I have a sense that mathoverflow is much less welcoming than it used to be of questions that can be understood by non-experts. I'm not talking about philosophically-oriented questions, which I think are received about as well as they always have been, but rather technical questions that might reasonably be answered by a graduate student who is specializing in the relevant field. And when I say "less welcoming," I'm not just talking about having questions closed. If someone asks a question and receives no upvotes and a comment (with a number of upvotes) that the question would be more appropriate on math.stackexchange, then they are hardly likely to feel "welcomed," even if the question is left open and they receive useful pointers in the comments or in an answer.

If the questions would receive good answers on math.stackexchange, then this might not be a bad thing. But here's the thing: they won't. I have asked a few questions on math.stackexchange; in every case, I ended up feeling that, while nobody thought the question was inappropriate, no one could answer it--or at best, there was a small pool of people who had a chance of answering it, all of whom were also mathoverflow participiants. I also feel that when I do get answers on math.stackexchange, the answers tend to be addressed "under my head," so to speak; the answers I get on mathoverflow tend to be better for a student at my level, even when the question is not particularly "welcomed."

The result is this: Sometimes, there are questions I would like to ask that occupy a sort of "middle ground": I know they are too hard for math.stackexchange, but I don't want to risk the embarrassment of being told (explicitly or implicitly) that my question is too easy for mathoverflow. The end result is often that I never find out a good answer to the questions. Moreover, I have the sense that other people--especially new users--have a similar experience, which has led to a dearth of questions asked by others that I, as a graduate student, can actually understand. Mathoverflow used to be useful to me as a place where I could learn new math simply by browsing. Now, it is much less so. (Admittedly, this may have something to do with the fact that Brian Conrad no longer seems to post anything, but I don't think that's the primary reason.)

In the provocatively overstated language: I sometimes feel that mathoverflow has become too elitist since the introduction of math.stackexchange.

Do other people have the same experience? Or is the general sentiment relief that graduate students like me have stopped crowding the forum with too-easy questions?

I agree with Mariano, it's best to keep things concrete and on a case-by-case basis if we want to make any progress.

I suppose you could easily make a counter-argument: perhaps the only reason why questions appear to be better-answered on MO is because of whose mouth the answer is coming out of? I haven't seen much evidence to support your claim, Charles.

And MO has always been elitist in a certain strict sense. MO is about research mathematics, which basically by definition is a type of elite. There's a criterion, is what I mean.

In that regard, an abstract discussion is kind of pointless.

I'll try to get some concrete examples, but obviously I won't be able to provide concrete examples of questions that should have been asked, and were not. On a larger scale, I'm not so much talking about specific cases of an inappropriate reference to mathoverflow, as a general trend to be too quick to put in a stackexchange reference. Even if each individual reference were defensible, the number of them makes mathoverflow feel unwelcoming--especially since a referral to math.stackexchange, even with the best of intentions, can feel humiliating to someone who is, in fact, a member of the mathematical establishment. I am not sure I myself have ever received such a comment, but I can't help fearing it when I see it applied to questions that I do not immediately know how to answer. And I doubt I am the only one.

Here's a question that I first asked on math.SE; it was fairly well received, but not very well answered. When I finally decided to try posting it on mathoverflow, most of the "answerers" left their answers as comments, which suggested to me at the time that they did not really think it was a difficult enough question to be interesting, even though it was too difficult for math.SE.

http://mathoverflow.net/questions/72004/in-what-generality-is-the-natural-map-operatornamehom-rl-m-otimes-s-to-oper3

Here's a question for which I specifically replied to a comment that it would be more appropriate on math.SE. I don't mean to suggest that an exercise from Hartshorne is typically a good question on mathoverflow, but I don't think math.SE should be suggested as a viable alternative. (I should probably add that, generally speaking, I have very high respect for Sándor Kovács's activity on mathoverflow.)

http://mathoverflow.net/questions/87014/questions-about-cohomology-class

There have been a number of other examples in which I have considered leaving such a comment, but since I did not, I don't know how to locate them.

