Let's make the relevant question more personal: will machines replace me? I'm a mathematician; my profession is often seen from the outside as a very complicated but ultimately purely mechanical game played with fixed rules, like checkers, chess, or Go. These are activities in which machines have already demonstrated superhuman ability. But for me, math is different: it is a creative pursuit that calls on our intuition as much as our ability to compute.

In 2010, a startling rumor filtered through the number theory community and reached Jared Weinstein. Apparently, some graduate student at the University of Bonn in Germany had written a paper that redid "Harris-Taylor"--a 288-page book dedicated to a single impenetrable proof in number theory--in only 37 pages. The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry. "It was just so stunning for someone so young to have done something so revolutionary," said Weinstein, a 34-year-old number theorist now at Boston University. Mathematicians at the University of Bonn, who made Scholze a full professor just two years later, were already aware of his extraordinary mathematical mind.