From Child Prodigy to Fields Medal Nobel of Math

It was July 1993. In Williamsburg, Virginia, the humidity was bad enough to make a person question their life choices leading up to that time and place, especially if those choices had led them to an examination hall filled with the scratching sounds of pencils on paper. Inside this room sat the future of physics. They were the competitors of the 24th International Physics Olympiad. Most of them were 18 or 19 years old. They were on the razor's edge of adulthood. They had facial hair, driving licenses, and were thinking about university entrance exams and scholarships. Then there was the boy at the small desk in the middle. His name was Akshay Venkatesh. He was just 11 years old. His feet did not quite reach the floor. He looked less like a competitor and more like someone's little brother who wandered in by accident and decided to stay because the air conditioning was running. He was representing Australia. While the older students around him were sweating over the calculation of torque on a rotating rigid body or the magnetic field of a solenoid, worrying about their futures, Akshay was doing something else entirely. He was playing. For him, the questions were puzzles. They were games. He scribbled his answers with the focus of a child building a Lego castle. He was not intimidated by the older boys. He did not seem to realize he was supposed to be intimidated. The physics problems were hard, certainly. They demanded a mastery of mechanics and electromagnetism that most physics majors did not achieve until their second year of university. But for Venkatesh, they were simply the next interesting thing to look at. When the results were posted, the 11-year-old boy won a bronze medal. It was a stunning achievement, making him the youngest medal winner ever in the 50-year history of physics olympiads, a record that stays till date. The physics community prepared to welcome its next great prodigy. They expected him to return the next year and turn that bronze into silver and then gold. He chose to do none of those things. He walked away. He never competed in the physics olympiad again. He turned his gaze toward mathematics. He competed in the international mathematics olympiad next year at the age of 12 and won a medal there too. This was just the beginning of a stellar career trajectory of Akshay Venkatesh. Fast forward 25 years, he stood on a stage in Rio de Janeiro. The humidity was similar, but the stakes were different. It was 2018. He was accepting the Fields Medal, which is often described as the Nobel Prize of mathematics, though that comparison fails to capture the scarcity of the award. It is given only every 4 years, and only to mathematicians under the age of 40. It is a recognition not just of what you have done, but of who you are, in the pantheon of the mind. The man who accepted the medal was no longer the boy whose feet dangled from the chair in Williamsburg. He was tall and thoughtful. He wore a look of perpetual, mild amusement, as if he had just heard a joke that only he understood. He was a professor at the Institute for Advanced Study in Princeton, New Jersey. He worked in the same quiet corridors where Albert Einstein and Kurt Goodall once walked. In the siloed world of pure mathematics, researchers usually pick a lane. You are a number theorist, or you are a topologist, or you study dynamics. You dig a deep hole in your specific patch of ground, and you stay there, protecting your turf, deepening your specialized knowledge. Venkatesh did not do this. He wandered. He walked across the fences that separate these fields. He saw a problem in number theory, picked it up, carried it over to the world of topology, fixed it with tools that should not work there, and brought it back. He is the connector. Akshay Venkatesh was born in New Delhi, India, in 1981. By the time he was two years old, his family had packed their lives into suitcases and flown across the Indian Ocean to Perth, Australia. He grew up on the edge of the world, in the most isolated capital city on the planet. Sveta Venkatesh, his mother, was not a stage mother managing a prodigy. She was a powerhouse in her own right. She became a computer science professor, and later the director of the Center for Pattern Recognition and Data Analytics at Deakin University. She dealt with complex systems and machine learning long before those terms became buzzwords in Silicon Valley. His father was a mechanical engineer. Learning in the Venkatesh home happened through osmosis. It was in the air, like the smell of cooking or the dust motes dancing in the afternoon light. There were books everywhere, remnants of his parents' own college years. The young Akshay did not just read children's books about hungry caterpillars. He pulled his father's engineering textbooks off the shelf. He opened them. He looked at the diagrams of engines and forces. He asked questions. I learned a lot of things from their college math textbooks, Venkatesh recalled. His father did not dismiss the questions of a six-year-old. He did not say, wait until you are older. He sat down and answered them. They talked about how things worked. They talked about gas turbines, cycles of engines, and physics. When the boy struggled with Euclidean geometry in school, his father sat with him and worked through the logic. This environment created a mind that did not see boundaries between schoolwork and real life. Learning was just another form of playing. Akshay attended Scotch College, a prestigious boys' school in Perth. It is the kind of place with manicured ovals and a long tradition of producing lawyers, doctors, and captains of industry. Venkatesh was clearly different from the other boys, but he was not an outcast. His teachers faced a unique problem. What do you do with a student who finishes the textbook in the first week of the semester? What do you do when the curriculum is an obstacle rather than a guide? They did the only sensible thing. They let him go. They advanced him. They accelerated his learning in mathematics and science, but they