How to ask a good question.

Question

How to ask a good question.

This thread has advice on the following aspects of writing a good question on this site. Each item in this list links to an answer below about that specific aspect of question writing.

• Provide context, $\,$ include the source and motivation for your question, $\,$ and avoid "no-clue" questions
• Choose a good title
• Formatting and writing
• Tag your question correctly
• Mathematical typesetting: MathJax
• Pare question to its basics
• If the question you want to ask appeared in a Math contest, or a Contest training
• Use Approach0 to detect if your question has already been asked on this site
• Avoid confusing abbreviations and notation
• Ask one question per post

Answer 1

Provide Context

Context matters. A question can sometimes be answered in one sentence when the discussion is between two experts familiar with each other's background, while the same question may take many paragraphs of detailed computation when being shown to an undergraduate student. By providing a context you help the potential responders to your question give you the best help you need.

Some different ways you can add context to your question

• Include your work

  You have a question, and if you post it here, you've probably attempted, and failed, to solve it yourself. It is much easier for others to judge the most appropriate "level" for an answer to your question if you provide these attempts. So you'll receive answers better suited to your specific needs.

  Including your work also shows to the community that you're not using this website as an answer machine -- as such, your question will be received more positively.

  A further benefit of writing down precisely what you've tried is that, in the process of doing so, you will very likely spot your error and solve your problem yourself. Bonus!

• You can provide some motivation to your question.

  Instead of just asking us to find the roots of an equation, tell us where the equation comes from. This is especially the case when your equation comes from models of the physical worlds: those kinds of intuition are great guiding principles for formulating an answer.

• You can tell us where the question comes from.

  If your question comes from studying a textbook, let us know which book. This way the answers can be phrased in a manner and in a notation more familiar to you. Exposition varies from one book to another, affecting which theorems are appropriate to cite in answers, and which definitions you are starting from (see below).

• Indicate your own background

  In order to address your question in a useful manner, we need to be able to estimate your background to some degree. (Briefly) Indicate your familiarity with the subject matter so that the answerers have an easier job assessing the audience, and can adjust the level of their answer accordingly.

• Give full references.

  If you run across a question when reading a scientific paper, be sure to link to that paper using its doi link, or provide a proper bibliographic information. A question that reads "A theorem of Smith says that Widget X is a type of Gadget Y, but I don't see why Property Z must hold" is likely not going to be very comprehensible to other users without telling us which Smith said what when and where.

• Give definitions.

  Something that you are familiar with may not be so to another user. One should of course use one's best judgment in deciding what objects are sufficiently well-known to not need defining. But when in doubt, either provide the definition or provide a link to a resource that gives the definitions.

  Another case where this can be useful is when the same mathematical object can be defined in many ways, and the answer to your question may depend on the precise definitions used. For example, Widget X may be defined by Author A to satisfy property T. Practically everyone else may prefer to define it as satisfying property S. Showing the equivalence between property T and property S may happen to be one of the harder but lesser known theorems in the past fifty years. If you ask the question, after reading a treatise by Author A, that "Why is property S true for Widget X?"; the common answer "duh, that's by definition" will probably not be very useful to you.

Answer 2

Avoid "no clue" questions

Too many questions begin or end with "I don't even know how to begin with this problem". While this may be true (you may genuinely have no idea how to approach the problem), it is still not a valid reason to limit your post to the statement of the problem without any mention of your own thoughts. Such questions will most of the time be rejected by the community, which represents a significant waste of time - including for yourself - since the removal of poorly documented questions is not a fully automated process.

There are plenty of ways to get started on a problem when one has "no clue":

• Write down the definition of the keywords of the problem

This allows you to make sure that you understand them. Use examples ($\star$) when applicable.

Tip: if you realise that you actually don't know the definition of one or several keywords, then you are probably asking the wrong question. However, you now know where to start!

• If the problem involves formal computations, try with specific settings ($\star$) first

If you are asked to prove that something holds for any value of $n\in \Bbb N$, see if you could prove it when $n=1, 2$ or $3$. Doing that you may observe a repeating pattern or grounds for proof by induction.

If the problem involves an arbitrary orthogonal matrix $M$, replace it with your favourite orthogonal matrix. If you realise that you can't write one down, this means that you are not fully at ease with the notions involved, and what's more you know where to start: read about orthogonal matrices.

• If the problem involves large numbers, try with lower numbers first ($\star$)

You are being asked to simplify $7^{9999}\bmod 13$. What about $7^{20}\bmod 13$? Or $7^{20}\bmod 3$? What will happen if you multiply that by $7$, over and over? Take it down to something that you can do by hand, and look for a pattern. Having done that, if you can't find the pattern, that's fine, but now you have some material to include in your post and make it valuable.

