In Indiscrete Thoughts, Gian-Carlo Rota claims that:
It cannot be a complete coincidence that several outstanding logicians of the twentieth century found shelter in asylums at some point in their lives: Cantor, Zermelo, Gödel and Post are some.
Elsewhere, he hints that the rate of mental illness among logicians is much higher than the general population.
Do logicians suffer from mental illness at significantly higher rates than the population at large (or other similar groups, such as academics)? If so, is there an accepted explanation for this association?