kept him with his peers for social reasons where possible. They understood that a 12-year-old boy needs 12-year-old friends, even if he calculates like a 30-year-old professor. He grew up playing cricket. He devoured science fiction and fantasy. He lived in the worlds of Isaac Asimov. He liked the idea that the rules of reality could be different if you just imagine them clearly enough. Mathematics, he would later realize, is the ultimate fantasy novel. It is a world you build entirely in your head. It has its own laws, its own geography, its own monsters. But unlike a fantasy novel, once you build it, it is real. It is more real than the chair you are sitting on. The chair will eventually rot and fall apart. The number seven will never change. The structure of a prime number is eternal. For a boy growing up in the isolation of Perth, mathematics offered a landscape that was infinite. There is a difference between being fast and being deep. The Olympiads are a race. You have a set number of problems. You have a clock. You have a piece of paper. You have to find the trick. Every Olympiad problem has a trick. If you are smart enough and fast enough, you find the key. You turn it. The door opens. You win. Venkatesh was very, very fast. After his bronze medal in physics at 11, he switched his focus to mathematics. The next year, at 12, he went to the International Mathematical Olympiad, IMO, in Hong Kong. He won a bronze medal there too. He was the first Australian to win medals in both disciplines. In 1995, Akshay Venkatesh put on a backpack and walked into the University of Western Australia, Oowah. He was 13 years old. The other students were 18, 19, 20. They were driving cars and going to the tavern on campus. They were worrying about relationships and part time jobs. Venkatesh was a child, but he was not there to be a mascot. He was there to work. He enrolled in a four-year Bachelor of Science with honors. He finished it in three. He completed the second year math course exams by proving he could write all the exams without taking the classes. He just knew it. He had read the books. He had understood the concepts. Why sit in a classroom for a semester when you already know the ending? By the age of 16, he graduated with first-class honors in pure mathematics. He was the youngest person ever to do so at the university. He won the J.A. Woods Memorial Prize for the most outstanding graduating student. It was a triumph, but it was also a trap. When you are the boy who finishes everything first, you begin to think that speed is the only metric of success. You begin to think that if you cannot solve a problem in an hour, you are failing. You begin to believe that intelligence is measured by velocity. This was the mindset he carried to Princeton, and it almost broke him. Princeton University is the Vatican of mathematics. It is where the high priests live. It is a place of quiet lawns and gothic stone, where the air is thick with the ghosts of geniuses. In 1998, Akshay Venkatesh arrived in New Jersey. He was 17 years old. He was a Ph.D. student. He had left the safe, sunny isolation of Perth for the intense, competitive pressure cooker of the Ivy League. His advisor was Peter Sarnak. Sarnak is a legend, a South African mathematician with a booming voice and a presence that fills the room. He is known for his work in number theory and analysis. He is also known for being a demanding mentor. He does not suffer fools, and he does not coddle students. When Sarnak first met the teenage Venkatesh, he decided to test him. He gave the boy a book on the representation theory of semi-simple groups. This is dense, difficult material. It is the kind of book that makes young mathematicians weep. It is abstract, heavy, and unforgiving. Sarnak expected Venkatesh to come back in a few weeks, asking for something easier. He expected the prodigy to stumble. Venkatesh disappeared. A month later, he knocked on Sarnak's door. He started explaining the book to Sarnak. He hadn't just memorized it. He had metabolized it. Sarnak realized then that the boy had a tremendous intuition. He saw things. He didn't just follow the proofs. He saw the architecture behind them. He put things together in unusual ways, Sarnak said. But inside, Venkatesh was falling apart. The genius myth was turning on him. In Perth, he was the fastest. In Princeton, everyone was fast. Everyone was brilliant. But more importantly, research wasn't about speed. It was about being stuck. I don't feel like I had a happy time as a graduate student, Venkatesh confessed. He worked on his thesis, limiting forms of the trace formula. It was good work. It was solid. But Sarnak had suggested the key idea. To Venkatesh, this felt like failure. If the professor gave you the idea, were you really a mathematician, or were you just a technician? A pair of hands executing someone else's brainwave. He saw the other students and believed they possessed a spark that was absent in him. This led him to feel like a fraud and perceive himself as mediocre. He considered quitting. He looked at the tech boom happening in the late 90s. The internet was exploding. Machine learning was starting to be a thing. Maybe he should go work for a startup. Maybe he should just get a job, make money, and leave this painful world of pure mathematics behind. Venkatesh survived because of a conversation with a friend, Jordan Ellenberg. Venkatesh told Ellenberg he felt like he wasn't cut out for this. Ellenberg looked at him and said, sometimes people see things in you that you don't see. He stayed. He finished his PhD at 20. He went to MIT as a C.L.E. Moore instructor. Then he went to NYU. He started to learn the most important lesson of his life. A lot of the time when you do math, you're stuck, he said. But at the same time, there are all these moments where you feel privileged that you get to work with it. Venkatesh's genius is not that he is the best number theorist in the world. It is that he is the best topologist in the world of number theory, and the best number theorist in the world of topology. He smuggles tools. Most