• Write down what you know that seems related to the problem

Any relevant theorem not in that list will be spotted right away and other users will point it out easily.

($\star$) you have to make them up yourself, and that very process is excellent to make progress in the way you think in general: what is a good, representative example in a given situation? A good example is one that is not too far off from the general case, one that gives a good idea of what is going on. Knowing your definitions also means knowing one or two good examples.

Answer 3

A good title

The title of a question is the first thing people see. Like headings in newspapers, book, song and album titles, their importance is not to be underestimated -- the presence of a good, descriptive title for your question often greatly improves the exposure (and hence the amount and quality of answers) it gets. To ensure maximal descriptiveness of your question's title, review it before posting and ensure that it (still) adequately describes your question's content.

How to choose a good title

• Make your title your question

  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.

• MathJax works in titles

  Titles have MathJax support. This means you can e.g. include the integral your question is about in the title, and do not have to resort to vague descriptions like "difficult integral". In your use of MathJax, please adhere to the community guidelines for MathJax in titles. Most importantly, keep the vertical space your title uses to a minimum, and be sure to include at least some plain words.

• Don't be afraid to make the title long

  Titles are allowed to be anywhere from 15 to 150 characters long. 140 characters (the length of a tweet) of plain text take 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.

• Make your title interesting for others

  Mathematics.SE is designed to be a repository of good mathematical questions and answers. Thus, there is no need to refer to your personal situation in the title. Make your title a question of universal value. For example, the title Help me solve $a^2+b^2=c^2$ for my exam preparation is very specific to your personal situation. Deriving the formula for Pythagorean triples would be a more universal, better title for the same question.

• Your question should be clear without the title

  After the title has drawn someone's attention to the question by giving a good description, its purpose is done. The title is not the first sentence of your question, so make sure that the question body does not rely on specific information in the title.

Other Tips

When you are posting a question, write your title first. The system will then suggest possible duplicates: take a look at them, opening links in another tab. If none of those are actual duplicates, write out the body of your question. Then go back and put in a better title for the body that you wrote. (From Robert Harvey)

Answer 4

Mathematical typesetting using MathJax

Mathematics.SE uses the emulation engine MathJax for providing $\TeX$-like mathematical typesetting. This means that you can use mathematical notation in your questions in a visually appealing way.

How can I use MathJax?

• Basic information: This gives a quick start for people familiar with the $\TeX$-family of markup languages.
• Specific information: Not every $\LaTeX$ command is supported in MathJax. For extensive documentation of commonly used constructs, see here. That thread is also good for quickly getting to grips with MathJax if you're new to $\TeX$-like typesetting.
• Mathematical expressions in titles: The title of your question supports MathJax as well, so use it as deemed fit! However, please adhere to the specific community guidelines for their use in titles.

Answer 5

Tagging

Tags are a way to help us organize posts on this website. People also use them to locate the questions they will find the most interesting. Thus, good tagging helps to attract the best potential answerers to your question.

How do you select the best tags for your question

• Tags are about content. Tags (except "meta" tags, see below) are supposed to refer to the content of your question, and not so much to the context in which you encountered them (but please, do add context). For example, if you have trouble solving a polynomial equation, use algebra-precalculus, even if you encountered it while solving an optimization problem.

• Use many tags. You can add up to five tags to your question. A combination of tags gives more information about the question, and so increases the usefulness of the tagging process.

• Tag Wikis. Not sure if a tag fits? Move your mouse over the tag name to see its tag wiki excerpt. Read through it to see if the tag actually fits your question. Quite often the excerpts will also contain suggestions to other, more suitable tags.

• Be wary of the meta tags. Meta tags like soft-question and big-list do not give information about the mathematics in the question. They should be used as assistance to the tags describing content, not be the main, or only, tag to your question.

Answer 6

Formatting and writing

This is not some random internet forum. We strive for well-composed questions and answers of lasting value. Keep in mind that your question can be of interest to others as well.

• Use proper English to the best of your ability

  The use of proper spelling, grammar and punctuation makes your question easier to understand, more appealing, and more likely to attract knowledgeable experts to answer your question. If English is not your first language and you are concerned that you will be unable to express your question clearly in English, it might be better to post your question in your native language; it is likely that another user will be able to translate it for you.

• Make your actual question stand out

  If your question contains a lot of context, your work, or background information, others may find it difficult to figure out what exactly your question is. You can use bold text (**bold text**) or a heading “My question” (# My question in a separate line), or a horizontal line (--- preceded by an empty line) to make your question easily identifiable. See also MarkDown formatting below.

