Why you should care

A brilliant young mind finds the spotlight in the unlikeliest of places. 

You’d be forgiven for not having heard of Artur Avila, the prodigious Brazilian who won the world’s highest prize in math — the Fields Medal — last year. Outside of Brazil, the press focused on one of his co-winners, Maryam Mirzakhani, the first woman to win. And though the mathematician should have dominated local coverage, seeing as how he was the first Brazilian and Latin American to win the prize, the papers ran a different story: that of a presidential candidate whose plane crashed the same morning as the prize’s announcement. Avila, by all accounts the brightest math brain Brazil has ever grown, was overlooked.

The Fields is as close as one can come to winning the Nobel Prize, where there is no math category, and you’ve got to get there quickly to win (it’s awarded once every four years, and the cutoff age is 40). Avila, the 36-year-old star in the global math scene, shines all the brighter because of the darkness he rose out of. His home country, where math and science education hasn’t been prioritized, perpetually ranks terribly on just about any of these measures. According to the OECD, Brazil ranks 60th when it comes to math and science education, well below the average and somewhere between Georgia and Jordan. Almost improbably given its size and population of more than 200 million people, Brazil has never taken home a Nobel, much less a Fields. Avila, it turns out, is the outlier.

IMPA is considered the best math institute in Latin America and actively recruits. Avila would soon become its biggest recruit yet.

Avila knew expectations were high. “It turned out to be really quite a lot of pressure — optimism, but pressure,” he says. In a lot of ways, winning the Fields put a target on his back. Usually when someone wins the Fields, it opens them up to criticism — “people pick their work apart,” notes Edward Frenkel, a mathematics professor at the University of California, Berkeley. But Frenkel says he has heard only good things about Avila’s work: “It seems to have stood up to the criticism.”

Growing up in Rio de Janeiro, Avila, like many middle- and upper-class Brazilians, attended private school. His parents, who worked in the insurance industry, quickly recognized their son’s knack for math and began buying him advanced books to feed his appetite; by 11, he’d gotten his hands on his first calculus book. While the environment was “no pressure,” Avila says, pressure came soon enough, when at 13, he entered the Brazilian Math Olympiad, a tournament for young students, and found the types of problems presented “difficult, because they weren’t formulaic.” He returned home and redoubled his efforts; by 16, he had won a gold medal at the International Mathematical Olympiad in Toronto. That win put him on the radar of the National Institute of Pure and Applied Mathematics, or IMPA, the math paradise he would return to again and again.

IMPA sits in a forested spot down the coast from Rio de Janeiro. It’s considered the best math institute in Latin America and actively recruits bright stars. Avila would soon become its biggest recruit yet. By his senior year of high school, Avila was already studying at a master’s level at IMPA; they let him quickly earn his bachelor’s diploma, “to not waste time,” he says. During this period his focus was so much on the learning that, he says shyly, “my social side developed afterward … at that time it was kind of on the back burner.” Avila thrived at IMPA, guided by math wizards like Mikhail Lyubich and Jean-Christophe Yoccoz, and by age 21, he’d earned his Ph.D.

Since that time, Avila has split his years between IMPA and the University of Paris, focused on the research side of the field of dynamical systems, or simply, the changing nature of objects over time. Along the way, he has solved a famous problem known as the “Ten Martini Problem” (another mathematician offered to buy 10 martinis for anyone who could solve it), which elaborated on a theorem first presented by Erwin Schrödinger, a Nobel Prize winner in physics. The Fields award committee stated that Avila’s “signature combination of tremendous analytical power and deep intuition about dynamical systems” has “unblocked a whole direction of research.”

But back home, the math scene isn’t so promising, and Avila recognizes that he has a “responsibility” to spread awareness of his field. He thinks the future of math in Brazil is dependent on improving the basic understanding of professors. “How,” he asks, “can they teach innovative, in-depth thinking if they don’t fully understand the concepts themselves?” The key, he says, is investing in advanced math training for students who can then become a new generation of teachers — “a complicated problem,” he acknowledges, squinting his eyes and furrowing his brow.

Meanwhile, some Brazilians are finally taking notice. During one of Avila’s lectures at a literary festival in the town of Paraty, people filled up the largest venue, then crowded under an outside tent — in pouring rain, no less — to hear the golden son speak. Though reticent and even a bit defensive at times during our lunch of fish stew the day before, Avila came alive under the warm stage spotlights, drawing laughter from the crowd and posing for photographs afterward in a tight black T-shirt and freshly confident smile.


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