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As I understand it, MathStackExchange is for homework level questions and MathOverflow is for research level questions. As a student, I always posted in MathStackExchange unless I had some weird question that came up in undergraduate research.

However, as a beginning graduate student, I'm starting to ask for facts that might not be contained in a basic textbook, but are still very basic for experts in the field. When I ask on MathStackExchange, it gets read by very few people, not because the question is hard, but because it is specialized for the audience. (In addition to the two or three on my main account, I have a couple more on a separate one.)

However, I'm afraid (and know for some of the questions) that asking these on MathOverflow would probably not go over well. Do you know how to tell when a question that is not research but is better answered by an expert is appropriate for MathOverflow?

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    $\begingroup$ I don't agree with the characterization of math.SE - questions of all levels are on-topic here, although the really high level or research level ones tend to get drowned out due to the overall volume. So you can ask questions here, and there's enough community overlap that the same expert may very well answer the question as on MO. That being said, see here for a discussion of what's on-topic on MO. $\endgroup$ – user296602 Jan 16 '16 at 6:34
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    $\begingroup$ If it can reassure you, I'm a beginning PhD student too, and at first I was a bit scared of asking questions on MO. So far I've asked 4, and they've been well-received each time. Three of them were questions I directly encountered during my research, the fourth one was about a topic that interested me but not directly related to my research. I mean, worst case scenario, your question gets downvoted... It's not the end of the world. Most people (if not everyone) were genuinely helpful with me. $\endgroup$ – Najib Idrissi Jan 16 '16 at 7:40
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    $\begingroup$ Read this: meta.math.stackexchange.com/questions/41/… and then go over the "Linked" questions on the right-hand side menu of that thread as well. $\endgroup$ – Asaf Karagila Jan 16 '16 at 10:36
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    $\begingroup$ As I understand it, mathstackexchange is for homework level questions - Does this look like homework ? $\endgroup$ – Lucian Jan 19 '16 at 18:42
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    $\begingroup$ @Lucian: Yes, actually. I wasted so much time in quantum field theory classes churning through horrible integrals... $\endgroup$ – anomaly Jan 20 '16 at 18:54
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    $\begingroup$ @Dtseng: My advice would be not to worry. There is a noticeable overlap between the m.se and MO levels, and there is a considerable difficulty for just about anyone to assess the level of a question without knowing the answer; and both of these facts are well-known to the users of m.se and MO. $\endgroup$ – darij grinberg Jan 21 '16 at 0:17
  • $\begingroup$ on SE esp MathOverflow, "inappropriate" questions as decided by the community (collaboratively/ collective wisdom) are closed/ and/ or deleted very quickly, sometimes utterly vaporized without trace, and nobody will remember them, so there is no risk to reputation. also do not regard any individual question as a sign of anything greater. questions are cheap, answers are hard. ask routinely (but not frequently) to sharpen your own intuition for what "flies" & dont be discouraged by rejections (which generally "cost" nearly nothing). as an old english expr goes cant get hung for trying... $\endgroup$ – vzn Jan 26 '16 at 19:48
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I think you should err on the side of just asking on MathOverflow. There aren't enough interesting questions on MO these days anyway. If you're worried about your reputation (in the colloquial sense) post under a pseudonym.

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    $\begingroup$ I agree. (Not only because of the last sentence. :-)) On closures, not unlike rejections for journals, one could also recall that many well-known users experienced them sometimes too. It is not that big a deal, and it usually better not to start an argument over them. $\endgroup$ – quid Jan 21 '16 at 7:58
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    $\begingroup$ That last sentence has been my strategy for two years now; the plan is to start a new account once I know enough mathematics that I'm not potentially jeopardizing my career simply through curiosity. Of course, even once this level has been reached, using a pseudonym can still be a reasonable strategy when venturing into fields very far from one's own. $\endgroup$ – goblin Jan 24 '16 at 13:35
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    $\begingroup$ @goblin it seems extremely far-fetched that your reputation as a mathematician is going to be strongly affected by "asking too many questions" on a math Q&A site. $\endgroup$ – djechlin Jan 28 '16 at 21:46
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    $\begingroup$ @djechlin, the issue is that whenever you're asking questions in fields you've never formally studied and therefore know very little about, you're likely to ask a few silly questions. So I guess what I'm saying is: perhaps you're right, but its better to play these kinds of things safe. $\endgroup$ – goblin Jan 29 '16 at 2:46
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Do not be afraid. Most* MO users will, when they see an off-topic question, vote to close it. If it is closed (put "On Hold" as they say here), then you can ask to have it migrated to M.SE if you wish.

* Only impolite users will downvote these.

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    $\begingroup$ Most MO users cannot vote to close. :-) $\endgroup$ – quid Jan 27 '16 at 15:14
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In my brief experience with SE questions are monitored by a fair number of high-level experts. As a graduate student you can easily gain some reputation points and offer bounties for the more specialized questions.

I do not know SO but given the opinion of another poster that there are not enough interesting questions on MO these days, I suspect that we may be observing a phenomenon, well known to economists, whereby the larger network gradually absorbs all the smaller ones even if their charters specify different (niche?) purposes - see Facebook and LinkedIn.

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    $\begingroup$ I very much doubt we are seeing any sort of absorption of users from MO to MSE. $\endgroup$ – Tobias Kildetoft Jan 25 '16 at 19:10

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