MO questions are supposed to be of interest to research mathematicians. This doesn't necessarily mean the same thing as research questions. Many questions that are "sent" to MSE would probably stand if the OP had given a little background on themselves and the problem (and in particular make clear it is not HW). That said I think it is also confusing to potential posters that the reaction to more elementary questions is very field dependent. For example rarely are Set Theory or Category theory questions closed in my experience. In part I think most mathematicians aren't so familiar with these areas and so are less likely to close and also I think the experts in these areas are friendlier to questions from non-experts.

Just as another data point (I make no claims that it is representative, but I do agree with Mariano and Ryan that the discussion really needs some specifics)

This question struck me at the time, and still does now, as something where it's not a question of the level being inappropriate, or necessarily being homework, but where more thought should have been put in. Then again, here is another example where the OP should really have just thought harder, but which didn't get redirected to MSE.

In general, I instinctively agree with Benjamin Steinberg's view that "many questions that are "sent" to MSE would probably stand if the OP had given a little background on themselves and the problem (and in particular make clear it is not HW)", but I admit this is based on my impressions and memory rather than an actual count.

Charles, there is a world of difference in the two examples you give. The first is clearly stated and references SE. It is the type of question that a non expert in a subject might ask. You got good responses, I think, even if possibly not the complete answer (which, as far as I know, might not exist) you hoped for.

The second question is a good example of a bad question. The grammar is bad, part of the question is unclear, and the question is an exercise from a book. When this last is pointed out to the OP, the OP acknowledges that he or she knows that! Thanks for pointing it out--I just cast the first vote to close while wondering why mine is the first.

Charles,

I'm sorry if you feel if this forum has become less friendly to grad students. I sincerely hope it isn't the case. But speaking entirely for myself, since I don't have a huge amount of free time, I admit to being unlikely think about a question unless I feel that the person asking has put some serious thought into it, or if it is sufficiently interesting. The last question you mention is a good example of one where I felt that no effort was demonstrated. Had s/he said "I know this is a problem in Hartshorne. I tried the following but got stuck. ", some of us might have been inclined to say something like "write the divisor as a difference of two ample divisors..."

Or: what Donu Arapura just said.

I think that counting by tag is not so accurate. I would only count 2 of the 5 closures listed by Joel as being questions about Set Theory. One was about basic facts about injective maps, one about the definition of a relation and one about T-shaped sets in the plane. Probably the other tags above also have mislabeled questions. But in any event my unscientific memory is that many textbook level questions about choice do not get closed (which is not a bad thing since I have learned a lot from them :))

How are you proposing those questions be handled?

Mariano: I think that the OP should be told nicely in the comments that if s/he wants help on an exercise from a textbook, s/he should give more information--how s/he has attempted to solve it, why s/he is interested in this question, and the like. I see the closing of questions as a necessary evil. If questions like this one should grow in number, then closing them would be an appropriate tool to keep them under control. But since this question has not received an answer in this long, it seems unlikely that a "cheap answer" will be forthcoming for the OP. My perception (which certainly may be mistaken) is that questions from graduate-level textbooks are not currently a big issue, and people who ask them might one day be useful contributors to mathoverflow. While I don't think such questions should be answered, I also am inclined to think that closing them is not necessary--at least, not with the dynamics of the site as they are at the moment.

How about this? http://mathoverflow.net/questions/87768/a-question-on-gauge-functions

I have written uncountably many comments saying all that. Saying it as nicely as I managed.

Isn't all this spelt out clearly in the FAQ? If not, we should strive to make it clearer, possibly pointing to good real examples of questions. But familiarizing oneself with a site, seeing what gets asked, what gets answered —even the average level of grammar and punctuation!— is something that I expect users to do as part of the work of asking a question. Most people would not enter a bar without checking out first what's going on inside... yet we end up coming up with the nth rephrasing of "you will get more luck if you tell us what you have tried".

I'd like to push back against some of Ryan's comments, because I think they are a very good explanation of how many "closing" users are thinking, and I disagree with them.

