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1.
People have gone out of their way to describe probability problems as homework level which were not. At least, not for the courses on probability that I took.

http://mathoverflow.net/questions/7949/a-probabilistic-inequality-closed
http://mathoverflow.net/questions/6444/how-long-for-a-simple-random-walk-to-exceed-sqrtt

Probability isn't my main area of research, but I have proved a few theorems in probability, and these look like good questions to me. They are not on the level of research; they seem right for MO. Many of the comments look like they were made by people who missed the point of the questions.

This question was too vague:

http://mathoverflow.net/questions/12462/limsup-and-liminf-for-a-sequence-of-sets-closed

However, if you have gone through the Borel-Cantelli lemma under the notation usually used, then you should recognize what the questioner meant, which is why the question got detailed answers even though it looks close to meaningless to some.

If you don't understand a question, and just suspect that it is homework-level even though you can't do it immediately, don't comment that it looks like homework, and don't vote to close it. Don't block people who actually do understand the question from answering. If you close 1 good question and 6 bad ones, you are closing too many. That the structure of MO gives you the power to do something does not make it appropriate at all.

I still contend that it takes some expertise in an area to determine whether a problem is on the level of homework, and therefore, that it is helpful to other mathematicians to point out *correctly* when a problem is below the level of MO. But don't declare a problem to be homework-level unless you are very confident that you are right.
• CommentAuthorEmerton
• CommentTimeFeb 13th 2010

I agree with Douglas's statement that closing 1 good question and 6 bad ones is closing too many questions. In general, I hope that people who are not expert on the area of a problem will be very cautious in voting to close it.

2.
I agree with both the general points that Douglas made, and his assessments of the individual questions.

I'll also take this as an opportunity to repeat an apposite quote from Persi Diaconis: "It's a theorem that mathematicians don't know probability."
3.

I agree with you about the limsup liminf question and I've voted to reopen. It was more meaningful than I thought. But I don't regret voting to close it. It's not that hard to compose a question so that it's clearly meaningful, even if the meaning requires some expertise. For example, this question could have defined it's terms and provided some motivation for the question (or at least used some capitalization).

More generally, I think we as a community will have to change our understanding of what it means to close a question. As more people break the 3k reputation boundary, this will become more and more important. Right now, I think many people think it means that the question is totally hopeless and shouldn't ever have been asked. Closing a question should usually mean something closer to, "this question should be (temporarily?) taken out of circulation for some reason." Typically, this means that the asker needs to clarify the terms, the motivation, or the question itself. I don't see what's wrong with voting to close a question for these reasons, even if the question is outside your area of expertise. But I do think you should leave (or vote up) a comment explaining what's wrong with the question and how it can be improved and reopened (if it is indeed salvageable). This is exactly why you can still edit a closed question and why an edit bumps the question to the top of the home page, so that people can re-evaluate the question and vote to reopen if appropriate.

4.

To put it another way, as the number of 3k+ rep users grows, I expect that fixing up and reopening questions will become much more common. This will have two very beneficial effects:

1. Closing questions won't carry the same stigma it does now.
2. The overall quality of questions will increase. To avoid the minor hiccup of a question being closed and reopened, people will put a little more effort into composing clear, coherent questions.

By the way, if you have >2000 reputation and you think you can improve a closed question without seriously distorting the meaning of the OP, do it! If you're lacking some information, so you can't improve the question without changing the meaning significantly, think about what the OP would need to do to improve the question and ask them to do exactly that. Perhaps link to some part of the How to Ask page. If there's something you wish were in the How to Ask page so that you wouldn't have to repeat the same thing all over the site, tell me and I'll add it.

5.

+1 to Douglas on all points made.

6.
I agree with Douglas Zare's main point -- don't act based on a lack of knowledge (by retagging, voting to close, etc.) -- and also with Anton Geraschenko's response -- please don't take the closure of a question as a personal affront.

Let me only note one thing: the question

http://mathoverflow.net/questions/6444/how-long-for-a-simple-random-walk-to-exceed-sqrtt

has zero votes to close. (If you don't know, this implies that it has never received a close vote, since close votes cannot be undone; although if the question is closed, you can later vote to reopen it.) There is one user who commented that it looks like homework, and then that it is not of interest to a research mathematician. Many more people chimed in to say the opposite. There's very often going to be that one person (on MO, it is often the same person), or a few people: it seems all but inevitable. I don't think this question is an example of essential room for improvement, although such examples do certainly exist.
7.

@Pete: I haven't done something like that in a while (The question is from Nov 22). It's not necessary to take a shot at me like that. I'm going back to being silent.

• CommentAuthortemp
• CommentTimeFeb 13th 2010

I agree with the thoughts that Zare and Emerton expressed. In the long run I do think that it serves MO's purpose better to go in the direction that they suggest.

MO is an amazing resource. I think all serious researchers and students of mathematics must be encouraged to use it.

