Galois - shot in duel.
Turing - committed suicide by cyanide-laced apple.
Boltzmann - committed suicide while on vacation.
Gödel - died from starvation and exhaustion.
Cantor - died from starvation in an insane asylum.
Ramanujan - died from malnutrition.
de Moivre - predicted the day of his death by calculating his sleep cycle.
Lie - became insane and attacked his friends.
Erdös - did amphetamines all his life.
Nash - was legally insane for 30 years.
Perelman - refuses contact with anyone except his mother.
Grothendieck - refused contact with anyone.
Kaczynski - serving a life sentence in maximum security prison.
Erdős took amphetamine in the second half of his life, and apparently it helped him a lot to stay productive. There is a story about it.
Erdős’s friends worried about his drug use, and in 1979 Graham bet Erdős $500 that he couldn’t stop taking amphetamines for a month. Erdős accepted, and went cold turkey for a complete month. Erdős’s comment at the end of the month was “You’ve showed me I’m not an addict. But I didn’t get any work done. I’d get up in the morning and stare at a blank piece of paper. I’d have no ideas, just like an ordinary person. You’ve set mathematics back a month.” He then immediately started taking amphetamines again.
His biography “The Man Who Loved Only Numbers” is a very good interesting book.
Turing committed suicide to escape government persecution for being gay. That's not the same as a case like Grothendieck or Nash; it can't fairly be called paranoia when someone really is out to get you.
More exactly turing was suffering due chemical castration mandated by the government, I don't want to imagine what such procedure does to one's mental health.
Given that the regimen at that time involved high doses of some of the same hormones used in MtF HRT today, I suspect it'd be not totally unakin to being forced into severe gender dysphoria, with gynecomastia and permanent sterility as just a couple of the side effects.
I'm afraid Kaczynski is probably more famous than most of them among those not interested in mathematics. And he was an assistant professor of mathematics at UCB when he turned, after all.
Gödel's story is certainly a fascinating one. However, he did
have a paranoid fear of being poisoned most of his life and weighed 30kg when he died - of malnutrition.
I think there's an issue with saying that extremism is necessarily an issue. For most theoretical thinkers, extremism is a necessary result of theory. And there is nothing wrong with that, if extremism in an ideology is an issue it's generally that the ideology itself is problematic.
there's certainly a pattern here, that people that walk the edge of what a human brain can do often drift to paranoia and/or extremism.
I'm thinking: Bobby Fischer, Grigory Perelman, Évariste Galois, and to a certain extent, Isaac Newton. I suspect the list is a lot longer.