What topics can I ask about here?
If your question is not specifically on-topic for MathOverflow, it may be on topic for another Stack Exchange site. If no site currently exists that will accept your question, you may commit to or propose a new site at Area 51, the place where new Stack Exchange communities are democratically created.
What kind of questions can I ask here?
MathOverflow's primary goal is for users to ask and answer mathematical questions related to current research in mathematics. These can be questions that arise when you are working on or preparing to work on a mathematical research-problem, but they also may be questions that you come across when you are reading scholarly journals or advanced graduate level books in mathematics. A question does not have to be about new mathematics. A typical example is, "Can this hypothesis in that theorem be relaxed in this way?"
The site works best for well-defined questions: math questions that actually have a specific answer. You'll notice that there is the occasional question making a list of something, asking about the workings of the mathematical community, or something else which isn't really a math question. Such questions can be helpful to the community, but it is extremely tricky to ask them in a way that produces a useful response. So if you're new to the site, we suggest you stick to asking precise math questions until you learn about the quirks of the community and the strengths of the medium. If you have a very broad question (like "Please explain topic X"), try searching Google, Wikipedia, nLab, or looking for survey articles on the arXiv.
Please look around to see if your question has already been asked (and maybe even answered!). If you do post a question that was asked here before, don't worry; somebody will give you a link and close your question as duplicate.
The best way to get great answers to your question is to write a great question. To help you do that, we've written down some guidelines on How to ask a good MathOverflow question.
What kind of questions should I not ask here?
There are several broad categories of questions that should not be asked on MathOverflow. If your question is closed or put on hold, it's probably because it fell into one of these categories. Note that questions are first marked as [On hold], and then a few days later marked as [Closed]. If your question is closed, please don't take this to mean that you are not welcome on the site, or think that this will be held against you in the future. A lot of active users have had questions closed at one point or another. It is possible to edit a question which has been marked as [On hold], to make it more appropriate for MathOverflow, and then to request, either in the comments or on meta.mathoverflow.net, for the question to be reopened. Consider, however, that often it's best to cut losses and simply ask a new, better question, especially if substantial changes are needed.
- MathOverflow is not for homework help. Try to make sure your question is of interest to at least one other mathematician. Though there are no hard and fast rules about who may post here, the intended audience is professional mathematicians, mathematics graduate students, and undergraduates involved in research. If your question is closed as "off topic," it might be because it was too elementary. This doesn't mean that your question is "bad," just that MathOverflow isn't the right place for it. But there are lots of other math Q&A sites where your question might fit right in, and we have a list of such sites. If your question was closed with the message "Questions about homework are generally off-topic." it was probably an explicit homework problem (or looked like one). MathOverflow is not the right place for such questions; they send the message that you want somebody else to do your work for you, and you're not even willing to ask it in a general form. Be careful if you're asking a question that merely looks like it could be a homework question --- be sure to explain your motivation for the question, and perhaps explaining what progress you've made so far. If you are asking a question related to a problem from a graduate course, please be sure that is appropriately interesting and relevant to the site, that you have permission from the instructor, and provide an appropriate citation.
- MathOverflow is not a discussion forum. As a side-effect of being very good for to-the-point questions and answers, the Stack Exchange software is bad for discussions and designed to minimize them. There's a place for discussion about mathematics, but it isn't MathOverflow. Blogs and threaded discussion forums are a more appropriate place for discussions.
MathOverflow is not an encyclopedia. MO is a site for questions that have answers. MathOverflow visitors should know how to learn new things and do mathematics on their own, but we all get stuck sometimes, and this is where MO saves the day. When you're stuck, you can come to MathOverflow and say "I'm trying to do X. How can I do that? Does this work? Does anybody have a reference?" The idea being that for an expert, it should take very little effort to understand your confusion and set you on the right path. Or maybe a non-expert has come across the same sticking point and can explain how she resolved it. MathOverflow is not the appropriate place to ask somebody to write an expository article for you. If you want somebody to write an article about some subject, you should make a stub on Wikipedia, make a query block on nLab, or make a request on PlanetMath.
- MathOverflow is not for questions about MathOverflow. Mathematicians don't come here to learn about the intricacies of this site; they come here to get answers to their questions. Let's try to help them out by not cluttering up the system with navelgazing meta-discussion. If you want to report a bug, suggest a feature, or discuss the dynamics of MathOverflow, visit our meta-discussion forum, meta.mathoverflow.net. If you're just really interested in how the underlying Stack Exchange software works, consider visiting meta.stackoverflow or meta.stackexchange, but please don't ask MathOverflow-specific there; it will annoy them.
Have a look at the tips on how to ask a good question. If your question can't be made to follow the guidelines laid out there, it's likely not a very good question for this site.
What about open problems?
MathOverflow is not the right place to ask open problems. You should post questions you're actually seriously thinking about. If you're thinking about a well-known open problem, provide some background and ask about something specific related to the problem, like "Such and such is a well-known open problem. So-and-so proposed this and that approach in the 80s. Does anybody know if this aspect of their proposal can be made to work under these circumstances?" If you want to contribute to (or view) a list of open problems, visit the Open Problem Garden.
If it turns out that a problem is equivalent to a known open problem, then the [open-problem] tag is added, and the question is converted to community wiki. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?" That way, the MO thread for the problem becomes a repository of resources related to the problem. Perhaps the answers could be organized by approach, with an outline of the basic approach, followed by a horizontal rule and a summary of what is promising about the approach and why it doesn't give a complete solution.
To join the discussion about how MathOverflow should deal with open problems, go to this meta.MO question.
Where's the rule that says I have to wear pants?
MathOverflow doesn't have formal rules about every possible thing that could come up. Roughly, you should think of this site as a large seminar. Be nice. Treat others with the same respect you'd want them to treat you. We're all here to learn together. Be honest. If you see misinformation, vote it down. Insert comments indicating what, specifically, is wrong. Even better—edit and improve the information! Provide stronger, faster, superior answers of your own! Be professional. Doing math with your colleagues is supposed to be fun; that's why you became a mathematician. But just like in a seminar, a certain minimum level of professionalism is expected. If you're unsure about whether something is appropriate, ask yourself, "would I do this in a seminar?"
We also encourage you to use your real name as your username. In your own enlightened self-interest, realize that participating in blogs, MathOverflow, the arXiv, and mathematical publishing are all forms of advertising for your "brand", even if that’s not your principal purpose (and hopefully it’s not). Since job applications require you to write your real name, you might as well use it everywhere else, too.
Using real names reminds everybody that they are corresponding with real people, and it demonstrates a certain level of personal investment in your MathOverflow identity. If you use a pseudonym and you get into some kind of trouble (e.g. fights in comment threads or spammy-looking posts), the moderators are much less likely to give you the benefit of the doubt.
How can I become a MathOverflow ninja?
Just be really awesome at asking and answering math questions. Supposing you've done that, you can have a look at the help pages. You may also want to learn about how to use the editor to effectively format your posts.
How can I help?
The best way you can help us run the site is to use it. Ask good questions. Give good answers. Vote up good questions/answers and vote down bad questions/answers. As you gain more reputation, you can help in more and more ways, like editing posts to make them clearer and voting to close inappropriate questions.