“FAR-REACHING CONJECTURES”: Akshay Venkatesh, recent appointee to the Institute for Advanced Study faculty and Princeton University alumnus, has been awarded the 2018 Fields Medal, widely considered as the Nobel Prize for mathematicians. (Photo by Dan Komoda, Institute for Advanced Study)

By Donald Gilpin

Akshay Venkatesh, recently appointed to the permanent faculty of the Institute for Advanced Study (IAS), has been awarded the Fields Medal, widely considered as comparable to the Nobel Prize for mathematicians.

The 36-year-old Venkatesh, who earned his PhD in mathematics at Princeton University in 2002, has worked as a math professor at Stanford University since 2008 and served as a distinguished visiting professor at IAS’s School of Mathematics during the past year.

In presenting the award to Venkatesh, along with three other recipients, at the International Congress of Mathematicians in Rio De Janeiro on August 1, the International Mathematical Union (IMU) cited Venkatesh’s “profound contributions to an exceptionally broad range of subjects in mathematics, including number theory, homogenous dynamics, representation theory, and arithmetic geometry.”

The IMU citation noted, “He solved many longstanding problems by combining methods from seemingly unrelated areas, presented novel viewpoints on classical problems, and produced strikingly far-reaching conjectures.”

IAS Director Robbert Dijkgraaf stated, “The Fields Medal is an incredible honor for a young mathematician, and the Institute is exceptionally pleased that Akshay Venkatesh has received this most deserved recognition.” On the occasion of Venkatesh’s appointment to a permanent post at IAS in May, Dijkgraaf commented on the importance of his work: “Akshay is among the most influential contemporary mathematicians, and his appointment ensures the furtherance of the Institute’s pioneering research in the interconnected fields of number theory and representation theory. With his enthusiastic drive to explore unknown territories and his ability to develop new insights and relations between fields, Akshay’s contributions are bound to be revolutionary and will help to define the future shape of mathematics as a whole.”

Forty-two of the 60 mathematicians who have received the Fields Medal, as well as 33 Nobel Laureates, have been affiliated with the IAS. The Fields Medal is awarded every four years to scholars less than 40 years old to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.

“The breadth and richness of Venkatesh’s work, as well as the ease with which he works with mathematicians in different fields, has resulted in a large worldwide following, especially among young mathematicians,” according to an IAS press release.

“The signature of his work is great originality and intuition coupled with the development of powerful and general techniques in novel and unexpected settings,” the release continues. “As a result, his developments on long-standing problems in number theory have a broad impact in related areas.”

Memories

Venkatesh was born in New Delhi, India, but raised in Perth, Australia, where his family moved when he was only 2. Mathematics has always been an important part of his life. “I think just manipulating numbers makes me feel happy,” he said in a biographical video made by Simons Foundation in cooperation with the IMU. “I was involved in these problem-solving competitions.”

When Venkatesh was 12 and already a senior in high school, he went to the Math Olympiad international competition and won a bronze medal. When he graduated from University of Western Australia four years later, in 1997, he realized, “I was interested in number theory and there weren’t so many people in Australia who were interested in number theory, so that was an impetus to go on to graduate school.”

Venkatesh enrolled in Princeton University’s graduate school in mathematics at the age of 16, and received his PhD four years later in 2002. In the following years he taught at the Massachusetts Institute of Technology and served as associate professor at New York University’s Courant Institute of Mathematical Sciences before joining the faculty of Stanford University in 2008.

Venkatesh has won numerous rewards for his research. He served as a distinguished professor in the IAS School of Mathematics in 2017-18, leading a special program on analytical and topological aspects of locally symmetric spaces.

Currently in residence at IAS with his wife Sarah, a music teacher finishing her doctoral dissertation in musicology at Princeton University, and their young daughters Tara and Tuli, Venkatesh does find time for life outside the world of mathematics.

“In math we tend to be obsessive, and it’s good, I think, to be forcibly stopped from thinking about something,” he said in the Simons-IMU video. “Children are very good at really shutting off your attempt to think about anything else.”

Venkatesh is also an enthusiastic runner. “So running definitely clears my mind,” he said. “It’s very meditative. If I’m thinking about a problem and I’m running and I’m still thinking about the problem, I just have to run a little bit faster, and then I can’t think about it any more.”

He described the frustrations and joys of his profession. “A lot of the time when you do math, you’re stuck,” he said. “But at the same time there are all these moments when you feel privileged that you get to work with it. And you have the feeling of transcendence. you feel like you’ve been part of something really meaningful.”

Praising Venkatesh’s virtuosity and his role as a trailblazer of new directions in research, the IMU commented on Venkatesh’s work in mathematics. “Most mathematicians are either problem-solvers or theory-builders. Akshay Venkatesh is both. What is more, he is a number theorist who has developed an unusually deep understanding of several areas that are very different from number theory. His breadth of knowledge allows him to situate number theory problems in new contexts that provide just the right setting to highlight the true nature of the problems. Only 36 years of age, Venkatesh will continue to be an outstanding leader in mathematics in years to come.”

Commenting on the excitement of the past week, Venkatesh said, “The award came as a surprise for me, and my brief moment of fame was quite an experience! But I am much looking forward to some peace and quiet, or at least as much as my kids will let me have.”