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As I mentioned in another thread, I think we should have a page on MO that documents how to craft a good question. If nothing else, I want to have something to link to when I think a question can be improved. To that end, I've slapped together a (very) rough draft of such a page. Hopefully it's mature enough that it will benefit from some exposure rather than be killed by it.
I've also pasted it into a public wave, which you should be able to find by logging into wave and typing "with:public how to write a good Math Overflow question" into the search box. If you don't have a wave account and want one, let me know. I have 53 invitations.
I corrected some typos.
"...will not be as good as ... the Wikipedia page." In some cases, that's harsh! But that sentence is saved by "or".
I see where you're coming from, but I really want to use "and" there. The point is that for focused questions, an MO answer is quite likely to be better than the Wikipedia page, but for extremely broad questions, it basically can't be because it's unreasonable for somebody to spend more than a few hours writing an answer. I've rewritten it as
Worse, somebody who is too kind and too generous with her time may spend a great deal of time and energy crafting an answer that might not satisfy the asker and that will be just a shadow of a proper survey paper. Such questions can't be reasonably answered in a few hours, even by an expert who knows the "answer."
Actually, maybe the last paragraph of "Be specific" would be better suited for a separate page or section of the faq on suggested voting practices.
The reasoning behind putting that paragraph there is that I want the page to serve two functions:
Since composing a good question is a matter of writing a question and then evaluating how good it is (then repeating several times), I feel like these two functions are not worth separating. More generally, I feel like advice on how to respond to a violation of a rule should occur very close to the rest of the discussion about that rule.
I don't think we should dismiss "review articles" entirely: for a positive example, see http://mathoverflow.net/questions/6517/double-affine-hecke-algebras-and-mainstream-mathematics. To my knowledge David Ben-Zvi doesn't regret spending time on writing that answer :)
Excellent page, Anton!
One small suggestion re the "do your homework" section: There's certainly more that you should do other than try to find a reference! If I have something which I think might be a good MO question, but it's not immediately apparent what exactly I want to learn, I'll almost always play with it for a while (usually at least half an hour, and sometimes as long as off and on for a couple of days) before I ask it. Even if I don't think that I have any chance of being able to solve the problem or answer the question myself, making an effort to do so to the best of my ability always "clears the fog" and helps me to understand where I'm having trouble or what it is I really want to know. And apparently it works, since people have very generously upvoted even some of my embarrassingly trivial questions.
Anyway, it seems like one of the underlying themes to the page is: "Put some effort into your questions!" It might pay off to make that more explicit.
This text is a wonderful idea!
The formatting is broken currently for a paragraph that starts with "There are few things worse than a question which is too vague, too broad, or imprecise."
There are quite a few links pointing to nowhere (http://mathoverflow.net/turnitaround, http://mathoverflow.net/motivation) because they should look like http://mathoverflow.net/howtoask.html#turnitaround
The one little piece of advice in that page with which I disagree (somewhat emphatically :) ) is «Even better, turn your question around by giving your particular example as motivation and ask a more general question» I would suggest instead that people do ask about specific examples and, if they are they want and if this is justified, that they ask more general questions. A few reasons that come to mind: they may not be aware of what the more general question is and refrain from asking as a consequence, they may get answers for the more general question which have nothing to do with what they intended to ask (!), they may focus in one particular generalization precluding other generalizations of which they are not aware, and, finally, generality is something that should be justified (there is a difference between general nonsense and boring, useless general nonsense...)
An example: a while ago I asked about certain special measures on convex sets and I purposedly phrased the question in the least general way possible and involving as little technology as I could: I was quite sure MOers would be able to jump from a triangle to a convex set by themselves, and if they knew about it, see the connection with the Radon transform, and so on.
Maybe as a section title instead of "Turn it around," you could use something like "Choose context carefully" or "Choose context so that it will be of broad interest"?
While over explaining what is a good question is surely a bad idea, a line discouraging unmotivated "are there generalizations of X which relate to Y?" questions, as in this example, would be useful, I think :)
Formatting: I suggest ### instead of ##, example:
Look at how well this looks here and also this works in the question.
And this is the text which looks too small compared to the title.
Thanks for all the great feedback! I've just made some changes.
@Jonas: it looks like you can't, or rather couldn't. I've just changed a setting on this forum so you should now be able to delete your own comments.
I've added links to the "how to ask" page from the FAQ.
@gilkalai: Unfortunately, an upvote does not stand for "this question is useful and clear." There are many forces to explain why many questions that violate the guidelines that get lots of upvotes:
I think these problems will always be with us, but that doesn't mean that we shouldn't push for people to ask better, clearer questions. If anything, we should push for people to change their voting habits.
