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## How to write a good MathOverflow question

Using MathOverflow 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!

### Ask a focused question that has a specific goal

It should be absolutely clear what constitutes an answer to your question. Here are some examples of vague and specific questions. For each one, ask yourself, "If I saw an answer to this question, could I confidently determine whether it tells the asker what she actually wants to know?"

 Too vague/broad Focused What can I deduce from X? Does X imply Y? Is there an example of X such that Y? What is known about the X conjecture? Is the X conjecture true in situation Y? What are all the ways to do X? Is there a way to do X other than Y (which I can't use because Z)? Tell me about elliptic curves.

Note that being specific does not mean plugging in specific numbers or otherwise making your problem look like an exercise in a book. It means asking a to-the-point question that has an answer.

### Be precise

Being precise means communicating the parameters of your question so that others know where to start answering it and know when they've given you a complete answer. Of course, the includes stating the hypotheses and goal of your problem. If you suspect that you're asking an elementary question outside of your field, you may also want to explain your background a bit. This makes it easier for the person answering your question to know what she can take for granted.

It is especially important for "soft" questions and "big list" questions to be precise. Otherwise they'll be boring and useless. "What are the best number theory books" is a bad question. Best for what? Assuming what background? A better version of the question might be "What are the best textbooks for an undergraduate number theory course?" or "After an undergraduate number theory course, what should I learn if I want to study elliptic curve cryptography?" These questions aren't great, but they make it clear what the starting point is and what the goal is.

Make sure it's clear exactly what your question is. It's extremely frustrating to read a long question which explains what the general problem is but doesn't contain an actual question. I usually resort to searching the body of the post for question marks, but it often doesn't help. After defining all your terms and motivating your question, consider visually distinguishing the final version of the question (see the formatting section).

Before asking your question, try to solve it. Search Google, Wikipedia, and nLab, check any references you can think of, and try to figure the problem out yourself (maybe even sleep on it). Doing so will help you break the problem down and understand it better. Even if you don't solve the problem, putting some work into it will often help you understand exactly what it is you're having trouble with, so you'll be able to ask a better question.

### Break it down

You may have a specific problem you're trying to solve, and you may have done your research, but the problem might be a monster. Even if it's not a monster, you'll probably benefit from trying to break the problem into smaller pieces and posting one or two of the pieces on MO. To modify a quotation of Pólya, "If there is a problem you can't solve, then there is an easier problem you can't solve: find it." You may worry that the the pieces are not interesting enough or are too specific to post on MathOverflow, but you shouldn't. It's much better to post a question that is too focused than to post a question that is too vague or too broad.

It's okay to ask several questions related to a project you're working on, but try to limit yourself to one or two per day. Rather than posting all the parts of your problem at the same time, work through them one at a time. After all, the solution to one part may completely change your plan for solving the problem.

### Consider different formulations of the question

Sometimes your question is boring, but you can often make it much more interesting by recontextualizing it.

### Provide background and motivation

Use your title to convey as much information about your question as possible. Since the tags already convey the general subject area of your question, the title should communicate the question itself as faithfully as possible. If necessary, leave out hypotheses in the title, and in the body of the question, explain why the question requires those hypotheses.

Don't be afraid to make your question title long. Titles are allowed to be anywhere from 15 to 250 characters long. 140 characters (the length of a tweet) takes up about two full lines on the home page, so try to keep it less than that. But 140 characters is a lot longer than you might think. Too many people restrict themselves to 20 character titles. They're trying not to waste your time by making you read a long title, but they end up wasting more of your time because you have to actually open the question to see if it's interesting to you.

The readability of your question can often be greatly improved if you learn to use formatting commands, especially if your question ends up being quite long. Here is an example that contains a few good uses of the formatting commands:

## Background/Motivation ##

A *doodad* is a thingumabob together with a sheaf of doohickies (which is usually called the *doo structure* on the doodad). A doodad is said to be *regular* if the sheaf of doohickies is regular. Intuitively, regularity makes a doodad "rigid" since information about the doo structure at a point can be translated into information about the doo structure at nearby points.

A *widgit* is a whatsit which is flat (in the sense that its Plotsky curvature is zero). Showing that a space has a widgit on it is extremely useful because the flatness allows you to apply Foobar's gadget construction to prove many useful results about the space.

---
Based on the above intuition, it is natural to ask if every doodad is a widgit. However, the answer is clearly no, since a widgit is always regular, but [some example] is a non-regular doodad, so it is clear that we must impose a regularity hypothesis.

> Is every regular doodad a widgit?

## Background/Motivation

A doodad is a thingumabob together with a sheaf of doohickies (which is usually called the doo structure on the doodad). A doodad is said to be regular if the sheaf of doohickies is regular. Intuitively, regularity makes a doodad "rigid" since information about the doo structure at a point can be translated into information about the doo structure at nearby points.

A widgit is a whatsit which is flat (in the sense that its Plotsky curvature is zero). Showing that a space has a widgit on it is extremely useful because the flatness allows you to apply Foobar's gadget construction to prove many useful results about the space.

Based on the above intuition, it is natural to ask if every doodad is a widgit. However, the answer is clearly no, since a widgit is always regular, but [some example] is a non-regular doodad, so it is clear that we must impose a regularity hypothesis.

Is every regular doodad a widgit?

Notice that the background/motivation is clearly labelled with a section header and clearly delimited by the horizontal rule, making it easy for experts to know what to skip or skim. The words being defined are italicized. After the nuances about why the question introduces some hypotheses, the precise final question is visually distinguished in a blockquote, making it easy to know exactly what constitutes an answer to the question.

### A final note

Not every piece of advice on this page may apply to your problem, and it may even occasionally happen that you can make your question better by violating some rule laid out on this page. As with any writing you do, it is important to know what the basic rules are. If you violate one of them, it should be a conscious choice and you should be doing it for a very good reason.