A very cool story here about an unheralded lecturer in math who in isolation from the big names in his field (and who even had to work at a Subway at one point) comes up with a huge advance in solving a famous and very vexing problem in numbers theory. How did he come up with the solution to the challenge that had really worn on him?:
To take a break, Zhang visited a friend in Colorado last summer. There, on July 3, during a half-hour lull in his friend’s backyard before leaving for a concert, the solution suddenly came to him. “I immediately realized that it would work,” he said.
This scene fits quite well with what the recently deceased Kenneth Waltz thought about where theories come from. To Waltz, a theory doesn’t come from the collection of more and more data but from this: a moment when a “brilliant intuition flashes, a creative idea emerges” (Theory of International Politics). Richard Ashley described Waltz’s view of the theory construction process as “all very mysterious.” Waltz himself said: “One cannot say how the intuition comes and how the idea is born.”
Perhaps we should spend more time in the backyard and less time in the office?