## Math Award to Brazilian

Artur Avila, a Brazilian, has won the Fields Medal, the most prestigious award in the world given in mathematics. The Fields Medal is considered the equivalent of the Nobel Prize, as there is no Nobel award given in math. Dr. Avila works at the National Institute of Pure and Applied Mathematics in Brazil and the National Center for Scientific Research in France.

The International Mathematical Union has made Avila the first Brazilian recipient of the Fields Medal, awarding the 35-year-old what many consider the equivalent of a Nobel Prize in mathematics for his “profound contributions to dynamical systems theory” that “have changed the face of the field,” according to the prize selection committee. There are no exact mathematical solutions for many dynamical systems, even simple ones.

“He’s one of the very best analysts in the world,” said Jean-Christophe Yoccoz, a renowned Collège de France mathematician and 1994 Fields medalist. Of the many talented post-doctoral researchers Yoccoz has advised, he said, “Artur is in a class by himself.” Most mathematicians focus on a narrow subfield and have a low success rate, Yoccoz explained, but Avila “attacks many important problems and solves many of them.”

As expected, Avila is humbled by this great honor. He notes that world opinion focused on Brazil asks how the world’s seventh-largest economy that has managed to win five World Cup titles has never won a Nobel Prize. Even Argentina, with a population one-fifth the size of Brazil’s, boasts five Nobel Prize winners. “It’s not good for the self-image of Brazil,” Avila said.

Months before the Fields medal announcement, the Brazilian mathematics dynamicist Welington de Melo predicted that his former doctoral student would win math’s highest honor. “It’s going to be extremely important for Brazil,” he said. “We never before received such a high prize. It is especially important because Artur was a student in Brazil the whole time.”

Avila was born to parents who could not envision their son growing up to become a pure mathematician because they had never heard of one. His father’s formal education in the rural Amazon region didn’t start until his teenage years, but by the time Artur was born, his father had become an accountant in a government reinsurance agency. Artur’s father was able to provide a middle-class lifestyle in Rio for his family and buy math books for his quiet son, who was more interested in reading than imitating Pelé’s bicycle kick. As the years passed, Avila increasingly focused on mathematics to the exclusion of almost everything else. He often did poorly in other subjects and was expelled after the eighth grade. He said he “left his Catholic grammar school completely unprepared for normal social interaction.”

While in high school, Artur discovered IMPA, where Brazil held its Olympiad award ceremonies each year. There, he met prominent mathematicians like Carlos Gustavo Moreira and Nicolau Corção Saldanha. While still in high school, he began studying post-graduate-level mathematics. By the age of 19, he was making important contributions to his field of math. He earned his Ph.D. at age 21.

In Brazil, Avila could focus on mathematics without the career pressures he might have faced in the United States. “It was better for me to study at IMPA than if I were at Princeton or Harvard,” he said. “Growing up and being educated in Brazil was very positive for me.”

Asked about his working habits today, Artur confessed: “I would get fired pretty fast from most jobs,” he said, adding that he sleeps well past noon and is “not good at managing time.”

Now a dual citizen of Brazil and France, Avila spends half the year in Paris as a research director at CNRS, France’s largest state-run science organization, and the other half in Rio as a fellow at IMPA, Brazil’s national institute for pure and applied mathematics.

The Fields Medal is given every four years, and several can be awarded at once. Dr. Avila was among four recipients this year. The others were Manjul Bhargava of Princeton University; Martin Hairer of the University of Warwick in England; and Maryam Mirzakhani, a professor at Stanford University in California. Dr. Mirzakhani, an Iranian mathematician, is the first woman ever to receive a Fields Medal. The 52 medalists from previous years were all men.

“This is a great honor. I will be happy if it encourages young female scientists and mathematicians,” Dr. Mirzakhani was quoted as saying in a Stanford news release. “I am sure there will be many more women winning this kind of award in coming years.” While women have reached parity in many academic fields, mathematics is still dominated by men, who earn about 70 percent of the doctoral degrees.

The Fields Medal was conceived by John Charles Fields, a Canadian mathematician, in recognition of work already done and as an encouragement for further achievement. Judges have interpreted the terms of the Fields trust to mean that the award should usually be limited to mathematicians age 40 or younger.

Brazil is set to host the 2017 International Mathematical Olympiad and the 2018 International Congress of Mathematicians, where the next Fields medalists will be announced. “These next four years are naturally going to be a good period to develop math in Brazil,” Avila said.

*[Information for this article comes from research done by The New York Times and the Quanta magazine website. It was edited by CIE.]*