Machine Learning Confronts the Elephant in the Room

At the playground on the leafy campus of the Institute for Advanced Study in Princeton, New Jersey, one afternoon in May, the mathematician Akshay Venkatesh alternated between pushing his 4-year-old daughter on the swing and musing on the genius myth in mathematics. The genius stereotype does the discipline no favors, he told Quanta. “I think it doesn’t capture all the different kinds of ways people contribute to mathematics.”

Venkatesh’s other daughter, 7, wandered somewhere with her friends on the serene grounds of the institute’s visitor housing complex, which lends itself to the kind of free-range childhood that has become rare these days. Venkatesh had been visiting IAS for the past year, on leave from Stanford University; as of mid-August he will join the institute’s permanent faculty, whose previous members include Albert Einstein, Kurt Gödel and quite a few winners of the Fields Medal, the highest honor in mathematics.

Now the IAS can boast a brand-new Fields medalist in Venkatesh himself. The citation for his medal – awarded today at the International Congress of Mathematicians in Rio de Janeiro – highlights his “profound contributions to an exceptionally broad range of subjects in mathematics” and his “strikingly far-reaching conjectures.”

His ideas are “a vast expansion of the imagination,” said Michael Harris, a mathematician at Columbia University.

But back when Venkatesh was a graduate student at Princeton University around the turn of the millennium, the genius myth almost derailed his budding career. His early education – which carried him to college at age 13 and graduate school three years later – neatly fits the genius narrative. But on arriving at Princeton, Venkatesh was startled to discover that “there are a lot of people who are just as good at the things you thought defined being a mathematician, like being able to learn the material or solve problems fast.”

Mathematics research, with its winding paths and dead ends, was very different from the kind of math Venkatesh had excelled at in school, with its problem sets and clearly defined endpoints. Accustomed to meeting the highest of standards, he saw his dissertation as mediocre. Quietly, Venkatesh started eyeing the exit ramps, even taking a job at his uncle’s machine learning startup one summer to make sure he had a fallback option.

But then a plum job offer fell in his lap: one of the prestigious C.L.E. Moore instructorships at the Massachusetts Institute of Technology. Clearly, his adviser must have written a glowing letter of recommendation for him – but why? Venkatesh took this question to Jordan Ellenberg, a friend and fellow mathematician. Ellenberg’s reply has stayed with Venkatesh over the years: “Sometimes, people see things in you that you don’t see.”

Now 36, Venkatesh carries himself with the ease of someone who is thoroughly comfortable with his life choices. But it has taken him many years to see what other mathematicians have long seen in him. “It took me a long time to really feel satisfied with what I was doing,” he said.

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