To show "how far MathOverflow has come", consider the following question from the very early days:

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.

Andreas: That was precisely the point, in a way: the impression I got from this encounter was that this question was inappropriate because math.SE existed, but would otherwise have been okay (except for being an exact duplicate). The following statement is stronger than I really feel, but I'm going to propose it anyway for the sake of moving the conversation along:

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.

Exhibit B14: http://mathoverflow.net/questions/88002/nakayama-module-closed

Charles: Harry Gindi may not represent a consensus view.

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.

The original version of this post has been removed on account of a very good point made in the post immediately following it. I don't want to say anything that could be misinterpreted to encourage the sorts of questions that quid is talking about.

Just wanted to put in my $.02. Rather than give background, I'll just quote from comments on http://mathoverflow.net/questions/33230/ :

"I disagree with the suggestion that this question be closed. It's a basic question, with a simple answer, but if you don't know the field it's not obvious where to look this up and the subject is hardly one which most mathematicians cover in grad school. As per this discussion, meta.mathoverflow.net/discussion/506/… , consider me a vote against closing. – David Speyer Jul 25 2010 at 2:13 "

...

"The grumpy old man in me can't resist: an order of magnitude more people surely learn about Markov processes than coherent sheaves or motivic homotopy theory or whatever "most" mathematicians supposedly study at any level. – Steve Huntsman Jul 25 2010 at 13:17"

(Not really on-topic, but) Harry,

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.

I haven't been involved in MO for a very, very long time (except for occasionally stopping in to vote to close only the worst of the worst questions, e.g. this one), so I think my opinions about its policies should carry a correspondingly small amount of weight, but as a moderator on math.SE and soon-to-be grad student I'd like to add my two cents as well.

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.

My sense about Yemon's linked example is that it is probably either a question of interest to non-specialists who know the area better than I do, or a question that does not really make sense to someone who knows the area. (I'm not qualified to judge.) It has, in either case, the appearance of having been thought through carefully. Thus, I'm inclined to doubt that a referral to math.SE is helpful. And in truth, I don't think anyone would have suggested moving the question to math.SE if the OP had not specifically asked about this.

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>

Yemon, I was actually thinking of this exact idea a few days ago. On your department website, you should have an alternative picture of you equipped with John Steed/Patrick Macnee hat and umbrella, http://www.imdb.com/name/nm0001495/ . If the picture comes out well, also as MO icon. P.S. a Russian co-author put in multiple occurrences of "laconic," I got him down to just the one.

This one is odd. OP ignored all requests for clarification, all hints. I suggested a move to MSE after giving a part answer, http://mathoverflow.net/questions/88243/cubic-residues-modulo-primes/88250#88250
The part that is not unusual is an OP responding only to demand more help, while indicating no effort.

@Yemon (Offtopic):

Smackdown =D

Tom Copeland: How do you handle deleted comments in your analysis? For instance, I sometimes give constructive comments with the sole content of "here's a minor error in your question/answer, and here's how to correct it," and will typically delete these comments once the correction has been made. This could cause me to be rated as more "polemical" than I really am. On the other hand, extremely polemical comments will often be deleted later (sometimes at the recommendation of others), so this could cause some people to appear less "polemical" than they really are.

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.

Uh, I think I still have a similar downvote/upvote ratio to Bill Johnson, and it doesn't seem right to "name names" to try to discourage downvoting, Tom. The only thing that bothers me is malicious downvoting, but we all know that Bill doesn't do that anyway.

Yeah, but I think that Bill Johnson is a more credible source than I am, even though we have roughly the same "negativity rate".

@Tom Copeland: Are you continuing your joke or were you really not kidding?

@Will Jagy: ?

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.

Will Jagy: You gave good advice to Bill. He should check my website and meager contributions to MO to assess how seriously I should be taken—just as I suggested in my first comment about recommenders for SE.

Bill Johnson: Who knows how I actually feel? How serious am I? You could follow Will’s advice. I will say that contrary to insinuations by Trimble I haven’t branded you as a hypercritical gatekeeper and haven’t stooped to name-calling (e.g., “homework grubber”—yikes!). I view the ROTFL as an obviously pure editorial expressing your feelings with little other info. (Hard to tell if you’re laughing at me or with me, though. We are in the same boat as the new user and commentators to his question w.r.t. mutual understanding.) It does make an anecdotal case (and therefore weak case) for my hypothesis that there is a rough correlation between behavior (downvoting vs. upvoting) and temperament (in this case a compulsion to editorialize). Your other comments seem well-balanced and reasonable, but I, as well as other new users, have very little info to rely on to make judgments. I hope you can take my observation good-naturedly, just as I'd like to interpret your ROTFL.

Todd Trimble: How did you obtain your impression/stereotype of the typical MO user? BTW, “a shouting New Yorker” doesn’t equal “New Yorkers.”

To reiterate, I’ve suggested some crude statistical measures off the cuff, rather than relying on some sparse anecdotes and in lieu of a detailed analysis of the recommender’s behavior and contributions (neither of which the new user has at his ready disposal), mainly to assess the question in the title—Are people TOO ready to suggest a move to SE? The statistical analysis would be a fun exploration/experiment, given the time and resources, that could possibly reveal some trends or fail completely as some suggest. Sorry if I’ve appeared sardonic or too facetious. Just thought a look at the question from another angle would be interesting.

Also, as a loudly complaining New Yorker who comes from a family of loudly complaining New Yorkers, I've gotta say that taking our complaints less seriously is a mistake, if you know what I mean.

Yemon, I'm inclined to agree with you on this one. I would expect math.SE to be able to handle almost any assigned exercise in point-set topology.

Kaveh, it may be that closing a question and suggesting it's re-asked at MSE shouldn't be humiliating, but I think it's the case that many people do find it humiliating.

(See Tom Leinster's comment for a much briefer version of mine.)

@Storkle, I think there is no reason to feel humiliated. It seems quite normal to me that sometimes we don't know the answer to a question which has a simple and easy answer, particularly when the question is not from our area of expertise. If someone is asking a question which is at the level of undergraduate textbook exercise (without any explicit or implicit indication that the answer they are looking for is not the standard answer) then the right thing to do in my opinion is to politely forward them to 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.

Kaveh: While I applaud your desire to encourage students to ask questions, I think that telling them they should not find it humiliating to ask questions with simple and easy answers is about as useful as exhorting the hungry and naked to be fed and clothed. Many people will feel humiliated when they find that they have asked a question with an easy answer. Pretending that there is no issue here, or telling them that they have no rational reason to feel humiliated, is likely to compound the shame by suggesting that there is something wrong with them for feeling humiliated. When I am in a lecture and not understanding something, I am far more likely than most of my peers to ask questions--perhaps too many questions. The way I achieved this was not by trying to pretend I did not find it humiliating when my questions revealed my own ignorance or lack of understanding, but by training myself to continue in spite of the potential for humiliation.

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.

Suppose that the question is "How do you embed the complete graph on a countably infinite set of vertices in 3-space?" One very easy answer (to a mathematician) is to take any discrete subset of 3-space for your vertices, and then use transversality to ensure that no two edges intersect. To someone at a more basic level, this answer would be extremely confusing; such a person would probably need an explicit construction, which a mathematician might find tedious to read through.

(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.