(NOTE: I'm not claiming that this question is necessarily mathoverflow-appropriate in any case.)

More generally, scheme-theoretic language can make a lot of commutative algebra more transparent and geometric to someone who understands it. Category theoretic language can do similar things. And so on.

Concerning MO more directly, I think that, for the most part, the "inappropriately forwarded" questions we are talking about are at least at the level of the Springer GTM ("Graduate Texts in Mathematics") series. (I don't mean to say that anything at this level should be kept, but that few if any questions below this level should be kept.) However, I also would like to point out that a question asked on MO is likely to be answered differently from the same question asked on MSE, because of the assumed mathematical maturity of the asker. Someone who has the mathematical maturity to understand a more advanced (and probably briefer) answer may well find it easier to understand than the more elementary answer they are likely to receive on MSE.

I think it is the wrong attitude to act as if people who feel humiliated are right, and IMHO, this attitude is partially responsible for many students being reluctant to ask questions, not only on MO but also in lectures. I don't like this perspective being encouraged on MO. If you agree that there is no reason to feel humiliated, then what we need to do is not to act as if those who feel so are right, but to make it clear that being forwarded to MSE is normal and is not humiliating.

Personally, I would already feel more comfortable asking a research question on math.stackexchange: though my questions on MO have always been well-received, I feel a bit nervous every time I ask one, and I wouldn't worry at all on math.se. This seems to me to be a problem for the long-term health of MO.

Kaveh: as others have pointed out, it is an empirical fact that people do get offended when their questions get the more-appropriate-for-math.SE treatment. The way your post was written it seems that you disagree. Do you still disagree, or are you ready to agree that people "can get offended"? Or perhaps what you really meant was what Tom suggested, that people "should not" get offended?

In the particular case of recommendations to StackExchange: There are certain types of questions which I agree can be redirected to MSE without any irrational implications of inadequacy. A good example would be the question, asked before the advent of MSE, about how fast to move in a rainstorm to minimize how wet you get. Although many professional mathematicians might find this question interesting, they have no particular expertise (versus, say, an engineer or a physicist) at answering it.

However, in most situations, asking a question on MathOverflow involves admitting, publicly, that we were unable to figure out the answer on our own. If we are subsequently told that the answer is easy, we experience a sense of humiliation. If we are told that the question is at the level of an undergraduate textbook, it is hard not to see this as humiliating, since there is a common if somewhat irrational feeling that a graduate student ought not to have difficulty with undergraduate-level problems in his own field.

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 want to express disagreement with this view point. I don't see anything humiliating about suggesting a question is more suitable for MSE. These recommendations should not be taken as personal, they are about questions not persons. They are not judgments about people.

Moreover MSE is not a bad place that one should avoid, it is a nice place to ask questions which are not research level. If I have a question at level of undergraduate textbook MSE is a nice place to ask it. There are many users who participate in both of MO (as researcher) and MSE (as a teacher) and it seems that they like keeping them separate.

Bill, I'm so sorry I made the incorrect choice from the list offered by Tom. Apparently, based on your upvoting/downvoting habits, you are more likely to be the "compulsive editorializer" type. Glad we got that cleared up.

This is "Trimble's" last comment on Tom's subthread. It was a lot of fun, though.

I knew Tom had a math blog which is not full of jokes, but he could well have a sardonic sense of humor. If I were more clever I might have written much the same without considering that anyone would think that I was serious.

I guess I am out of touch.

"this is not the appropriate venue"--why don't these users just use upvotes or downvotes?

Very simply, because it might be the wrong course of action. If a question isn't appropriate for this site, it is much more effective and informative just to say so (and cement that with a vote to close), than it is to give a downvote, which is very weak information.

I can't get behind your methodology at all (nor do I much care for the stereotypes, e.g., New Yorkers vs. Japanese). It's way too crude. My own impression is that many people downvote far less often than they might, and not for particularly commendable reasons (maybe they don't feel like giving up a point, or maybe they are being soft when it would be better to be honest). And then those who are being honest (here we could take your example, Bill Johnson) get branded as "hypercritical gatekeeper" or the like. (I agree with Harry about "naming names".)

