Wiles explained the process of research mathematics like this: “You absorb everything about the problem. You think about it a great deal—all the techniques that are used for these things. [But] usually, it needs something else.” Few problems worth your attention will yield under the standard attacks.

“So,” he said, “you get stuck.”

“Then you have to stop,” Wiles said. “Let your mind relax a bit…. Your subconscious is making connections. And you start again—the next afternoon, the next day, the next week.”

Patience, perseverance, acceptance—this is what defines a mathematician.