Michael, consider this:

H1: All mathematicians are smart
H1': All non-mathematicians are not smart

So, by the same logic, observing a not so smart lawyer (a non-mathematician and a non-smart) would be in evidence in favor of H1. Now, according to your logic, if we observe all non-mathematicians and we verify that none of them is smart, then the Bayesians are correct. Did I get it right? I think so…

But what does the Bayesian analysis say about someone who is a mathematician AND a teacher, or a mathematician AND a singer?

The Bayesian analysis fails, my friend, because it does not take NATURAL KINDS into consideration. It is ontologically-agnostic, and the quantitative analysis alone would not work.

BTW, I did not mention the other SERIOUS problem with the Bayesian analysis: observing a black non-raven, negatively confirms the hypothesis, which is also non-sensical