# How do I ask a good question about a topic I am not completely familiar with?

In my classes, it is easy as my professor would correct my question if it bad, or ask me to re-state it and I would learn something new if my question was good or bad. However, in this site I have found people have a little less patience when dealing with questions like this. Often, I find myself being bombarded by irrelevant things in the comments below that have nothing to do with my question, no help to help me with where the problem is and such. It is kind of demotivating seeing all this negative feedback when posting a question while it would take the same amount of time to suggest a fix on the question its self and help me understand what I am doing wrong.

• Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ? – Peter Jun 27 at 17:14
• math.stackexchange.com/questions/3276243/… – bguner Jun 27 at 17:15
• and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such. – bguner Jun 27 at 17:20
• The linked question does not contain enough context for a good answer. The purpose of this site is to help people having a particular question in a particular topic, but not for general advices that are necessarily opinion-based. – Peter Jun 27 at 17:42
• what does it need for good context? I showed effort by showing what I am currently doing. – bguner Jun 27 at 17:43
• The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post. – Micah Jun 27 at 17:51
• To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely. – Micah Jun 27 at 17:53
• you know, if someone would have commented that, I would have been able to give more detail. What does down-voting bring me other than confusion? – bguner Jun 27 at 17:59
• The question is a bit of an oxymoron. If you are “completely familiar” with a subject then what’s the point of asking questions in the first place? Of course this is a rhetorical question as a complete mastery of any given subject is arguably impossible. – Shalop Jun 27 at 21:36
• "What does down-voting bring me other than confusion?". The downvoting isn't so much for you but for the other users of the site, mainly those who answer questions. If you can't understand and work with the fact that there are other people here you probably won't have a good experience. One thing you could do is read other people's questions and see which ones get good answers, and try to model your posts on them. – JonathanZ supports MonicaC Jun 28 at 1:41
• The question you linked to, about how to write a physics paper, is simply off-topic. If you show us where to find the other question you mention, about irreducible blah-blah, people might be able to explain why it got the response it did. – David C. Ullrich Jul 9 at 16:48

First, I want to praise you for asking a good question here!

Alas, teachers and professors generally only encourage students to ask "clarification questions," and don't otherwise instruct students how to ask good questions. (Of course every teacher answers questions... a different matter.) There are even cultures in which asking any questions is discouraged because it is considered an affront to the teacher ("who didn't explain the material well enough"), or the student him/herself ("who couldn't understand what everyone else understood").

At least your teacher and you realize that some questions are good, others bad.

A meta-technique: listen closely to the questions from other students and figure out what leads to good questions.

Here are guidelines:

• Ask about extremal cases (what's the most? the least? the farthest? the closest? the biggest? the smallest?...) as appropriate to the topic.
• Ask about how one knows some fact is true (how can one prove that? what is the evidence for that?...)
• Ask about analogies (is this similar to X? to Y?...) or ask for an analogy (what other thing is this analogous to?...)
• Ask how some fact is used in the real world. If the fact is about the real world, as about the theory that gave rise to it.
• Of course if there is a particular matter or step in a teacher's explanation ask a clear, cogent clarification question.
• Always make your questions clear, relevant, and well stated. Don't ramble, or mixup lots of questions (some good, some not, some related, others not...). Avoid discursive, rambling questions ("I was thinking about triangles the other day and wondered about right triangles and realized I was taught proofs of the Pythagorean theorem, I know there are many such proofs, so I wondered if anyone knows which is the shortest proof." Instead: "What's the shortest proof of the Pythagorean theorem?")

Finally, do a YouTube search on my name, "TEDx", and "How to ask good questions" to see a video on this topic.

Good luck!

• No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books. – Peter Jun 27 at 17:31
• @Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case. – David G. Stork Jun 27 at 17:46
• A good answer (+1) – Peter Jun 27 at 17:48
• Good answer! One thing I've found to be very helpful is to see examples and counterexamples (why cases work or fail...). This could probably fall under the "extremal cases" point (understanding the limits of a theorem or given idea). Another is to find analogies between proofs (interesting steps in two proofs that work in similar ways). Unfamiliar poofs can often be understood better this way, and in any case, it's nice (and even enlightening) to think about connections between seemingly-unrelated theorems. – Aaron Jul 8 at 10:12

None of these are meant to directly relate to your own questions, but they're things I think about both when asking and answering questions online (although I can always do better).

## Understand the social contract

This is a tricky one to express clearly, partially because it depends a lot on where you're asking the question. In some places, like this site, the social contract may be expressly written - there are guidelines in the help center that tell you about things like questions to avoid, or what to do if no-one answers your question.