If a person gives no downvotes, do we take him or her "more seriously" or more credible than we do someone who downvotes heavily relative to the population?

The credibility of a person ought to be based on quality of comments and contributions to this site. I am skeptical about applying such simple statistical measures to gauge credibility.

It does blunt the psychological impact of a criticism when someone says something to the effect of , "He's always like that. Don't take him too seriously."

But it blunts the psychological impact a good deal less if there's just a link you can click on to find statistics that might suggest this, as opposed to someone actually saying it. Additionally, a large part of my concern is not simply the impact on the OP, but the impact on others who are trying to get a general impression of MO to decide whether their own questions are appropriate. I think that the such users are much less likely than the OP to go to any extra effort to investigate the credibility of the recommender, even as simple as clicking on a link.

I suppose that one could post the "credibility index" or "criticality index" next to each person's name on every comment, but given the number of people who find reputation (which operates, for the most part, under clear and simple rules) too prominent, I hardly think this suggestion is likely to be popular.

More seriously, I think the bigger issue is one of perception. The ability to find out that a particular commentor is hyper-critical does not necessarily blunt the psychological impact from a criticism by that commentor. A more effective (and much easier to implement) solution might be for community members to keep an eye out for over-zealous "transfer to math.SE" recommendations, and be prepared to make counter-comments.

Smackdown =D

Now to go off topic: as someone who has been speaking English longer than you have, I am well aware of what "spartan" with a lower case 's' means ;) I was making an allusion to the Spartans' reported methods of child-rearing, and indeed to what they came to epitomize as regards "manning up", to use the parlance of our times.

The sigma-algebra questions seem, to me, to represent a user who quite possibly should be referred to math.SE, even if his questions, taken individually, are borderline-appropriate. (I'm not making any claims as to whether or not these questions should have been closed.)

<english-language pedant>Tangential comment: I don't think "Spartan" is the best choice of words here--that word (when not used to refer to the ancient Greek Spartans) typically refers to a lack of luxury. Perhaps "stingy" (as in, stingy with your approval) is more what you have in mind.</english-language pedant>

On the other hand, all those recent sigma-algebra questions could have gone either way: I don't really want things that smell of "do my hard homework" on MO, but then this could just be me being too Spartan.

Mainly, I would just like to express my strong agreement with Charles's original observation that

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.

with David Speyer's post, and with Andy Putman's post (though as Todd Trimble points out, even what constitutes "first-year graduate" or "second-year graduate" varies widely). In my opinion, several of my math.SE questions meet Andy's criteria, and simply on a personal level I'd like it if MO were a place I could even hope to use (and contribute to) in the near future; but I further think that if MO were accepting of questions meeting Andy's criteria, many people (ranging from grad students to professional mathematicians pursuing interests outside their field) would benefit greatly. (By the way, isn't one of the standard counterarguments to this that "superstars" would stop using the site if it got too "low level" for them? My guess is that this is mainly false, but I don't think people have addressed this yet in this thread.) I think it would be great if something close to Andy's proposal would replace the current FAQ's stated criterion of "research level math questions".

Regarding the original topic of when to suggest that the OP try math.SE, I think this is very simple in both the current MO paradigm and in what I described above. I am sure that someone has said this before on this thread or another, but my opinion is: if the question is being closed here only because of the level of its content, and not because of its tone or homework-grubbing nature, then by all means suggest math.SE; if instead the question needs serious improvement, suggest math.SE only if you also describe the main flaws that would need to be fixed first. We are quite used to all sorts of flawed questions on math.SE - if someone to whom you suggested improvements fails to implement them when they post on math.SE, that's their fault, not yours, and it is not nearly as much of a disruption for the usual content on the site as it is here on MO. Besides, I'm sure that they'd sooner or later have found math.SE anyway.