Where did you feel like the language was too strong?
@ Igor —
It's progress that the Management-Ownership of the site is beginning to clarify its values. Yes, there's always a Management-Ownership — it resides in the Power to flip the switch off any time the arc of state deviates too far from its owned or unowned objectives — that's just the way the Internet was designed, no matter what mumbo-jumbo anyone gives you about “we are not a hierophancy”.
The local definition of “Question Worth Asking” (QWA) appears to be converging toward “Question With Immediate Answer” (QWIA), so long as it's not too “local”, the definition of “local” being somewhat out of site, out of mind right now. I don't think the rest of the world would agree that QWA = QWIA, but we are only talking about site-local definitions here.
At any rate, it's still a kind of progress …
@ Qiaochu Yuan
Sure the "Management-Ownership", as Jon put it, will make the wise and ideologically correct decision on the subject of this discussion, which I respect in advance. But can I ask you: why exactly do you want to push me, with my broad questions, out of this forum into some obscure "blogs"?
Again @ Qiaochu, about fostering the ability to think and communicate clearly:
everything is clear in the already finished parts of mathematics. So, why not foster the ability to do at least something where everything is still unclear, vague and evasive? This is much trickier of course, going off the beaten track...
@ plclark
Specifically, I asked my question http://mathoverflow.net/questions/10700/self-similar-matrices because I needed any hint on any type of self-similar matrices or whatever resembles that in any manner.
My experience in Yang-Baxter equation and related issues strongly suggests that whatever looks at first sight vaguely similar, in some 5 years or so becomes just the same thing.
Regarding one liners: I think the goal is to write in a way which makes it easy for a reader to determine whether or not they have relevant knowledge. The first two examples in buzzard's post strike me as fine; I am quite certain I don't know the answer to the first, and that I could work out the answer to the second but an expert could do it faster. I am also quite confident that I don't know the answer to the question fedja points out.
I complained about buzzard's third example because I do know a lot about maps GL_n(K) ---> GL_N(L) when L is R or C, K is R or C and N is finite and I have some knowledge about the case K=Q_p, L=C, N finite. I couldn't tell whether or not this was the knowledge the original poster wanted. (As it turned out, "admissible" was the clue that it was not. Perhaps it is my fault that I wasn't sharp enough to pick up on that.)
If I were to try to turn this into rules for inexperienced posters, I would say "link or cite your definitions" and "if you know your question lies in a particular field, indicate it." For example, I have a question which starts out something like: "This is a question about quivers with potential in the sense of Derksen, Weyman and Zelevinsky..."
@buzzard: Yes, except it's senseless to repeat information in the text that is already contained in the tags. The text needs to be more specific than the tags.
We ask questions because we want to know the answers and because we think others will also would like to know. The most important property of a question (in math overflow or elsewhere) is that it reflects what you want to ask. Yes, you have to give thought to the question and to try to present it in an interesting, clear and useful way (this does take some creativity, at times).
The questions "what is the right definition of a ring" and "why are functional equation important" are very good questions and so are the questions "why is the exterior algebra so ubiqutous" and "interesting applications of the Pigeon-hole principle". In the page how to ask a good question these four questions would be in the column of being too vague/board. The page advices to ask something like: "Does the pigeon-hole principle can be used to prove Y?" I disagree with such a general advice. It depends what the person asking the question really want to know. If what he really wants to learn about interesting applications of the pigeon hole principle this is reasonable, can be of interest to others, and this is precisely what he should ask.
One important aspect that is missing is that we should strongly encourage questions about mathematics (pure math, applied math, connections to other sciences and academic areas, even teaching/presenting math and math-history) and not encourage (but allow nevertheless within limits) questions around math; namely questions "of interest to mathematicians" which are not questions in mathematics.
Dear Anton: Being interesting is impornat for a question (or answer) in order to be useful and in order to be clear. Strong language: "criminally undervoted", "Such questions (imprecise) are as bad as (or worse than) homework questions; they waste everybody's time." " There are few things worse than a question which is too vague, too broad, or imprecise. Not only is it lazy to ask a vague or imprecise question, it's also rude. You're essentially asking somebody to do the work of figuring out what you want to ask, and then answer it..". However my main problem with the two last quotes, is not just the strong language, I simply disagree with the content. (But I would avoid such language anyway.)