• Make your question visible, searchable, accessible

  Don't force someone to click on an external link just to see or understand your question, it should be immediately visible after clicking on your title. The key parts of your question should not be in an embedded image such as a photo/screenshot/etc., such images are not searchable, they are not accessible to those using screen readers, and they don't show up in question summaries. See here for further information regarding accessibility.

• Use paragraphs

  Nobody likes to read a densely packed monolith of text. You can enter a blank line in the editor to start a new paragraph at natural places. Add them in a natural frequency that makes for a pleasant read.

• MarkDown formatting

  Markdown is the markup language used to format posts on this site. Most frequently used things are italics and bold, which you can achieve using *italics* and **bold**. To include links you can use this syntax: [Markdown](http://en.wikipedia.org/wiki/Markdown), which gives you Markdown. For more details and other stuff you can do using Markdown see help.

Answer 7

Pare question to its basics

Pare your problem down to the minimum core problem. Instead of asking for

$$\frac{\sin 2 k \sqrt{3 + q^3}}{b! (b-2)!} \int\limits_{x=0}^{\infty} \frac{e^{-x^2/(2 \sigma^2)} \cos \sqrt{3 + \sqrt{y}}}{\sqrt[3]{2 - 1/g}}\ dx$$

for constant $k$, $b$, $\sigma$, $y$, and $g$, eliminate all constants and ask about

$$\int\limits_{x=0}^\infty e^{-x^2/(2 \sigma^2)}\ dx .$$

Actually, if you have the requisite mathematical skills, you'll scale variables even further and ask about:

$$\int\limits_{x=0}^\infty e^{-x^2/2}\ dx .$$

Making such simplifications will garner more assistance, and may even help you solve the problem on your own.

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A small pet peeve: Avoid the useless throat clearing that wastes everyone's time.

Don't write:

"Hi everybody!! I really didn't like math very much until I took a course on trigonometry from a great teacher back home in Belgium, Mr. Leboeuf, and he would always give us little problems at the end of class for us to think about over lunch, even though they weren't part of our homework. (He also had the coolest poster about Mandelbrot sets on his wall.) So, like, I think I came across a problem that reminded me of one of his. I can't figure it out, but I thought I'd post it here to see if one of you math geniuses can help:

Two rival schools, Fairmont High School and Columbia Preparatory School, each want to send a team of math students to the annual math competition that is held in July. Mr. Jones (the coach of Fairmont High's team) and Mrs. Richardson (the coach of Columbia's team) each have to choose five contestants from 10 finalists in each school. I would really like to know how many possible distinct pairings could result from Mr. Jones' and Mrs. Richardson's choices.

I'm really stuck. I know I should be able to solve it, but I keep getting tripped up. Thanks for all your help!!!!!!"

Instead write (for the whole question):

How many distinct sets of 10 elements can be made when five must come from one set of 10 unique elements, and the remaining five must come from another set of 10 unique elements?

Of course, then add your attempts at a solution and your particular difficulties.

Another pet peeve: Don't start a question with the English word "So". It is never ever needed.

Another pet peeve: Please use the simplest, non-confusing notation possible. If you want to talk about a constant $\theta_{ij}$, instead use $a$ (so long as it doesn't conflict with other terms). Along this line, don't use $d$ as a variable in calculus, because it becomes confused with the differential operator, e.g., $dy$.

Answer 8

If the question you want to ask appeared in a

Math contest (or contest training), then

• You should make it clear that the question is from a contest. Adding the contest-math tag is a good way of achieving that, but I recommend that you also make this explicit in either the question body or the title, because this affects how many users approach the question (and some of them may neglect to check the list of tags).
• You absolutely must give the source of the question. This is to comply with our policy on questions from on-going contests. We will not help someone cheat in a current contest, and this is the simplest way to achieve that goal.
• The other suggestions described in this thread also apply to contest questions. If you are preparing for a contest you can undoubtedly already solve simpler problems. Some thoughts about how to best turn that into context, necessary to make your question stand its ground, are being collected here. For example, you have undoubtedly been told to try a simpler version first when facing a tough contest question. Including the fruits of such an attempt improves your question, and protects it from attracting negative attention. Prove to us that you are not like a clueless homework help seeker!

Answer 9

Include source / motivation for your question

According to recent discussions on this Meta post-Is it a good idea to include source from where a question is taken? , and by the responses of many experienced users we have decided to make it into a good practice to include the source or motivation of a question.

For eg. in contest questions, citing the source definitely helps future readers, makes the thing more professional and guarantees authenticity of the question which prevents wastage of time of answerers as is seen some times due to incorrect "prove that" type questions.

