I knew a few mathematicians when I was at university. They were wonderfully strange and generally not very happy people, though I hardly knew a representative sample. The mathematics faculty was notorious for being a sort of playroom: very serious people sitting around staring into space or playing three-dimensional chess, and then one of them would say “Ah, I’ve had a thought about the scaling limits of critical Ising correlation functions in planar domains,” then get up and jot down a few equations and this would be a good day’s work. In some cases it might be a good year’s work. The whole place looks like a funhouse these days:
I never met a mathematician who was much of a walker, but now thanks to an article in the New Yorker, by Alec Wilkinson, I know about Yitang Zhang – a Chinese-born American mathematician who’s done some genius-level work on prime number theory, who is also something of a walker.
Although Zhang was thoroughly trained as a mathematician, with a PhD from Purdue, he nevertheless spent many years outside of academia, doing various bum jobs: delivery man for a New York restaurant, working in a motel in Kentucky, and in a Subway sandwich shop, before doing his great work, formalized in a paper titled “Bounded Gaps Between Primes” which won him a bunch of prizes including a MacArthur “genius” grant and enabling him to become a professor at the University of New Hampshire.
In the New Yorker article Wilkinson asked Zhang if he was ever frustrated in those “missing” years. and he replied, “I was tired. But many times I just feel peaceful. I like to walk and think. This is my way. My wife would see me and say, ‘What are you doing?’ I said, ‘I’m working, I’m thinking.’ She didn’t understand.”
Wilkinson also tells us about Zhang’s current situation, “Outside his office is a long corridor that he likes to walk up and down. Otherwise, he walks outside.” You can see why he might stick with a tried and trusted method since his great mathematical breakthrough came while he was walking.
He was visiting his friend Jacob Chi, a music professor, in Pueblo, Colorado, a visit on which he taught Chi’s son calculus. Wilkinson writes, “Zhang had planned a break from work in Colorado, and hadn’t brought any notes with him. On July 3rd, he was walking around the Chis’ back yard. ‘We live in the mountains, and the deer come out, and he was smoking a cigarette and watching for the deer,’ Chi said. ‘No deer came,’ Zhang said. ‘Just walking and thinking, this is my way.’ For about half an hour, he walked around at a loss.”
And then came the breakthrough, a theorem that proves there are an infinite number of prime pairs that differ by some number N, and that N is less than 70 million. I think that’s the deal, anyway.
There is a documentary about Zhang by George Csicsery titled Counting From Infinity which shows Zhang walking, and to be fair sometimes not walking.
Of course, Zhang’s is a great story because it’s about a genius who spent a some time in the wilderness and then returned in triumph. From what I know of mathematicians, quite a few of them walk in the opposite direction.