Lastly, some amusing additional data points demonstrating the change in MO culture: I have several questions that would now be considered borderline to downright silly from which I gained a nontrivial amount of reputation. Even in (what is now) my ideal vision for MO the latter two ought to be closed / migrated to math.SE.

Regarding Steve Huntsman's point: I think this is an illustration of the "cultural" bias of MO. I am inclined to think that we are more inclined to be harsh toward basic (and easy, which is not the same thing) questions in, say, algebraic geometry than in some other areas (like analysis, set theory,...). I'm inclined to think that, in general, the algebraic geometers are too intolerant, rather than the other way around. (I will admit that this comes in part out of frustration that I am nowadays more likely to understand a question tagged "set theory" than one tagged "algebraic geometry", in spite of the fact that I am myself an algebraic geometer.) Unfortunately, I don't feel qualified to comment on Steve's specific example.

The point is that it was basically a misunderstanding of notation, rather than an actual question about mathematics.

That of course is speculation. It's a good speculation, but you don't really know for sure it was notation that was the problem.

More on-topic: just because a question is about notation doesn't mean it's unsuitable for MO and belongs on math.se. Notation is important, and is frequently confusing.

For some of us longer-term users, that is delightful understatement :)

Mariano, I don't think Charles (or indeed anyone in this discussion) has been saying questions like the Nakayama Me Now exhibit shouldn't be closed. The question is whether redirection is (a) appropriate (b) sending out the right message to people, like Charles, who worry that asking questions from books is in some sense taboo. In this particular case, I think closure with a comment explaining why this kind of thing is bad manners here (and, let's face it, anywhere) is the right course of action, rather than just shunting the problem over to MSE.

Here's the meta thread:

http://tea.mathoverflow.net/discussion/1304/is-the-category-of-elements-a-coend/#Item_0

Statement: Whether or not a given question is appropriate for MathOverflow should be independent of the fact that math.SE exists.

Now, why I consider the opposite groups question at least somewhat "interesting": in essence, because it makes good browsing. The notion of "opposite group," and the question of whether or not it is isomorphic to the original group, would probably not have come up in my mind; and even if it did, I would probably not have bothered to figure out the answer, because it would not have been obvious to me how little effort would actually be involved. The question and its answer are not incredibly interesting, but given how easy they both are to read, I think the ratio of "interest value" to "time investment" is quite favorable. And I, personally, derive a certain amount of satisfaction (it's almost like relief, in some sense) from tying up a "loose end" in my mathematical knowledge. It also helps that this is a general fact that relates to things I have considered before (like how to convert a right action to a left action).

Certainly, this question would be entirely appropriate on math.SE, and would probably receive a good answer there (and not necessarily by a mathoverflow regular). But it also has the virtue that a mathematician is likely to care, at least a little bit, about the answer; and that there is a nice, elegant, answer. (If nothing else, it would make a good exercise for students. And I don't think I'm the only mathematician who enjoys seeing good exercises, even at a basic level, that I have not seen before.) Most of the questions I see on math.SE, I find that I simply don't care very much what the answer is.

http://mathoverflow.net/questions/90/fn-2n-is-not-surjective

Most definitely not appropriate any more.

I'd also like to defend the calls to "show your working" on all questions. I'd be fine with Andy asking questions for sheer curiosity's sake - most of mine have been of that type (since most of my research-level questions go unanswered - I'm hoping that one day Bill Johnson will go through my question list and take pity on me). The key is to explain that it is for curiosity's sake.

When the user-base for MO was smaller, one could get a sense of someone's thinking by following their questions for a bit. Now, it's harder to spot and that's a shame. But we can make up for it by giving more details. This is purely for selfish reasons - I want to know a bit about the person I'm helping, or even if I can't help them then knowing why they're asking that question makes it more likely that I'll get curious in it as well and want to know the answer. So the extra information doesn't have to be of the "here's what I've already tried" type, but could be of the "this is just out of curiosity" type[1].

