But not homework does not imply good question (for MO, of course)...

The thing I don't like about this is we're cementing MO's reputation as a website to go to for solutions to homework problems.

I can understand when undergraduates and non-experts have weak write-ups of their questions but for a research mathematician I tend to expect at least a motivational write-up to a problem. In contrast, I'm less concerned about math.stackexchange developing a reputation as a homework solution webpage, as they do not have anything in their mandate specifically against that.

The structure of MO is to have community norms enforced by the community but it appears the community is pulling the website where it will be indistinguishable from math.stackexchange. I don't think this is a good idea. If the websites aren't any different, what's the point?

@Todd, regarding your quote: "Far easier questions have been posed in MO and not closed as `too localized'", if we're to go by the mandate that any question is okay if and only if there is an easier question present on MO, this would be not be productive, long term, for the webpage. We have a very different sensibility than the easy-ness of a problem for acceptability at MO, I hope. I think Henry Wilton's comments above are quite reasonable.

Ryan, that's not really what I meant. The question is why is this such a bad question for MO; I'm just not convinced it's that bad. Okay, so put "easy-ness" aside: IMO there are far worse questions appearing on this site than the one we're discussing, where it looks like the questioner didn't think *at all*. I do agree that Henry's comments are reasonable, and in comments I *did* offer to edit some more so that it looks less like a class handout of a solution. Maybe I'll go back and do just that. Generally I try to write mathematics as clearly as I can; the suggestion is that I went too far this time? (Thanks for the feedback Henry -- I learn from such well-expressed advice.) Added in edit: you make a good point, Ryan, that OP could have designed his question more thoughtfully, but obviously he was new to the site and I think something like Andrew Stacey's comment should have been tendered first, before shutting his question down entirely. Oh well, hindsight is 20/20.

I do understand. I did want to bring this up on meta first, but had some trouble signing in. I then wrote Qiaochu (whom I know a little from private emails and other fora), and before I knew it the question was re-opened. And so, having thought about the question a bit, I jumped right in, which I thought was okay. I am a little dismayed that I seem to have upset some people.

Ryan, as long as we're talking: do you have a reference for the assertion that this question (as stated) is a well-known homework exercise?

Yeah, I think Mark said in his graduate algebra courses. The general question of what types of "homework" are "fair game" for this site is probably an interesting one which deserves some careful thought. I'm not saying this particular question is a great test case or anything, but I can think of problems from say Hartshorne that I found very difficult when I was a graduate student and probably would still find difficult, and the idea of being able to consult MO on such old unresolved questions is very attractive to me, as though I can at last die peacefully. Perhaps we could discuss this sometime. Or has it already come up here?

@Todd: I don't think you've upset anyone at all. As you can see, acceptability of questions and answers is by no means a clear-cut issue, and something struggled with on meta on a near-daily basis. It's an unfortunate by-product that the askers and answerers of such borderline questions are by necessity put in the uncomfortable position of watching others debate the significance of the effort they just put forth.

(In case this is what you're referring to, I did downvote your answer, but immediately went and upvoted a different response of yours that I hadn't yet upvoted -- the intent of this being that the downvote was to discourage answering questions like this to the community at large, not to punish you in particular for writing a very clean write-up to a question I think is inappropriate for the site.)

To your other point, there's a big range even among Hartshorne exercises -- there are certainly Hartshorne exercises I would downvote for being inappropriately low-level for the site, and agree that more difficult Hartshorne exercises make for perfectly appropriate questions (assuming they pass all of the other metrics of a good question -- motivation, evidence of effort put forth, etc.)

Todd, I personally have no problem with your answer itself. There will always be grey areas to any policy, and obviousness is in the eye of the beholder. I'm glad these issues have been raised, and I think it's been good to have a discussion about them: it's certainly helped me clarify my thinking. As far as I'm concerned, your answer was nothing more than a useful example in that discussion, so I very much hope that you don't take anything said above personally.

I mostly agree with Todd. The objection that a question is a homework problem seems about as relevant as objecting that something would make a nice homework problem. There are plenty of interesting results that make good homework questions once they are proven. The possibility that an undergraduate could solve a problem, or even the fact that undergraduates often solve a problem given context, doesn't feel like sufficient grounds for closing a question. I also don't think that an answer being easy to understand is sufficient grounds for closing a question. After all, when you post a question to MO, you're hoping that it's easy for somebody.

While I agree that we wouldn't want MO to have the reputation of being a repository of solutions to homework problems, it is supposed to be a repository of problems and solutions, so some friction is unavoidable. If something makes a good homework problem in a graduate course (or even an upper division undergrad course), it's probably because is made what would've been a good MO question at some point in the past.

I suppose it's largely a question of what reputation MO has, but I really don't get the feeling that we're currently in danger of acquiring the reputation of a great place to go to get your homework done. So long as that isn't an issue, I don't see what's wrong with people being able to find solutions to (these kinds of) homework problems on MO. After all, they can and do already search Dummit and Foote for solutions to exercises in Lang, and nobody is making the argument that Dummit and Foote should be removed from the mathematics library. Even with very high-tech math you can argue that it would be much better for everybody to work it out for themselves, but it's often the case that these things are incredibly confusing even if somebody is carefully holding your hand the whole way (as in a textbook).

It's certainly true that there's value to solving a problem on your own and that we should discourage people from simply avoiding that. But we have no reason to be so insecure about mathematics that we make it artificially more difficult. If somebody just tells you the answer to a question you have or shows you some piece of machinery that swiftly solves your problem, you'll have no trouble finding other problems to build your character. If you digest the answer, I can't imagine what argument anybody could give that you are worse off.

The objection that a question is a homework problem seems about as relevant as objecting that something would make a nice homework problem.

Agreed. That a question is the same as a homework problem is not in itself sufficient to vote to close, though it is evidence that the level might be too low. However, that someone is asking a problem that they were set as a homework is sufficient. A question is not just a question, it's about the questioner as well. So I would consider who was asking the question when deciding whether or not to vote to close a seeming homework problem.

Francois, that's a very useful formulation of "too localized". Something like this should be in the FAQ (I can't recall whether all these reasons for closing are explained there or somewhere else on this site).

[Was the present question too localized then? Based on just my own answer, I tend to believe "not quite", but it could be a close call.]

In fact, should some sort of consensus emerge from this discussion, then it might be good to put down somewhere more visible.

Anton and Andrew, thank you for your remarks. People here seem pretty vigilant about policing questions that look like homework requests, as is only right, so I can't imagine that MO has acquired anything like a reputation of go-to place to get your HW done. But in this case and others I've seen, people have seemed a little <i>too</i> vigilant and too quick to judge intent from the bare question. Perhaps a warning shot along the lines of, "I'm voting to close unless OP explains better where this is coming from; it looks like a homework request to me" should be employed more often (I think I've seen this used). If the OP responds with something reasonable, keep it open. The random undergraduate passing by will probably be unable to say anything reasonable.

I appreciate the feedback, Tom.

Gerry, we have a thread on the interpretation of "too localized": http://tea.mathoverflow.net/discussion/274/what-does-too-localized-mean-exactly/

How many examples of questions to which the geographical interpretation applies as a reason to close?

I usually use "too localized" to mean "this is a math problem but it does not belong here".

+1 Cam.

Regarding 'Too localized', for what it's worth I'm with Gerry: if it's homework then it's 'Off topic'. I think Scott's comment in the thread that Ryan linked to is a decent characterisation of 'Too localized'.