematics and above), then they are welcome. How would we tell the difference between them and ordinary professional mathematicians? But for the vast majority of researchers in other areas I suspect that math.stackexchange.com would be a better fit. $\endgroup$
    – Andy Putman
    Commented Apr 22, 2014 at 4:46
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    $\begingroup$ If the barber who shaves only those who do not shave themselves is a woman, then she can refrain from shaving herself, without fear of contradiction. $\endgroup$
    – Gerry Myerson
    Commented Apr 22, 2014 at 6:03
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    $\begingroup$ Why the downvotes? It seems a perfectly reasonable question. $\endgroup$
    – Kim Morrison Mod
    Commented Apr 22, 2014 at 6:35
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    $\begingroup$ @ScottMorrison I would suspect them to be due to the overly confrontational tone of the question. $\endgroup$
    – Tobias Kildetoft
    Commented Apr 22, 2014 at 7:25
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    $\begingroup$ I am a professional researcher. Hath not a professional researcher eyes? hath not a professional researcher hands, organs, dimensions, senses, affections, passions? fed with the same food, hurt with the same weapons, subject to the same diseases, healed by the same means, warmed and cooled by the same winter and summer, as a pure mathematician is? If you prick us, do we not bleed? if you tickle us, do we not laugh? if you poison us, do we not die? and if you wrong us, shall we not revenge? If we are like you in the rest, we will resemble you in that. $\endgroup$
    – Will Jagy
    Commented Apr 22, 2014 at 20:02
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    $\begingroup$ Act III, scene i. $\endgroup$
    – Will Jagy
    Commented Apr 22, 2014 at 20:17
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    $\begingroup$ There are currently 110 users with reputations over 10,000. Of those, at least 3 are not professional mathematicians, and I conjecture that this lower bound is not strict. $\endgroup$
    – Steven Landsburg
    Commented Apr 24, 2014 at 14:16
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    $\begingroup$ @Will: Answers to your questions, by order of paraphrasing Billy S: some do; most do; depends on the definition of "food"; yes; not quite; depends on the local health care system; depends on the geographic location (both winter and summer); let's try that and see; I'll take your word for it; yes, I think; I hope not, but I wasn't going to tempt you. $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 27, 2014 at 17:23
  • $\begingroup$ @Asaf, now I've got to figure out who Billy S. might be. Meanwhile, I never read The Merchant of Venice. I did a college course twofer, Edmund Spenser and Christopher Marlowe. Marlowe I understood, Spenser not so much. $\endgroup$
    – Will Jagy
    Commented Apr 27, 2014 at 17:30
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    $\begingroup$ @Will: We had a reasonable bottle of Merlot last night. My preference remains with the Cabernet Sauvignon (I'm not crazy about the 60-40 mixes either). $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 27, 2014 at 17:32
  • $\begingroup$ @Asaf, sure, in context, that makes perfect sense, explains everything. Wait, unless Billy S. is William Shakespeare? That works. $\endgroup$
    – Will Jagy
    Commented Apr 27, 2014 at 17:33
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    $\begingroup$ @Will: Recall that it's already night here. It is you who is living in the past. And yes for Billy S. $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 27, 2014 at 17:35

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May other professional researchers ask questions at MO?

Yes, they can, and they do.

However, questions have to be stated clearly and in a way which is understandable to mathematicians. Keep in mind that the audience of the site are mathematicians. It is mainly the job of the person asking the question to state the question clearly and rigorously in the language of mathematicians.

How do they decide whether their questions are at research level?

Researchers in that area can tell if it is a research level question or not, and often other mathematicians can also. It is more difficult for people who have much less knowledge about the area of the question, the first thing to try to answer the question by themselves, Google, check Wikipedia, check undergraduate textbooks, etc. Demonstrating your own effort to answer the question result in a much more positive feedback.

In practice being a research level question is not as strict as it might seem at the first sight. E.g. a researcher in one area of mathematics while working on a problem may face a question from another area of mathematics. The question might be quite easy for an expert in that area but not the original researcher. That can be a fine question. A question doesn't need to be difficult or on the edge of the mathematical research to be considered research level.

What is really expected is that the question is related to research, the author of the question has tried the obvious things to answer it, the question is well written and interesting to others and is not trivial to answer (e.g. something that almost all mathematicians should know or a good undergraduate student who have taken a course on the topic can answer).

When

  • you have good reasons to believe that a mathematician can answer the question and that the expertise of a mathematician is required to answer it,
  • you have spent time to write a clear question in the language of mathematicians,
  • you have written a brief motivation section explaining why you are interested in the question,
  • you have demonstrated that you have done your own research and have tried to answer your question yourself first,

then it is much more likely that your question will get positive feedback on MO even if it is not strictly speaking a research level question, it will just get migrated to MSE if it is really off-topic for MO.

Also keep in mind that there are several other sites where the question might be more suitable: Mathematics, Physics, PhysicsOverflow, Computational Sciences, Theoretical Computer Science, Computer Science, Cross Validated, ...