In other contexts, you may have to interpret the social contract based on observation, questioning and/or experiment - you try asking a question in class, and your professor tells you to make an appointment to discuss it; or you notice that there's a green button on each desk and the professor somehow knows who wants to ask a question, you press the button and get called on so you realise it's a paging system.

## Be humble

You've come to ask a question. That means that whoever answers it will, hopefully, know more about the subject than you. Or at least they know something about the subject that you don't, namely the answer to your question.

In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points. The person answering the question doesn't normally gain much of real value by giving you the answer, so be polite when they answer and take their response in good faith - particularly noting some of the things I write later about cases where you might have gotten something wrong or expressed things unclearly, don't get annoyed at them for trying to understand your question better.

Additionally, if you're asking a question that relates to a more esoteric aspect of mathematical theory, don't expect an answer immediately (or possibly at all) - if there's only one person in the world who knows anything about doubly-invertible homeopathic hyperfields, what even are the odds that they frequent this site? (Actually, probably quite high if they're the kind of person who compulsively searches for things where they can jump in and show off their expertise, but you can't always count on it.)

## Provide meaningful context

There are a few reasons why context is important to your question

Think about the mathematical rules you learned in school, and how they evolved. At some point you were probably told "You can't subtract a bigger number from a smaller one", but then a few years later got told about negative numbers. Of course "You can't take the square root of a negative number", until you get introduced to the imaginary numbers and the complex plane. And while back in your formative years the question "Why is $$1+1=2$$ and $$1 \times 1 = 1$$?" gets little more than "Because that's the rule", several decades later you may be introduced to binary numbers, field theory, or the set construction of arithmetic (or maybe just the classic $$1 + 1 =$$.

By providing sufficient context for your question, people can answer it within that context, so you get the answer you actually need.

### Identifying mistaken or alternative assumptions

Think about the question "Why is $$\pi = \frac{22}{7}$$?". We know it's not actually true, but it's an approximation that is used often enough in schools that some people might reasonably think that it is. And so, while there's no answer to the question (since it's built on a false premise), if we know why the asker thinks that it's true we can help show them the truth, and possibly discuss the topic of how these approximations come about and what a good approximation is.

This happens a lot in tech support type forums, but it can also happen in mathematics. You're trying to do X, and you've worked out that it looks like you can use Y to do so, but you keep hitting problem Z. So you go to the forum, and you say "Why doesn't Z work?". Sometimes, the answer is because Z never works, especially when you try to use it for X, because Y is the wrong tool for the problem.

If you come along and say "I'm trying to do X. I looked at approach Y, but keep hitting problem Z. Is there a way to get around Z or is there maybe a better approach to X?" then it's a lot more likely that you'll actually get a working solution to X, which is what you really wanted in the first place.

### Demonstrating effort

This relates a little bit to the whole "People are doing this out of good will and/or a desire to show off knowledge" thing - we often want to reward people who have tried to figure the answer out for themselves first. Sometimes this is because answering no-effort questions breeds more no-effort questions and drowns out the actually interesting ones. Sometimes it comes from a belief that trying to solve a problem for yourself gives you a better understanding than spoon-feeding you the answer, and I think a lot of people here think of ourselves as being educators to some extent.

• "In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points." Don't underestimate boredom as a factor. – Peter Taylor Jul 2 at 15:22
• True. Or putting off doing something else you're supposed to be doing. – ConMan Jul 2 at 23:11
• I'd like to add to the second point that another reason why I answer questions is because that helps me revise some contents that I might otherwise forget if I haven't been using them lately. There are also times when I'm new to the subject but I'm able to understand the question after reading about it and come up with a solution. So I learn too when I answer questions. – Javi Jul 3 at 12:46

I haven’t looked back over your previous questions, so this may not be one of your vices. But I will say it all the same because some other reader may benefit.

DO NOT ASK PEOPLE TO DO THINGS

Ask people to help you do something, and they will be delighted to help, because they know that at the end of it you will know more than you did, all thanks to them. Help them help you. Show them what you have tried. Even ask them what technique would be best for solving this problem or that one. But don’t say “Solve it for me!”. It makes people feel murderous.

And (again I don’t know whether you fall into this trap, and probably you don’t) - do read your question and see if it makes sense to someone far away who can’t see you and can’t see what you are doing. It is tragic to see people asking how to find the value of $$x$$ when the problem they have described doesn’t have an $$x$$ in it anywhere!

And do be encouraged by the answers to this question to ask more questions in future.

This is by no means a full answer to your question, but I've asked a lot of bad questions in my time, so I have a pretty clear idea of what winds people up and leads to negative feedback:

• failure to demonstrate any effort on one's own part
• multiple misconceptions in the same question
• being unclear what you're asking for
• anything that wastes people's time (especially convoluted questions containing any of the above)