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It is a truth not-quite-universally acknowledged that a newish Stack Exchange user in possession of the knowledge that there are two sites named "Math Overflow" and "Math.StackExchange" will be in want of an explanation.

A reasonably careful reading of "What topics can I ask about here?" will reveal this information, but I wonder why it isn't more prominent. For example, a sentence in the "How to Ask" box next to the Ask a Question form.

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    $\begingroup$ Never has such a beautiful sentence been crafted before, as I was just telling Mrs. Bennett. Bravo for your erudite wit, Master (or Mistress) Foo Bar ! $\endgroup$
    – Georges Elencwajg
    Commented Feb 26, 2015 at 22:34
  • $\begingroup$ MO-MSE differ similarly to AMS-MAA (for example); the latter takes newbies (let alone the general public) a little time to digest, so anyone already familiar with it has a head start for understanding the former. $\endgroup$
    – mathematrucker
    Commented Jun 24, 2018 at 14:35

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I think you ask a quite reasonable question. One certainly could have a more condensed description of what is on-topic on MathOverflow, and put this in a prominent place where people see it before asking their first question. In particular one could make more clear what is the difference to Math.SE. As a draft of such description, one could take e.g. the following:

A mathematical question is on-topic and appreciated on MathOverflow if it is a question which professional mathematicians may ask each other. If you are not a mathematician yourself, you should rather ask your question on Math.SE instead -- unless a mathematician has encouraged you to ask it here.

Apart from this, the main rules are the following:

  • Questions should be brief, clear, self-contained, well-formulated and allow well-defined, short (at most about 1-2 pages) answers. Don't expect anyone to spend time on answering a question which is vague, overly long, full of language mistakes, or which looks like it has taken you only 5 minutes to ask.

  • Questions which are or look like homework or contest problems are off-topic, i.e. not welcome on this site.

  • MathOverflow is not the right place to announce your results or to ask people to check your proofs ("Is my proof of the Riemann hypothesis / Goldbach conjecture / ... correct?" etc.); doing that anyway is likely to cause harsh reactions of the community.

  • Avoid asking questions which can easily be answered via a Google search. In particular avoid duplicates, i.e. questions which have already been asked before on this site.

  • If you know the answer to your question, then don't ask it here -- it would waste other people's time.

  • To avoid duplicating efforts, ask a question either on Math.SE or here, but not on both sites. If you would like to have an exception from this rule for a question which remained unanswered on Math.SE for a long time, enquire on Meta.

  • Answering your question should not require reading particular books, papers etc.. This also means that questions about particular preprints are off-topic.

Questions which do not fulfil the above conditions usually get downvoted, closed and removed. However note that as everywhere, it is accepted that respected members of the community sometimes do not follow some of the rules. As a new -- possibly even pseudonymous -- user unknown to the community, don't make the mistake to copy such behavior!

For a longer and more detailed explanation of what is on-topic on MathOverflow, see here.

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    $\begingroup$ Given the disturbing quantity of very low-level questions (not so huge, but enough to bother people to comment/downvote/vote to close), I strongly support your proposal, though I don't see where and how the message could fit, so as to make it widely and instantly read by (most of) newcomers. $\endgroup$
    – Hachino
    Commented Feb 18, 2015 at 10:14
  • $\begingroup$ @Hachino, maybe a new-user tag with the message in the roll-over? Then a note for new users to use that tag: if you are a new-user, use this tag. $\endgroup$
    – Fred Daniel Kline
    Commented Feb 18, 2015 at 14:37
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    $\begingroup$ Hm, I was more thinking about something to put on the frontpage, more or less close to the "take the 2 minutes tour" message. The idea is that anyone coming on MO for the first time should immediately see "research-level" and understand what it implies. I like your idea of a tag, but it might not be as visible as needed for our purpose. $\endgroup$
    – Hachino
    Commented Feb 18, 2015 at 14:40
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    $\begingroup$ I'd rather suggest something like this: when a new user clicks the "Ask Question" button, a box appears which says "You are about to ask a question on a Q&A site for professional mathematicians. Before you continue, it is recommended that you read about the site rules.". Here "site rules" links to a text along the lines of the one I gave, and the box provides two alternatives to choose from: "continue" with a thin frame (and which is greyed out before the user has clicked on "site rules"), and "cancel" with a bold frame. If the user clicks "continue", they can enter their question as usual. $\endgroup$
    – Stefan Kohl Mod
    Commented Feb 18, 2015 at 15:06
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    $\begingroup$ @StefanKohl, agreed, and I think such a popup ought to explicitly mention and link to math.stackexchange.com as an alternative. If they already know what math.se is then there is no harm done, but if they are a new user and they don't know what math.se is, then probably it is worth their time to check it out because there is a good chance that their question is better-suited for math.se. $\endgroup$
    – usul
    Commented Feb 18, 2015 at 20:36
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    $\begingroup$ @StefanKohl : Nice solution indeed. Could we reasonably hope to see it implemented in MO 3.0 ? :) $\endgroup$
    – Hachino
    Commented Feb 19, 2015 at 11:53
  • $\begingroup$ Interesting point, but what if the Riemann hypothesis were solved and then months later one (not necessarily the solver) makes a question and answer pair showing how it was solved with proper citations. Would that be allowed seeing as how it provides knowledge to the community? $\endgroup$
    – user64742
    Commented Apr 1, 2017 at 21:26

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