One benefit I can see in a comment like `this is not clearly stated, restate it and we will consider opening it' is that it may discourage abuse. I have been following MO for a while. The only abusers seem to be several anonymous people who ask questions that clearly have a mocking tone (such as, `2+2=4? I don't get it please help.' To my astonishment, even these got comments along the lines of `this question is not appropriate for MO').

I think that it is very discouraging when a question from a student or scholar of math gets this type of negative response. It is discouraging both to the person who asked the question and to people who are new to the site. Furthermore, it is damaging to the site. I can imagine able mathematicians resenting the attitude and stop interacting in MO.

Another thought: consider a professional mathematician, i.e., a university professor. Say they are not at a top school and they don't study algebraic geometry or a related field. What is the likelihood that they will ask a question here when they know that there is some not small chance that they will be ignored or get a beating for it?

I am thankful to the people who thought of MO and realized it. It has been very useful to me and I am sure to everyone else who has been using it. I am looking forward to seeing it grow and be more inclusive.
8.
@Harry Gindi: If you no longer stand by a previous comment, there's an easy remedy: delete it.
9.

Anton: I am not sure that you can expect new users not to see "closed" as a harsh rejection. The question gets stamped with a big [closed] label and cannot be answered. Additionally, all the reasons for closing look like pretty firm rejections. I would rather change our behavior to match the UI -- if a question is vague but might be fixable, request fixes in the comments but leave the question open. Is there some harm to this that I am missing?

10.
I very much agree with what Douglas Zare, etc. say.

I would like to suggest the following "policy" to the community : "A user should only mark as homework or vote to close a problem in a field that they feel they are competent to answer research-level problems". Another possible wording would replace "answer research-level problems" with "teach a class".
11.

@David: I don't think there's any way of getting around the fact that having your question closed is a form of rejection. Part of my response is that people shouldn't post stuff on the internet if they are unwilling handle any sort of criticism. But the meat of my point is that when a question is closed, the question on everybody's mind (and in their comments) should be "what needs to happen for this to be reopened?" If we can successfully cultivate this outlook, I think that closing a question will be viewed as part of the life cycle of a question rather than its permanent death and people won't take it as such a rejection. As we get more high-rep users, questions will get closed and reopened more often anyway just because there will be more voices. The earlier we start treating it as a normal quality control procedure, the better. I know we've had trouble getting people to leave positive comments, but I'm still optimistic that things will get better.

I agree that it's not always necessary to close a question if it needs to be improved, but sometimes it is. One rule I use for vague questions is, "if any answer would have to start of with a guess of what the question actually is, the question should be closed." That's a situation where I think allowing answers to accumulate is actually harmful. This is the reason I voted to close the limsup liminf question, though it turns out my assessment was off.

12.

I feel like I should say something about declaring that something is a homework problem. Even if you're absolutely sure that a question is a homework problem, it doesn't do any good to say so. Frankly, I don't see what's wrong with people posting homework problems if it's helping them and others understand the material better. The real problem is usually one of the following:

1. The asker is asking others to do his work for them. Whether or not it's a homework problem, this sort of thing should be discouraged. Typically, the problems are completely unmotivated and weirdly specific (they look like they've been taken from a textbook), which is why we tend to close them as "too localized". A probabilistic inequality falls into this category. In these cases, I'd vote to close and leave a comment along the lines of, "This looks like you're asking others to do your work for you. Please provide some motivation. What have you tried already? Etc." Even if it is a homework problem, if the person puts in the effort to motivate the problem, perhaps generalize it, and explain what they've tried and why it didn't work, I think it's fine to leave it open (or reopen it).
2. The material is too elementary. I think we get very few of these, but sometimes it does happen. For example, I remember somebody asked about whether any power of 2 is divisible by 3. Again, it doesn't really matter if it's a homework question, these question should be closed and politely redirected to another site. I hasten to add that a mathematician trying to learn a completely new field could have "undergraduate-level" questions, and I don't see any reason not to allow these on MO. Only really elementary questions fall into this category.
13.

@temp:

consider a professional mathematician, i.e., a university professor. Say they are not at a top school and they don't study algebraic geometry or a related field. What is the likelihood that they will ask a question here when they know that there is some not small chance that they will be ignored or get a beating for it?

I think I fall into this category, thus providing a case study for your speculative thought. I admit to having asked only two questions; one was actually related to algebraic geometry, and got some good answers. The other was from PDE theory, and has so far received no answers – most likely because there are hardly any PDE people here. Do I feel ignored? Yes, a little, but I realize that nobody has an obligation to take an interest in a question waaay outside their own field, so it doesn't bother me. Have I received a beating for it? Not at all, and it would have been a tremendous surprise if i did. If I have a problem on MO, it's just that gathering reputation is taking a lot of time, because my interests don't match those of the majority here very well. (But is that a problem really? No, reputation only results in higher powers which implies some sort of obligation, and being without could be considered a boon.) In short, I wouldn't worry too much about the treatment of hypothetical professors from second-rate universities.

