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.

General Public has so much misunderstanding toward math world. My cousin once asked me why I should continue studying Mathematics after graduation. She believes all the students majoring in math will transfer to other business such as financial or IT related areas. She told me affirmatively:”Jingrun Chen spent all his life focusing on the proof of 1+1=2”. Then what? “Of course he ended up mad.” She said.

I couldn’t find anything to say.

You can explain to your cousin that it was Russell and Whitehead who spent some of the best years of their lives proving 1+1=2. Jingrun Chen spent a decade proving that every (large enough) even number is the sum of a prime and either another prime or the product of two primes. I do recall that that had an effect on his health – he became famous, got proper medical attention for his tuberculosis, and lived to a reasonable age.

Now, what moral your cousin will extract from that story, I don’t know. I mean, presumably one shouldn’t have to do anything in particular to get proper medical attention, but surely an understanding of prime numbers neither helps nor hurts to get that point, and that’s not a moral of the above story, anyhow.

Not that I am old and wise. I think a certain answer to your cousin can be http://online.wsj.com/article/SB123119236117055127.html

I do not think there is any job in the world which does not have its own problems. As stated in the interview, mathematical thought process is healthy in my belief. You probably want to go for mathematics because you like it. You do not want to go for a Financial/IT job because you do not like it. Why do people start playing sport? For the money? I doubt Ronaldo or Maradona cared about the money when they began playing. Yes you do need to eat, if that is what your cousin is worried about. The days when mathematicians die due to poverty have far been left behind( though I still believe they are underpaid.)

There are a lot of people who take math major and go into other things. Well they like it that way, let them. Why should this be generalised to everyone.

The misconceptions regarding mathematics cannot be gotten rid of. They are here to stay. All we can do, is sit in our rooms, sip on warm hot chocolate and laugh till our tears come out.Someone recently commented ‘Its not their fault’

For even further reference read this lovely piece : http://gowers.wordpress.com/2009/12/20/wiles-meets-his-match/