[1] To be absolutely clear, I'm not advocating asking every "I was just wondering" question on MO. But if a question is borderline, then having the OP explain that it just came up in conversation and it seemed like the sort of thing someone would just know and they won't be able to get any sleep until it's solved and their partner is threatening to kick them out if they don't stop bringing a pad and paper to bed at night ... well, then it might just tip the balance in favour of the question for me.

"Show that you've worked on it" is certainly a natural reaction when faced with the "homework grubber". I agree it's not a fitting standard to apply to each and every question, but let's just say we all hope that the OP has tried to think about his/her problem before asking. And perhaps we can agree that an OP's effort to expose thinking can make a question better (it rarely makes it worse), and it's something quite conspicuously lacking in cases like grubbing for homework help.

And I think there are lots of not-quite-so-obvious cases where one feels like drawing out the OP more, because there is suspicion that he/she might be trying to avoid doing any work. It might help to have some specific examples of this.

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?

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.

When I was a second-year graduate student, I struggled for a number of months to understand an exercise on the second page of the book by Ballman-Gromov-Schroeder. The exercise was the most elementary case of the problem I was working on, so my lack of progress was quite frustrating. Eventually I was at a conference and asked a senior mathematician, who informed me that in fact this was a major open problem. (Needless to say, I changed directions.)

If Math Overflow had existed at the time, I hope I could have asked for some hints and, one way or another, broken through the roadblock I had hit. But in the current atmosphere I cannot imagine a graduate student having the courage to ask about an exercise that appears on the second page of a textbook.

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. (-: )

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.

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

So here is an instance where I might be tempted to vote to close, or to recommend trying elsewhere. I can see why there is a case against doing so, but it isn't the kind of question I want to see on MO.

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.

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".

IMO the two forums have a wide overlap and there's really very good mathematical questions that will get a far better response on the StackExchange site than on MO. One of my favourites would be this one: http://math.stackexchange.com/questions/2755/why-can-you-turn-clothing-right-side-out/ also this one: http://math.stackexchange.com/questions/11669/mathematical-difference-between-white-and-black-notes-in-a-piano

To follow up on Bill's comment on Charles's examples: I am not competent to judge how easy or difficult that second question is, nor to know if it is a standard exercise which people set students as part of the learning process. What I will say is that it displays a fault which I'm sure all of us have displayed, but which we as researchers ought to grow out of: it doesn't say what the OP is stuck on, or what he or she already knows.

Actually, on reflection, my feeling is that the question is deficient not because "it is an exercise in a book and so should automatically go to MSE", but because it is poorly worded and seems to want "money for nothing", see Ryan Budney's comments above. In a sense I think Charles has a point, in that the question is unlikely to get a good answer on MSE. On the other hand, I don't think it particularly deserves a good answer on MO in its present form.

*Before I get deluged with outrage, let me add, as Yemon knows, that I intend no disrespect to him.

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.

I suspect most people are worried about creating a repository of answers to homework problems, or doing someone's homework, or doing the leg-work that they should be doing, telling them what they should have been reading in their course-book, or should have got out of their homework assignments. If the question does not appear to be from the heart in some sense, there's little initiative to answer it. In that regard, my impression is your first thread seems more like idle curiosity than a real desire to know, but that's just a first-impression bias. I think in part it's because you never said why you want to know the answer to your question.

I apply similar standards when people ask me questions in person. If it's a grad student laying on a couch, barking off idle questions, they'll be ignored unless the question is awesome. If they seem to really have a reason to want to know the answer, if it's clear they've thought about it, with examples and such, then I'll engage them.

There's a phenomenon one notices as one gains seniority, more and more people start to treat you as if you're some walking automated library, with free answers to everything. When answering a question one wants to feel like you're not putting in any more effort into it than the question-asker. Otherwise one may feel like they're not really getting anything out of the answer. So there's a reverse desire to want to see the question-asker sweat a little.

Somewhere in there lies roughly the kernel of the push-back to your assertion that MO is becoming elitist.

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.

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.