"If the question appears to be a grad-student homework-type problem, especially if it's not well-motivated, it might be closed... I suspect most people are worried about creating a repository of answers to homework problems..."

If it weren't for the word grad-student, I would agree with all of this. When I'm answering questions over at math.SE which strike me as undergrad homework level, I try to give hints rather than answers, and I tend to direct those questions to math.SE when they show up on Mathoverflow. But, at the grad level, if the question asks for a solution, I usually give it. This is for a couple of reasons:

* I view graduate students as young researchers. I think they have the maturity to decide for themselves what kind of answer they are looking for.

* There are cases where, as a researcher, you really do need to just get an answer and move on, rather than understand all of the background. Now grad students have more free time than professors/postdocs, and they have more future years to reap the benefits of a deeper understanding, so they more often should learn the background. But not always. My advisor (Bernd Sturmfels) tells the story of, in grad school, needing the lemma that, for any polynomial p(t) and q(t), there is a point (x,y) in R^2 not of the form (p(t), q(t)). He went to one of the local algebraic geometers, who pulled out the section of EGA on dimension theory. That strikes me as a wildly bad answer to this question. Two better answers would be "see Sard's theorem" or "consider the monomials p(t)^i q(t)^j for i+j \leq N. There are roughly N^2 such monomials, and they have degree O(N) in R[t] so, for N large, there is a linear relation between them. This gives a polynomial relation between p(t) and q(t), which will not hold identically on R^2." Neither of these is as deep, but they would have allowed Bernd to move on and apply this result.

* Graduate level questions are not only asked by graduate students. In recent years, I have taught myself the basics of quiver representations, triangulated categories, the analytic Peter-Weyl theorem, Hodge theory and Riemmannian geometry. All of these are things which would be grad-school material for a grad-student with a particular syllabus, but none of them are things that I learned in grad school. I want MO to be a place that I can come and ask about the basic things that confuse me when I am learning new fields. As I mentioned on another thread, I have gotten a very positive response to these questions, because I have a very good reputation here. But I also want MO to welcoming to people who ask those questions without establishing their bona fides first. I have the impression that, at least here at UMich, grad students feel intimidated to ask questions on MO.

"as one gains seniority, more and more people start to treat you as if you're some walking automated library"

I definitely experience this. But the great thing about MO is that it is so easy to not answer a question! When someone stops into my office or sends me a personal e-mail with a question like this, there is real pressure to give an answer. I constantly see questions on math.SE which I think "that's not worth my time to answer", so I don't! MO has many fewer such questions, but I ignore questions here too.

Here is a proposal. I sometimes view MO by going to http://mathoverflow.net/unanswered/tagged?page=2&tab=newest&pagesize=15 . That will give you questions which have gone about 12 hours without being answered . It is a pretty safe assumption that none of these are too basic. Maybe Anton could create a convenient link to do this?

I think most of your concerns are pretty standard and already-voiced, David. For example "I have the impression that, at least here at UMich, grad students feel intimidated to ask questions on MO". Isn't that to be expected? I mean, MO is meant to be something like tea-time. When I would walk up to John Milnor to ask him a question at tea time, I certainly felt intimidated as a grad student. Perhaps I shouldn't have but I did. It's not clear to me it's possible to create a completely non-intimidating environment when you're not only asking experts, but there's essentially no privacy (unless you're anonymous), and on top of that there's an essentially perpetual public record (which does not happen at actual tea time, thankfully).

But I think we're getting off-track by not talking about specifics and instead picking at my comments in isolation. Much of my comments had to do with asking questions in a respectful way, where you do your due-diligence and put together a question that not only shows you really care about an answer, but that you've tried things yourself. The kinds of things we'd pretty much expect of any colleague.

Is anyone for not closing questions like the one Yemon just linked to?

(That question IMO makes for a good example for the Do Not Do This list...)

David Speyer said above: "* I view graduate students as young researchers. I think they have the maturity to decide for themselves what kind of answer they are looking for. "

This may be true where you are, David, and be true among most of those you knew as a grad student, but at least in the initial stages it is most certainly not always the case. In the less illustrious levels of maths where people like me work, it's not clear to me that people with PhDs whose work I have to read have attained that maturity, perhaps because no one educated them as to how to ask and solve questions.