mathematicians stare at a problem in number theory and try to solve it with number theory tools. They dig deeper into the same hole. They use the same shovels as their ancestors. Venkatesh climbs out of the hole, walks over to the field of dynamics, picks up a tool used to study bouncing billiard balls, walks back to the number theory hole, and says, try this. His signature move is translation. He takes a rigid, discrete problem about whole numbers, which are hard, spiky, and stubborn, and translates it into a problem about smooth, curving shapes, which are flexible and easier to work with. One of his major contributions involves the sub-convexity problem for L-functions. L-functions are infinite sums that are generalizations of the Riemann zeta function. They are deeply connected to the distribution of prime numbers. Mathematicians want to understand the size of these functions. The convexity bound is a standard limit on how large these functions can get. Breaking this barrier and finding a sub-convexity bound is a holy grail in the field, because it implies a deeper randomness in the distribution of numbers. Venkatesh used a novel approach. He imagined the problem in terms of a ball bouncing inside a triangle, or a shape where the ball does not slow down. He asked questions about what spaces the ball avoids or prefers. He used the physics of motion to solve the arithmetic of static numbers. He also drew on metaphors from the physical world to explain his work. He spoke of the mixing of paint to describe equidistribution. If you drop a dollop of red paint into a bucket of white paint and stir it, the red eventually spreads out until the whole bucket is pink. This is mixing. In mathematics, Venkatesh studied how arithmetic objects spread out over a space. He proved that in certain contexts, these objects become equidistributed just like the paint. He also worked on the topology of locally symmetric spaces. These are complex geometric shapes that can have holes in multiple dimensions. Venkatesh and his colleagues found unexpected symmetries in these spaces. They found that the homology groups, which measure the holes in the space, exhibited patterns that number theory could predict. He formulated bold conjectures that relate these topological features to motivic cohomology. This work is part of the Grand Langlands program, which seeks to unify all of mathematics. The culmination of this work led him to Rio de Janeiro in 2018. The International Congress of Mathematicians in Rio was a massive affair. It was the first time the event was held in the Southern Hemisphere. The opening ceremony was grand. He stood on the stage as the second Australian and the second person of Indian descent to win the prize. He joined the ranks of Terence Tao and Manjul Bhargava. When interviewed, he did not speak of conquest. He spoke of the emotional journey. He said that you have this sensation of transcendence, and you feel like you have been part of something really meaningful. He was acutely aware of the human cost of this transcendence, the long hours, the years of being stuck, the doubt. He wanted the world to know that the genius on the stage was also the graduate student who almost quit to write code for a startup. Venkatesh is not a monastic figure who lives only for equations. He is a husband and a father. He is married to Sarah Paden. She is a musicologist who has studied the intersections between Buddhism and experimental music in America. She studied at Princeton, and her work focuses on the cultural and aesthetic relationships in artistic practice. They have two daughters. Venkatesh joked in an interview that it was a lot harder to physically tie up his daughter's hair than to do a mathematical analysis of pigtails. In recent years, Venkatesh has turned his attention to the philosophy of his field. He is deeply concerned with the role of the human mind in an age of increasing automation. He has written and spoken about the difference between formal mechanical reasoning and human understanding. He argues that we must focus on humans rather than tech. He wants to understand mathematics in terms of the way we think about it, rather than just its symbolic trappings. He cites the work of David Hilbert, who tried to formalize geometry by saying one must be able to say table, chair, beer glass, instead of point, line, plane. Hilbert meant that the logic should hold regardless of the objects, but Venkatesh points out that while this is logically true, it is psychologically false. We cannot understand geometry if we replace points with beer glasses. Our intuition matters. He believes that the origin of mathematical questions lies in the realm of human volition. Computers can check proofs. They might even generate proofs one day. But they do not have the volition to ask why is this interesting, or what is beautiful. He warns that if we offload too much of the work to machines, the human insights will change. We will stop having insights about the math, and start having insights about the behavior of the computer program. He is currently a professor at the Institute for Advanced Study in Princeton. He occupies the Robert and Louisa Fernholz Professorship. He continues to run seminars and mentor students. He is known for his teaching style, which avoids excessive abstraction and focuses on the big picture. He tells his students that undergraduate teaching is nice because it forces you to put your subject in a larger context. Akshay Venkatesh is in his early 40s. In mathematics, this is often considered the afterlife. The field's metal is usually the peak. But Venkatesh seems to be pivoting again. He is currently working on arithmetic topology. He is trying to connect the deepest parts of number theory with the structure of quantum field theory. Recently, he has been exploring the tetrahedral symbol, a generalization of the six symbols from quantum mechanics, in collaboration with Griffin Wang. This work connects the symmetries of tetrahedra with deep arithmetic structures, seeking to find the electricity that runs through numbers. He is not done.