I am actually not even sure there is a single predictor for being a strong mathematician (such as strong aesthetic discernment as you put it, although I agree it is a strong predictor) -- I think people's math thinking is just that heterogeneous.

My own impression (coming from thousands of hours of conversation and reflection) is that there's less genetic variability than superficially appears to be the case: a lot of the variance in styles of mathematical thinking is environmental / circumstantial. There is more than a single intelligence variable and a single aesthetic discernment variable, but I think that there's a collection of 4-6 genetic variables that explain basically all genetic variance amongst mathematicians.

I agree that thinking in terms of mathematical ability being captured by a few numbers is connotatively misleading: it's like characterizing all human behavior as being about survival and reproduction, those were the influences that shaped who we are, but that's not what goes on on a day-to-day level.

I do think professional mathematicians need to combat the panic reaction people have to mathematics. Really, mathematics is just a gentle slope from common sense into the infinite.

Yes :-).