Professions and mental illness

Folklore says that mathematicians and grandmaster chess players peak early and have a greater-than-average chance of going mad.

I'm not sure if that's true, nor what exactly is meant by "madness" here, but suppose there is really a correlation. In both "professions" there's a very high bar to entry, so we can immediately rule out the hypothesis that people with a tendency to (e.g) schizophrenia gravitate to those jobs. It would be like saying people with a tendency to fallen arches tend to become basketball players--not unless they're 6'7" or so. I'm not so sure about other professions--lawyer, for instance. They need some intellectual horsepower, but it isn't as exclusive a group.

Some professions (police, surgeon) are obviously extremely high stress, to a degree that I doubt most mathematicians or engineers see. Maybe leaving out those would clarify the question.

Is there a pattern to the incidence of mental illness in the professions? I'm not thinking of a scientist with a bee in his bonnet about 9/11 conspiracies OK, I lie--I am, but I don't include conspiracy theory addiction unless it is a debilitating illness

If there is such a pattern, does it reflect a selection bias? (I was told that many speech therapists became interested in the profession because they needed that help in childhood.) Or does a raw talent set correlate with a weakness? Or is the way we teach some professions all screwed up? (horse whisperer in Columbia vs the horse breakers, or medical interns)

I have known of, though not personally, a few physics students who have had a "breakdown" of some kind, but I did not have the need to know the details and was not told. (And a few who washed out or decided they liked other things better--not the same thing.). So, less than a percent had a mental problem, plus or minus, and that may have been stress-related. One of the professors in the two universities I am most familiar with committed suicide, but again I have no details, except that there were no obvious problems beforehand. About 1 percent, plus or minus. That seems a trifle high. If one uses suicide rate as a proxy for the rate of all mental health problems then farmers and mechanics are at greater risk than policemen.

This looks complicated.