As Charles surmises, it might be pretty hard to implement (much less enforce) a "policy" for experienced MO users to follow, although we might try to come to some consensus on reasonable guidelines.

They don't come much more clueless or more obnoxious than the homework grubber of Yemon's Exhibit A, and I don't think much effort should be expended on such cases. If there were a bullet point in the FAQ that "blatant requests or demands to do the OP's homework, without reciprocal effort shown by the OP, will be summarily closed" -- or something similar -- then I guess we could point to that. But honestly, that's such a no-brainer that violators are probably lost causes to begin with. (What I really want to do is tell such clueless types to go to hell, and telling them to go to math.se seems an acceptable substitute. (-: )

Todd, while I agree that "homework grubber" questions deserve little or no effort on their behalf, I do not think that pointing them to math.SE is helpful to anyone. For one thing, if the problem really is a graduate-level problem, math.SE will probably not be a great place to get it answered. More significantly, do you really want to inflict such "homework grubbers" on the math.SE community?

This actually leads to the following suggestion: questions that are simply bad (as opposed to being at an inappropriate level) should probably not be referred to math.SE--out of courtesy to the math.SE community, if for no other reason.

About MSE, see http://tea.mathoverflow.net/discussion/1125/sending-people-to-math-stack-exchange

I have to say that my objection is almost never to a question itself but whether the person asking the question demonstrates at least some reasonable effort towards answering the question. If someone asks a question that can be answered almost directly from the definitions involved and shows no sign of having tried to do just that, then I am quite unsympathetic. If a person asks a question, indicates some effort made, and where the roadblock occurs, then I am much more likely to want to help.

There's a specific example I have remembered. I could not find it--I suspect it has been deleted--but at some point after math.SE opened, I noticed a question on mathoverflow about whether a group is isomorphic to its "opposite group." The question was quickly closed, and the user directed to math.SE. Another comment--apparently made after the question was closed--was from some user I recognized (I can't remember who), linking to his "first question" on mathoverflow and talking about "how far mathoverflow has come." The question linked to was the exact same, asked when MO was in its infancy, and had a number of upvotes.

I think it would have been entirely appropriate to close the question as an exact duplicate, but my impression (which I cannot now verify since I can't find the question) was that the question was closed as being "off topic" or some such before it was recognized as an exact duplicate. The impression I took away from this (the closing, the redirection to math.SE, and the comment left afterwards) was that "low-level questions that might have easy answers, even ones that mathematicians might find interesting, are no longer welcome on mathoverflow," and that this was progress. I can understand why the question was closed--the answer was easy and, in retrospect, the first thing someone would try if they had put any serious effort in before asking; whereas the original question was probably asked at a time when mathoverflow had only a few users who were struggling to come up with questions to keep the project going. But the fact remains that the question was closed--quickly--as being too low-level, even though it is the sort of question that mathematicians find interesting.

But there is a key point here. When you leave a comment that a question is inappropriate (and would perhaps be more appropriate on math.SE), or choose to post an answer as a comment, or decide that a question is too easy/basic to be upvoted even though you find it at least marginally interesting (I am certainly guilty of the last), you are not just giving a message to the asker. You are also giving a message to everyone else who looks at this question to get an impression of what sorts of questions are appropriate on mathoverflow--and, in particular, whether their own question(s) at a similar level are likely to be welcomed, tolerated, or closed. I think it is important to consider this second audience; a comment that is entirely appropriate to the asker, may still give the wrong impression to an observer.

+1 David. And -1 to the concept of "graduate level material": it's an almost meaningless term.

But the fact remains that the question was closed--quickly--as being too low-level, even though it is the sort of question that mathematicians find interesting.

I'm very sorry to say this, but I don't get why this is the sort of question that mathematicians find interesting. IMO the question was trivial (even for beginners in group theory), and I think the OP (who is a respected member of the MO community) simply wasn't thinking. Why was closing it as off-topic so inappropriate?