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I have read that https://mathoverflow.net/ is only for the very advanced mathematics, such as upper graduate level or research level, counter to https://math.stackexchange.com/ which is for any mathematics level!

  • How can I choose the preferred website to put my questions?
  • What if someone writes his or her question down on the not preferable website?
  • Do the users of both websites have the same chance to get answers to their questions?
  • Are there any tools to move the questions between the two websites? to derive less hard questions from that hard ones, and share them as parts of a question to allow the lower lever users participate also in the upper-level questions?
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    $\begingroup$ The (accepted, for unknown reasons) answer addresses one of your questions in a (characteristically) vague way, so I dare add this link:meta.stackexchange.com/questions/10249/… Otherwise, it's just nonsense, sorry! Officially, MSE is for maths at all levels, but in practice, a doubt concerning basic concepts will get you a slim chance of about 100% to be downvoted.Nobody can brag with a smart answer, you see... $\endgroup$ – Professor Vector Jan 12 '18 at 7:51
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    $\begingroup$ @ProfessorVector Actually officially the site is "for people studying mathematics at any level and professionals in related fields" and I am repeatedly on record as explaining that in my firm opinion the most reasonable interpretation of this is "roughly undergraduate and above" (some others have some other interpretations of it). For this question though this is not really relevant, as it was about the other end of the spectrum. $\endgroup$ – quid Jan 12 '18 at 18:57
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  • How can I choose the preferred website to put my questions?

I once read something along the lines "If you have to ask whether to ask on MO or math.se, likely you should ask it on math.se." I think this is a good rule of thumb.

  • What if someone writes his or her question down on the not preferable website?

If you post on MO and they think it is too low level, they'll close it, and maybe "migrate" it here. Since this site is for "any level" there is also not a too high level. No one will (or at least should) scold you for asking a too advanced question here. It could happen that you get no answer and/or somebody recommends that you could have asked it there. You then can still ask it there too.

  • Do the users of both websites have the same chance to get answers to their questions?

On the one hand, there are literally a few hundred thousand questions answered on this site that would not have been answered on MO (they could have been answered there but they would not have been answered there). On the other hand, there are likely several thousand questions answered on MO that would not have been answered here (and a reasonable fraction of could not have been answered here).

So it depends what you look at. Yet, generally, a question that would be considered as good on MO will usually be treated better and more completely than here.

  • Are there any tools to move the questions between the two websites? to derive less hard questions from that hard ones, and share them as parts of a question to allow the lower lever users participate also in the upper-level questions?

It is possible to move entire Q&A threads from one site to the other. This is called migration. It is not possible to move "slices" of a thread. Yet everybody is free to take inspiration from content on one site and post about it on the other site. (Of course, on should provide references as appropriate.)

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    $\begingroup$ Thank you for the rigorous answer @quid can you upvote my question if you see that it deserve, please. $\endgroup$ – The_lost Jan 10 '18 at 0:21
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    $\begingroup$ You are welcome. I upvoted it, since it is carefully written. Thank you for the reminder. On meta though there are no points, though. $\endgroup$ – quid Jan 10 '18 at 0:42
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    $\begingroup$ Thank you sir, even if there are no points that make me more enthusiast! $\endgroup$ – The_lost Jan 10 '18 at 0:46
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    $\begingroup$ One should emphasize that it is almost always a bad idea to ask a question in both sites. $\endgroup$ – Mariano Suárez-Álvarez Jan 22 '18 at 22:38
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    $\begingroup$ @Mariano yes, I agree, almost always and especially close in time. But if it does not get answered here for a long time and it seems on topic MO then I think it is alright to ask it there, too, with links. And this is, in this case, preferable to migration. $\endgroup$ – quid Jan 22 '18 at 23:03
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    $\begingroup$ Having two copies of a question is the worst possible outcome. Links between them are a poor way to patch a problem. $\endgroup$ – Mariano Suárez-Álvarez Jan 22 '18 at 23:17
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    $\begingroup$ @Mariano why? And what specifically do you propose in the scenario I described? (If OP decides to delete it here, more power to them, but I would not mandate it either.) Migration is a poor solution; it will not show up at the top of the new question list (IIRC), and the score might be distorted. Finally MO likes to stress their independence and how they can leave the network if they want. So, it is better to be circumspect in completely sending things there. (The last is a minor aside) $\endgroup$ – quid Jan 22 '18 at 23:26
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    $\begingroup$ I propose to migrate. Duplication of questions, of answers, and what not, is pure waste. I could not care less for the scores, really. MO can reject the migration, if needed —but we tend to migrate with common sense, so it does not really happen. $\endgroup$ – Mariano Suárez-Álvarez Jan 22 '18 at 23:30
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    $\begingroup$ @Mariano everybody can check if there already is an answer. It's annoying if it happens at the same time because if things happen within minutes than it is hard to check. You know very well that this form of cross-post is accepted practice since a long time. If you disagreed with it, you should have taken action years ago. That's it. $\endgroup$ – quid Jan 22 '18 at 23:36
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    $\begingroup$ Crossposting has always been regarded as bad practice here. And I have taken action years ago: I systematically tell people not to do this, migrate things that have to be migrated, add links when it is too late in both directions, and what not. I have no idea what you mean by "that's it", to be honest. $\endgroup$ – Mariano Suárez-Álvarez Jan 22 '18 at 23:44
  • $\begingroup$ @Mariano that I do not intend to continue this discussion. $\endgroup$ – quid Jan 22 '18 at 23:45
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    $\begingroup$ Ah. Very useful. $\endgroup$ – Mariano Suárez-Álvarez Jan 22 '18 at 23:45
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There is one more factor which should be taken into consideration when deciding whether to use MathOverflow or Mathematics and that is the level of answers you expect. (IIRC this was mentioned several times in the rather heated debate shortly after MO joined SE network: What, when and will we migrate questions to MO 2.0?)

According to description given on that site: "MathOverflow is a question and answer site for professional mathematicians." Even though this description might be vague, it definitely implies that at least some level of mathematical maturity is expected.

As a consequence, if the same question is asked on both sites, you can probably expect the answers on MathOverflow to be more terse. It is very natural to omit details which a person with sufficient mathematical training can easily fill in.

Very likely, if you are missing some details in an answer and you ask for clarifications, the MO users will probably help you. (And I would consider as a reasonable action even posting a question on Mathematics asking about some steps/details from an answer given on MathOverflow.) But probably when deciding where to post you should also keep in mind that the level of answers is likely to be tailored to the expected level of the audience of that site.

Still, in my opinion, a typical graduate student should not have problems with MO-answers from a subject they are studying. But if you consider yourself below such level in the area you're asking about, maybe it is worth considering also sophistication level of the answers you might get as a part of your decision.

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