This is more a comment but a bit long.
There was some discussion to include mention of math.SE prominently, for example Noah Snyder suggested repeatedly, getting quite some support, that the short summary should read
MathOverflow is a questions and answers site for research mathematicians. We accept mathematical questions at the Ph.D. student level and higher. Questions of all levels are accepted at our sister site Math.SE.
What we had when he said this was
MathOverflow is a questions and answers site for mathematicians.
now we have (this was the 'hover text' poll)
MathOverflow is a questions and answers site for professional mathematicians.
Note that this is in part fixed in form as
"Name of the site" is a questions and answer site for "scope".
Where "Name of the site" and "scope" also appear elsewhere, such as in the 'hover text' (I do not know if these are the official names of these parametrs but still that this is fixed in form, at least as a default, seems true).
In these discussions François G. Dorais said he would not like to mention another site there as this is not the place, but (if I understood him correctly) the ask page would be a good place, so what we are talking about now.
To make more precise what the suggestion is in OP as I understand it: Presently we have (on https://mathoverflow.net/questions/ask the site for asking a new question) a box:
How to Ask
Is your question about research level mathematics?
We prefer questions that can be answered, not just discussed.
Provide details. Share your research.
If your question is about this website, ask it on meta instead.
visit the help center »
asking help »
Where there are links (I did not reproduce) to the help center, to how to ask, and to meta.
Now, if this is possible, I would find it a very good idea to add a sentence on and link to math.SE in this box. (Possibly not exactly the one suggested but something along these lines, for example, since some seem to be worried to tell people to ask on math.SE we could provide it more as information.)
Say like adding (but this is rough just to get the idea across):
Is your question about research level mathematics?
If not, note that questions about mathematics at any level are welcome at math.SE
What I do not know is if this is technically possible (in an easy way). Since again this box seems to be fixed in form the only thing being specific to MO being the "research level mathematics", which is the "on-topic" of MO (and also appears elsewhere on the site). [This perhaps also in part addresses a concern raised by Todd Trimble, as there it can more or less only say the "on-topic" so if we do not intend to change this it must be "research level mathematics"; what the "on-topic" means precisely is to be defined in the help-center, where there is ample space.]
And as a reply to Steven Landsburg: I can understand why somebody would not want to individually suggest a question to be asked elsewhere (but this is not what this question is about), yet collectively and abstractly "we" suggested and suggest all the time other sites (in the official documentation). Thus, the question is not whether we do this at all but if we should do it at this precise place in addition (to other places where we do so already).
