On The Pursuit of Beauty
Today I read a profile by the New Yorker on Yitang Zhang, who proved an upper bound on the gap between consecutive primes last year. I found his profile strangely unglamorous for a MacArthur fellow. Many segments of the article made me stop and think about my own academic prejudices and goals. I also liked many of the quotes and the way some concepts were described. So I’ve collected below all the snippets from the article that caught my eye.
Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. Bertrand Russell called it a refuge from “the dreary exile of the actual world.”
Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended.
In “The Psychology of Invention in the Mathematical Field,” published in 1945, Jacques Hadamard quotes a mathematician who says, “It often seems to me, especially when I am alone, that I find myself in another world. Ideas of numbers seem to live. Suddenly, questions of any kind rise before my eyes with their answers.”
In the back yard, Zhang had a similar experience. “I see numbers, equations, and something even—it’s hard to say what it is,” Zhang said. “Something very special. Maybe numbers, maybe equations—a mystery, maybe a vision. I knew that, even though there were many details to fill in, we should have a proof. Then I went back to the house.”
In the Annals’ [of Mathematics] archives are unpublished papers claiming to have solved practically every math problem that anyone has ever thought of, and others that don’t really exist. Some are from people who “know a lot of math, then they go insane,” a mathematician told me.
Prime numbers have so many novel qualities, and are so enigmatic, that mathematicians have grown fetishistic about them.
“Is there a talent a mathematician should have?”
“Concentration,” Zhang said. We were walking across the campus in a light rain. “Also, you should never give up in your personality,” he continued. “Maybe something in front of you is very complicated, it’s lengthy, but you should be able to pick up the major points by your intuition.”
“Our conditions needed to be relaxed,” Iwaniec told me. “We tried, but we couldn’t remove them. We didn’t try long, because after failing you just start thinking there is some kind of natural barrier, so we gave up.”
“Unless you tackle a problem that’s already solved, which is boring, or one whose solution is clear from the beginning, mostly you are stuck. But Zhang is willing to be stuck much longer.”
Zhang’s preference for undertaking only ambitious problems is rare. The pursuit of tenure requires an academic to publish frequently, which often means refining one’s work within a field, a task that Zhang has no inclination for.
He does not appear to be competitive with other mathematicians, or resentful about having been simply a teacher for years while everyone else was a professor. No one who knows him thinks that he is suited to a tenure-track position.
“I think what he did was brilliant,” Deane Yang told me. “If you become a good calculus teacher, a school can become very dependent on you. You’re cheap and reliable, and there’s no reason to fire you. After you’ve done that a couple of years, you can do it on autopilot; you have a lot of free time to think, so long as you’re willing to live modestly. There are people who try to work nontenure jobs, of course, but usually they’re nuts and have very dysfunctional personalities and lives, and are unpleasant to deal with, because they feel disrespected. Clearly, Zhang never felt that.”