The n-category Café has a post about “Dangerous Knowledge”, the BBC documentary I reviewed here some time ago; there’s also a discussion in the comments on whether mathematicians (or academics, or creative types) are really different from “normal” people. If you came here from the link over there, welcome, and here’s hoping that you’ll enjoy this recent interview with John Nash. (Hat tip to 3QD.)
Around the 6-minute mark in the second video, Nash is asked explicitly whether his mental illness might have in some way contributed to his creativity and enabled his mathematical work. He points out in response that his work in game theory was all done before the onset of his mental problems and that he “did not develop any ideas, particularly on game theory, while being mentally irrational”. He also recalls a mistake in a published paper that he completed shortly before the breakdown and suggests that it may have been due to a malfunction of his mind.
A few minutes earlier in the interview, Nash talks about cognitive therapy: it “simply stimulates you to think. The more the mind really works, sort of like a computer, the more it tends towards rationality and maybe recovery”.
It would not require a lot of imagination to pursue this further. Could it be possible that mathematics, as an activity based on logical thinking and sustained intellectual effort, exercises the brain and keeps it healthier than it would be otherwise? Should we elaborate on how mathematics, far from being the ungrateful mistress of Dangerous Knowledge, might actually be the salvation of those of us who need its mental discipline?
Nash makes no such implications. There’s not a single sentence in the interview where he suggests that this or that might be true of mathematicians and mental disorders in general. He only speaks of his own experience and to some extent that of his family, all in a very matter-of-fact way. I couldn’t help thinking that facts are his friends – the good, immutable, trusted facts, preferably drawn from his own experience – whereas speculations and generalizations such as those above are not. That, and he also must have spent unimaginable time and effort training himself to sort through his thoughts in this way and discard anything with insufficient factual basis.
I wonder if the general public might imagine mathematicians as men (yes, men) who stare at formulas and apply some mysterious psychic powers until the formulas simplify themselves. Or we might be like Luke Skywalker or some other magical hero, giving ourselves over to the Force and hoping that it will guide us straight to
the heart of the Death Star the solution to the Riemann hypothesis. In that narrative, mental illness might be associated with a quickening of said psychic powers and, therefore, heightened mathematical ability.
I’m finding the real John Nash story to be far more inspiring.