I have recently flagged several questions for migration to math.stackexchange which were fairly clearly not about mathematics research and related topics. It was clear that in some cases these new users were simply unaware of the existence of math.stackexchange. [To be honest, I do not actually know how common this situation is, or whether it became more common after the migration to the stack exchange network.]
Prompted by the above situation, I want to ask if it is possible and/or beneficial to add a short sentence to the page where one asks a question saying something to the following effect:
If your question concerns mathematics, yet not at a research level, consider asking at math.stackexchange instead. [Edit: This sentence is only meant as a vague preliminary suggestion. As several people have pointed out, it is inaccurate and would probably require modification. See also quid's answer below for good ideas (especially the first and last quote blocks).]
and add a link there to math.stackexchange.com. The goal of this measure would be to reduce the number of questions asked at mathoverflow which actually belong on math.stackexchange.
The above sentence could maybe be added to the "How to ask" box shown on the right side of the page for asking questions. Also, it could be shown only to new or unregistered users, although I am not sure this exception would be helpful.
PS [This may require its own separate question]: It is useful to quantify the effect of such measures. If we were to test the above proposal for a short period of time, could we measure its efficacy? Here are two scenarios:
We show the above message to everyone for a month, say. Can we measure the difference in the number of questions closed as off-topic (too basic, really) or migrated to math.stackexchange before and during the test?
We show the above message to a randomly selected sample of (new?) users. Can we measure the difference in this case? I assume it would be harder. Perhaps the software does not even allow for the implementation of this scenario.
Edit 2: I have changed the suggested sentence above to address some concerns. The comments and quid's answer give a more complete overview of the possible messages.