@Igor: regarding your question... "Vague" ca be very good when it is good. But IMO in that question "vague" means without any context or even a definition. I've stared at the two links you provided, and after some work I was barely able to see that you are one of the authors. By no means do I know everything there is to know, but I do have a non-negligible general mathematical culture and after having read quite a few times your question and looked at the pictures in the papers, I still have no idea what it is about! (And I am still as intrigued as I initially was!)
One good way to evaluate questions is to look at the answers they get. This criterion is independent of whatever form of evilness the Management-Ownership has chosen to submit us to: presumably you wanted answers to your question.... Yet the question has not gotten any.
@Igor Korepanov: sorry that section makes you sad, but I stand by it. It's fine to think about broad questions, but when you come to a question and answer site, you should ask a question that has an answer. To do otherwise is like trying to use a hammer to get a screw into a piece of wood. If you have a broad or vague question you want to discuss, (a) you should use a different tool (a discussion forum or a blog rather than a Q&A site), and (b) I still think it's a good idea to figure out what your goal in asking it is. It's OK if Math Overflow doesn't touch every part of your mathematical activities; it's just meant to be a tool to use when that tool is appropriate.
More generally, I'd like to point out that crowd-sourcing (which is what MO is) works well when you have well-defined tasks for people to do and works poorly for large projects starting from scratch. Successful "open source" projects always have one (or a few) people who bring the project to a point where it is reasonable for others to make useful specific contributions. When you ask a question on MO, you have to be that person who brings the question to a point where others can meaningfully contribute to it. Asking somebody else to do it is inappropriate.
Re one liners: I hope the background and motivation section makes it pretty clear what the purpose of providing background and motivation is. Sometimes it's not worth it. Maybe everybody should already know what's going on, or if they don't then it would be too much trouble to bring them up to speed. As the final note at the end of the page says, it's okay to violate the guidelines if it's a conscious decision and you're doing it for a good reason.
@buzzard (re "You have to know it's nt.number-theory (or whatever it is) and not number-theory or number theory or numbertheory or whatever."): once you type in "numb" you should get a drop-down menu with the tags nt.number-theory, analytic-number-theory, number-fields, algebraic-number-theory, along with a number next to each indicating how common each tag is. On top of that (just below it rather) there's an explanation that you should use at least one arXiv tag and a list of what all the arXiv tags are. The site tries to make it easy to tag, but if newbies still don't tag, I guess old hands have to step in. If somebody is such a bad communicator that he asks a question that nobody else can figure out how to tag, I don't think adding a line to the "how to ask" page is going to help that person; they're not putting enough effort into communicating to ever be interested in reading that page.
@gilkalai: Just because it is possible to ask a good question that doesn't conform to all of the guidelines does not mean that the guidelines are bad (see the note at the end of the "how to ask" page). But I would argue that the questions you refer to do follow the guidelines for being specific questions. Though they are somewhat philosophical questions, in each case the body of the question lays out specifically what the asker is looking for. I can tell by reading an answer that it is an answer to the question the person is asking. That is, the person answering the question doesn't have to guess what the question is, or to answer several possible interpretations of the question.
Re strong language: I'm not convinced that the language is too strong (but maybe I can be). Each of those quotes is at the beginning of a paragraph which goes on to explain the criticism. It should be clear that those criticisms apply to questions that don't "have answers" (in the sense I described in the previous paragraph). Even [big-list] and [soft-question] questions really should have a focus to them. Even if they don't have a single answer, it should be clear what constitutes an answer. The fundamental examples question is extremely broad, but it isn't vague. It's clear what constitutes an answer, and an expert answering the question is not struck with a feeling of "how do I even begin?" upon reading it.
@ Anton -
I like your energetic way of writing, although I cannot guess what you meant by hammer and screw. Thank you anyhow; perhaps your site was indeed a wrong place to ask serious questions. Still, my question did already receive the very clear answer, in the negative (remember that it began with "Does anyone know... ?"). So I am already grateful, and my wishes of success to your site!
@Igor: the correct "tool" for questions like yours, I believe, is talking to other people in person. mathoverflow is a high-latency place compared to an actual conversation, and no one wants to put several minutes into composing an answer which probably wasn't what the asker was looking for anyways. If the details of a question exist only in your head, then you need to give people answering your question more direct access to them!
@Igor: I do not think "serious" means what you think it means.
@ rwbarton -
"If the details of a question exist only in your head" - no, that question did not have any hidden details. It was exactly as it was formulated: does anybody know anything like that.
And of course I am very serious. This site was recommended to me (and other members of some other forum) by Greg Kuperberg, who is of course a serious person, so it is indeed very seriously sad for me to find this rather totalitarian tendency of suppressing creative questions here. It is really serious!