UChicago Prof. Yu Deng receives Fields Medal, highest honor in mathematics

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University of Chicago mathematics Prof. Yu Deng has received the Fields Medal for his contributions toward placing the laws of physics on a rigorous mathematical foundation. The Fields Medal , announced today at the International Congress of Mathematicians in Philadelphia, is awarded every four years to recognize outstanding mathematical achievement for existing work and for the promise of future achievement. In the absence of a Nobel Prize for mathematics, the Fields Medal is regarded as the highest professional honor a mathematician can attain. “On behalf of the whole University of Chicago community, I offer warm congratulations to Professor Deng. Today he is receiving the highest recognition for the rigor and significance of his contributions to mathematics,” said UChicago President Paul Alivisatos. “In his work, we see a scholar who has pursued fundamental questions to great depths and illuminated new understanding in the process. He has solved a problem that puzzled generations of scholars and in so doing, he is a true exemplar of what dedication to knowledge creation can achieve. We are proud of his accomplishments and that he is a member of our community of scholars.” Deng was honored for addressing one of a famous set of problems laid out more than 125 years ago, at the 1900 International Congress of Mathematicians, by German mathematician and philosopher David Hilbert. These problems have since become benchmarks of progress in the field. Specifically, