A cursory search yields that actually mental health is correlated with academic achievement (and thus mental health problems must be anticorrelated): https://w

A cursory search yields that actually mental health is correlated with academic achievement (and thus mental health problems must be anticorrelated): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4443903/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4443903/ Of course, this is "academic achievement" as in getting a 4.0 at Stanford, not creating a new field of mathematics... I imagine your question would be hard to investigate as many of these high achieving mathematicians are rare outliers and would defy statistics on population averages...