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Where should I put questions asked purely out of curiosity, do they go in Meta, or in MSE proper? I'm talking about the type of questions having absolutely no bearing (sp?) on one's work, and which are clearly not homework questions. In my case for example, I might one day ask myself "what is known about the number of subgroups $S_n$ for a given $n$". I think it would be quite clear that it's not homework; on the other hand it's the kind of question I couldn't possibly investigate on my own, "I've tried such and such but can't find an answer, what is it?"

So the question is, where do I ask such a question, if anywhere?

Also, what about "stupid" questions? Suppose I've forgotten that subgroups divide the order of their supergroup, I'm kind of sure it's so but I need to know for sure, but after spending hours on trying to find the result in my books I still can't find it. Is it then ok to ask whether it's true, "is it indeed a fact that yada yada", a yes or no question?

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    $\begingroup$ They are mathematical questions, so they belong in MSE. (OT: The first example you give is interesting.) $\endgroup$ – Andrés E. Caicedo Jul 17 '13 at 21:17
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    $\begingroup$ I think you read too many discussions of PSQs and "showing one's work"... $\endgroup$ – 40 votes Jul 17 '13 at 21:36
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    $\begingroup$ I never read Meta nor do I have a clue what a PSQ is. $\endgroup$ – Erik Vesterlund Jul 17 '13 at 23:17
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    $\begingroup$ In reference to the above: A PSQ is a "problem statement question," and is a pretty controversial topic on meta... my best advice is to ignore it--you have no problem even getting close to that issue with your questions, and focusing on it too much is detrimental, methinks. :) $\endgroup$ – apnorton Jul 18 '13 at 2:38
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    $\begingroup$ For questions of the form "I seem to recall this being true. Is it, and what is a proof/reference?" I would recommend first trying in chat (or googling as suggested by Pete Clark in his answer). $\endgroup$ – Tobias Kildetoft Jul 18 '13 at 6:25
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    $\begingroup$ math.stackexchange.com/questions/76176/… is the example question $\endgroup$ – Jack Schmidt Jul 18 '13 at 14:51
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    $\begingroup$ BTW did you finally asked the question? $\endgroup$ – leo Jul 19 '13 at 0:02
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I think most of the heavy users of the site would be very happy to see questions asked out of pure idle curiosity: pure idle curiosity is one of the nobler motives in mathematical research, so far as I am concerned. It sure beats the hell out of "I was assigned this question so I'll try to get it answered online."

I can see that you are mostly questioning the desirability of sort of half-baked questions along those lines. To that I would say: it takes a certain amount of work to post a question on math.se -- probably at least a minute or two of typing, right? Before you spend a minute or two typing in any question, spend a minute or two -- heck, why not five? -- thinking about it. To an extent this is a bit counter to ordinary psychology: in many aspects of life, if a curiosity pops into your head, then since you're curious you necessarily don't know the answer, so to get it you need to look somewhere outside of your own head. But it is not necessarily so in mathematics. For instance, recently on this site someone asked a question of the form "Are there fields which have property X?" And I gave "the general answer": "A field has property X if and only if...." Another (much younger) answerer commented that he had looked through my field theory notes and not seen that theorem before. My reply: neither had I! Remarkably, in mathematics you can use what you already to know to discover entirely new things. Idle curiosity together with a willingness to try to answer your own questions: well, you can make a research career out of that.

Of course many times you simply won't be able to answer your question in five minutes or so. But you'll probably be able to come up with something to say about it, and I think you should include that something in your question to show your engagement in the process. For instance, if you want to ask about the number of subgroups of $S_n$, you could observe that by Cayley's Theorem every group of order at most $n$ occurs up to isomorphism as a subgroup of $S_n$, so very roughly speaking the answer is: "a lot". That's not the deepest observation in the world, but it shows we're thinking, right?

About "stupid questions"...Teachers are supposed to say that there are no stupid questions, but unfortunately that's not true in all contexts. There are, sadly, some questions which when asked make those who hear it think less of the questioner. I think a good modern-day answer to this is that no one can see your stupid googles (well, no one you know, anyway). You really can answer most of these questions simply by googling them, even when you don't know exactly the right keywords (i.e., google is miraculously good at what it does). Just now I googled "subgroups divide the order of their supergroup". "Supergroup" isn't really the right word, so I was curious to see whether that would get you to Lagrange's Theorem. It sure does.

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  • $\begingroup$ Well, not "miraculously" but mathematically. Excellent advice. $\endgroup$ – Andrés E. Caicedo Jul 18 '13 at 5:39
  • $\begingroup$ Yes, I second @Andres. It reflects also my own experience, even including the "think then 5 minutes more about it": many of such idle couriosities of mine I could then answer myself. But some of them I could not resolve myself and they made it through to MSE (I'm not a professional mathematician or student). Extending Pete's answer by one single aspect: this is the joy/desire to communicate. I think one should not give this up, on the other hand it is clearly needed to keep a certain self-discipline in that: we don't want MSE to become eventually a chat... $\endgroup$ – Gottfried Helms Jul 18 '13 at 6:47
  • $\begingroup$ +1 for the first sentence of the last paragraph $\endgroup$ – Ilya Jul 18 '13 at 16:01
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Meta is only for discussions about the actual running of MSE or the SE sites/model. No math content should be asked on meta. So the appropriate place would be the main site, assuming that thqe question itself is appropriate.

Further, I want to encourage non-homework questions, which are often the most interesting questions on the main page.

But ultimately, I think that this is what this site is really for. That is, when you have worked on something for a while, but you get stuck, or you want more references, etc, ask it here. But this does require you to put in some work, appropriately formatting a question and whatnot.

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  • $\begingroup$ Well that's kind of my point, if one can ask questions which one have not worked on at all, but is simply curious about. "Is this so?" "Yes, recall that.../read here..." End of story basically. $\endgroup$ – Erik Vesterlund Jul 17 '13 at 21:28
  • $\begingroup$ Pretty sure you meant "most" rather than "least". $\endgroup$ – Andrés E. Caicedo Jul 17 '13 at 22:44
  • $\begingroup$ Oh yeah - non-homework questions are definitely the most interesting. $\endgroup$ – davidlowryduda♦ Jul 18 '13 at 2:27
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I think, curiosity is the main reason for asking any kind of math question. I think Math.stackexchange and MathOverflow users cannot know your true reasons for asking a question, but many would assume you ask them out of curiosity.

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