Also, if someone extends theirs thoughts on something one read in a paper etc. including the source helps to understand the motivation of the user and makes it easier for others to comprehend and respond to the question appropriately. This makes the whole system more integrated, systematic and connected.

It is encouraged to willing users to help spread this idea in the main site and at times politely comment below applicable questions requesting askers to include source. Maybe like this-

This looks like a problem you have collected from / inspired by some source. According to recent discussions in Meta, we are looking forward to including sources for all applicable questions. Can you provide the source by editing the question?Refer-Is it a good idea to include source from where a question is taken?

Answer 10

Use Approach0

Use Approach0 to search for any possible duplicates of your question before asking.

We get hundreds of questions every day. If your question is about arithmetic, geometry, algebra-precalculus, combinatorics, probability / statistics (first-year university or below), calculus (first-year university or below, such as Calculus I and II), or from a well-known textbook (Rudin etc.), there is a high probability that your question has already been answered on this site.

This allows us to answer the most important questions: questions that do not have answers anywhere else. Why ask a new question, when you can get your answer without waiting for a reply? You save time, and we also benefit.

Even if you have searched for any duplicates on this site, the search engine here was not designed to handle MathJax expressions. You can search for questions which have the same MathJax expression as your question, which will give you much more relevant results.

If both the search function here and Approach0 do not work, check the list of generalisations of common questions, which covers limits, calculus, summations, probability/combinatorics, number theory etc. and proofs by induction. If the result is well-known, your question is most likely in here as well.

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If your question is related to inequalities, Approach0 also shows you results from AoPS. In most cases, your answer will already be there.

Answer 11

Avoid confusing abbreviations and notation

Try to limit the usage of abbreviations that are uncommon restricted to certain contexts, or may cause confusion. For example, not every user of the forum may know that CNN stands for Convolutional Neural Network, but could still be able to answer your question if you explained. It also removes ambiguity as those same initials could stand for something else. Another case is the usage of "iff" that, on a quick read, could be mistaken with "if", thus dramatically changing the perceived meaning of the question.

Something similar applies to notation. If you are going to use mathematical symbols that are rare, or have a different meaning in other contexts, please explain what they mean in your particular post. There is no shame in using plain English to explain mathematical concepts. Math notation should be a tool rather than a nuisance.

Answer 12

One question per post

Limit yourself to one question per post (according to the general StackExchange guidelines).

Maybe (but this should be an exception rather than a rule) two closely related questions with the second question a variation of the first one. For instance:

Question 1. Is it true that every topological manifold admits a triangulation?

Question 2. At least, is it true that every 2-dimensional topological manifold admits a triangulation?

Answer 13

Avoid non-descriptive/non-helpul titles

     Bad Example: Help me! $$$$ This is bad because it doesn't specify what specifically you need help with ( it might as well be going to the bathroom), second it doesn't take away effort of checking tags.

Tell us if you know the answer       This ties into other points, like it might help indicate the problem is with understanding a method of proof.

Add in background information   $$$$    Context: in what bigger problem did this come up? Terms change meaning, depending on scientific field for example.   $$$$    Knowledge: what do we have to work with, struggling might have to do with bad information, or lack of required knowledge.  $$$$    Source: is it homework, a thesis ( goes to context), a contest question, from a textbook, random thought, etc.

Tag with proper tags

Getting an expert in combinatorics, alert, to a modular-arithmetic question, waste both your time, and theirs.

Try to avoid multiple questions in one

They might be unrelated, generalizing each other, duplicates of other questions, dependent on each other, etc.

Meet answerers halfway

Answerers can get downvoted for answering poorly asked questions, duplicates, or questions with little effort shown.

Avoid opinion questions

Math is logical, opinions don't really matter that much.

Tell us where you are struggling

This tells us what to focus on, it shows what actually needs answering, and what is understood.

Ask a definite question

Answers may change if the answer to your question can change.

Try avoiding duplicates

This clogs this site, Google, and generally makes it hard to navigate.

Try asking a general question

Most strict number questions, have general procedures, that don't change much if the numbers change.

Answer 14

Check Small Examples

If you have a number theory question, on whether a certain property holds for some numbers, run a computer search to make sure that there are no trivial counter examples to your statement.

As Sarvesh says, If you're running any code pertaining to a question, please post the code as well, so that others can run it or modify it and obtain other patterns". This is extremely helpful because others may have higher computational power or have some hypothesis to test for which having the source code would be really helpful. Also, posting the code is an explicit demonstration of effort, unlike writing “I wrote some code and it spat out 3,17,1221 3 , 17 , 1221 , I don't see a pattern?”