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    $\begingroup$ Well said, Kaveh. $\endgroup$
    – Bill Johnson
    Commented Apr 27, 2014 at 19:29
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That sentence is not meant to describe a rule of the site, but rather the purpose of the site. Thus questions from non-professionals which further this purpose (being a great Q&A website for professional mathematicians) are very much welcome.

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You do not need to be a professional mathematician to ask or answer questions on the site. The questions need to be research level mathematical questions. It can be pure math or applied math or mathematical questions coming from other areas. Often, professional academics from other areas (and also non-professional but interested mathematicians) can make a good judgement (especially after some independent searching,) if a mathematical question they encounter is research-level, and if they pose a question which is not appropriate for the site it will be closed. Of course, math.stackexchange.com is also an option one can consider.

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I've often thought that the "for professional mathematicians" is an unnecessarily clumsy and possibly offputting way of stating what is actually meant.

Perhaps it should say

"MO is a question and answer site devoted to research-level mathematical questions"

or something like that.

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    $\begingroup$ The problem is that non-mathematicians have no idea what "research-level" means. And in my opinion the phrase "research-level" is also not quite accurate. I don't think it is necessary that a question arise from research, but rather that it of an appropriate level of difficulty and asked with the sophistication that one would expect from a professional mathematician. $\endgroup$
    – Andy Putman
    Commented Apr 30, 2014 at 2:33
  • $\begingroup$ Except part of the goal is to service people who are not yet professional mathematicians (those in Ph.D. programs) and need help that is likely to come only from people who "smell like" professional mathematicians. It may be an improvement (and still inaccurate) to say the content is about professional mathematics. $\endgroup$
    – The Masked Avenger
    Commented Apr 30, 2014 at 2:58
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    $\begingroup$ PhD students are "professionals". They just aren't being paid very well. $\endgroup$
    – Andy Putman
    Commented Apr 30, 2014 at 3:01
  • $\begingroup$ If first year graduate students are "professional mathematicians", what is all this fuss about oral examinations and dissertations? I think I should agree to disagree with you on this matter. $\endgroup$
    – The Masked Avenger
    Commented Apr 30, 2014 at 3:20
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    $\begingroup$ @TheMaskedAvenger : Aren't they being paid to do mathematics? $\endgroup$
    – Andy Putman
    Commented Apr 30, 2014 at 4:04
  • $\begingroup$ Not the ones I know. They may be paid to teach and assist in projects. Some few may get research assistantships. Based on insufficient data I would say less than half are paid to "create mathematics", and most who are paid are paid to make studying economically feasible until they reach the point of creating mathematics. I am willing to look at well founded studies that say otherwise. $\endgroup$
    – The Masked Avenger
    Commented Apr 30, 2014 at 4:10
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    $\begingroup$ Regardless of paycheck size, I take issue with the part of your comment that suggests to me that a questioner must from the start ask questions in the way professional mathematicians would. My observations are that Joseph O'Rourke and others on MathOverflow ask questions that are engaging, and could easily be presented by nonprofessionals. Further, such questions contribute to this forum and eventually to professional mathematics, but they don't start out that way, nor should they. $\endgroup$
    – The Masked Avenger
    Commented Apr 30, 2014 at 4:16
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    $\begingroup$ To beat this issue into the ground, suppose I ask "Hey, I got this neato idea! Instead of looking at the dynamics of euclids gcd algorithm a_i+2= a_i mod a_i+1, howzabout we mix it up and look at how long it takes to get to zero usin a_i+1 = a_0 mod a_i? Can u help me?" I won't do it for two reasons: I am still reeling from adopting that style of asking, and it would get closed as a duplicate as Jeffrey Shallit has already asked it, in a for me more acceptable fashion. $\endgroup$
    – The Masked Avenger
    Commented Apr 30, 2014 at 4:32
  • $\begingroup$ I am for encouraging people to ask good questions using good wording, but to insist that everyone get it right on the first or second go seems a bit too extreme to me. That may not be your position, but it is part of my take on your initial comment @Andy. $\endgroup$
    – The Masked Avenger
    Commented Apr 30, 2014 at 4:36
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    $\begingroup$ Two points: 1. every SE site has a "target audience" and an "on topic", as variables in some database, and various parts of the documentation are not free form but coded as: This site is for [target audience] to ask about [on topic], Is you question abou [on topic]? and so on. Of course things like this also can be changed. But still it is worth noting that not everything is free form and this also has some advantage for maintainance. In any case we need to specifiy a "target audience", which is currently professional mathematicians, while the "on topic" is research-level mathematics. $\endgroup$
    – user9072
    Commented Apr 30, 2014 at 8:06
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    $\begingroup$ 2. The target audience used to be "mathematcians" but this then caused issues as people did not understand the scope of site and then complained to us why we do not make it more precise. So, after considerable and repeated discussions the target audience was changed to what it is now, not out of some 'snobbery' but to solve a specific problem, that of people understanding (wrongly!) the site to be just about any reasonable math problem (somewhat like Stack Overflow for coding). The 'professional' specifically was agreed on also as it is also used by other SE sites. $\endgroup$
    – user9072
    Commented Apr 30, 2014 at 8:10

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