According to the film, Cantor had mental problems even before he dove into serious math - voices in his head, etc.
Turing: from the psychiatry standpoint homosexuality is a pathology too, and again, he had homosexual affairs before he started working on the problems that made him famous.
Which means, we may be confusing cause and effect here.
Then why you think he is in the list of "crazy" mathematicians, at least according to the authors? (It may be because of the suicide though, which is considered pathology even now.)
Cantor and Nash went through their mental health problems at a time when diagnosis of mental issues was much worse than it is now. Lots of people suffered the same thing, genius or not. I don't think it has much to do with the fact that they were brilliant mathematicians.
And Turing's "insanity" has a lot more to do with the diabolical treatment he received at the hands of the British authorities; indeed, his suicide was arguably the rational act of a rational man.
(I'd hoped the BBC were above such sensationalism; I guess the memory of that old fascist Reith has now been thoroughly pissed upon.)
I wouldn't. There are many flaws in this book, but the main one is he gets facts wrong, both biographical and mathematical. For example, he writes that Turing died of a lab accident when in fact he committed suicide. He also tries to define consistency for all formal systems, and does so with outlandish philosophy involving "all possible universes". In fact, consistency (or inconsistency) is a property only of formal systems based on propositional logic--a subset of all formal systems--and it's easy to define mathematically. I can only imagine how many inaccuracies are in it that I wasn't able to spot.
I thought the program communicated the material extremely well and I would definitely encourage others to watch it. I did feel it was a tad melodramatic but then again because the subject matter is so significant it could be in danger of being under-sold.
I watched the first few minutes of this a while ago. They were making unrealistic Faustian analogies, and it came off as unpleasantly dishonest.
I would contend that no one has ever been driven crazy by thinking about mathematics. We like to think that sort of thing, but the branch of science involved is almost always chemistry...
I don't know, I start to change for the worse when I isolate myself from all people while programming for a very long time. Good thing we have the internet these days.
Turing: from the psychiatry standpoint homosexuality is a pathology too, and again, he had homosexual affairs before he started working on the problems that made him famous.
Which means, we may be confusing cause and effect here.