• CommentAuthorLK
• CommentTimeFeb 13th 2010

@hanche
Lack of answers does not imply lack of interest. Your question was upvoted often enough to appear on the 1st page of the list of unanswered questions. Two users marked it as a favorite (including me, and I'm still trying to prove that nontrivial zero set forces u to grow at infinity.)
• CommentAuthorIan Durham
• CommentTimeFeb 13th 2010

I have to second the comments of temp. He/she expressed my sentiments in a much more cogent way than I could hope to myself. As someone who best identifies himself as a "mathematical physicist" I will note that this is one of my biggest disappointments with this site (though I realize it's new and evolving and I don't wish to take anything away from the founders). There seems to be an underlying assumption that everyone here is a pure mathematician with exactly the same background. Perhaps that is the intent of the site in which case it might be helpful to make that more explicit.

My other disappointment is with the reputation/voting/closing system. While I think its intent was ultimately good, in practice it seems to foster too much animosity. It's too divisive in practice.

I do disagree with Anton (and presumably with many other users of MathOverflow) regarding the ease at which a question may be formulated. Asking good, insightful questions is not an easy task. If it were, then science and mathematics would be a lot easier than they are. I try to foster this in my students by making them turn in 3x5 index cards with questions on them (one per class) that are graded. I also employ the Socratic method, even in pure math classes. Asking good questions takes experience, perseverance, and frequently assistance (i.e. it often takes a group to develop the best questions).

14.

I do disagree with Anton (and presumably with many other users of MathOverflow) regarding the ease at which a question may be formulated. Asking good, insightful questions is not an easy task. If it were, then science and mathematics would be a lot easier than they are. I try to foster this in my students by making them turn in 3x5 index cards with questions on them (one per class) that are graded. I also employ the Socratic method, even in pure math classes. Asking good questions takes experience, perseverance, and frequently assistance (i.e. it often takes a group to develop the best questions).

Actually, I think we agree on that. As it says at the top of the How to Ask page, "Using Math Overflow should be an extension of the way you normally do mathematics, and the same rules you use to effectively solve problems can be used to make good MO questions. Just like solving problems, crafting good questions requires you to put in some effort!"

I'm not completely sure what you're referring to when you say that I've said it's easy to formulate a question. I think I have said that it should be relatively easy to remove vagueness from your written question, assuming you really have a concrete question you're trying to answer. If you come to MO thinking, "I'm frustrated by elliptic curves; I'd like somebody to straighten me out" then you can expect to have trouble. You're looking to have a discussion, which is fine, but it just won't work well on MO. Getting from general confusion to a concrete question can be tough, and that's something you pretty much have to do before you come to MO. This step requires effort; nobody on MO can do it for you and you absolutely cannot skip it. The concrete question you come up with may just be the first step to resolving your confusion and it may be pretty broad, but it has to have a specific goal. It has to be possible to explain your question to somebody else so that they know what an answer would look like.

Once you have a question, it might still be hard to express it really well, but you should be able to "put all your cards on the table." If it turns out that you left something out or that there are multiple ways to interpret your question, you should be able to fill the gap or resolve the ambiguity without much difficulty. If you can't, then you probably came to MO too early in your problem-solving work flow and you should be mildly embarrassed. Following the advice in the How to Ask page should prevent these embarrassing situations where you don't really have a focused question or you're trying to ask too many questions at once.

• CommentAuthorHarry Gindi
• CommentTimeFeb 13th 2010 edited

@Anton: I like to think that voting to close your own question once you've realized you haven't thought about it enough lessens the embarrassment somewhat. If you've made a mistake, and you've been called out on it, the best thing you can do is admit your mistake. I've done this with several of my questions. (Which explains my request a few months back to have a question closed, if you remember that far back.) In fact, this same kind of thing happened yesterday.
15.

@fpqc: <fun>Of course the amount and duration of the embarrassment is entirely for you to decide; I was just making a suggestion.</fun> If you realize you don't have as concrete a question as you thought and you don't see a way to salvage it, asking others to help you close it is probably the best thing to do. With your question yesterday, this was probably the best course of action.

But sometimes I think you're too hard on yourself (and others) on this issue. If it turns out that your question isn't as insightful as you'd hoped or if it turns out that it's not as hard as you expected, I don't think there's any reason to close (or convert to wiki). In the question you asked two days ago, it looked like you converted to wiki and voted to close (I'm not certain it's your vote to close) when Emerton pointed out that the answer you accepted was fairly standard. One of the things MO is really great for is questions that somebody else knows the answer to right away. There's nothing wrong with not realizing that some standard result applies to your situation. Then again, maybe I'm biased because I answered that question, or maybe I misunderstood what happened.

16.
I just wanted that thread to die, so I community wiki'd it and voted to close.
17.

@Leonid: Of course. What was I thinking? (But apart from the bad example, the point stands.)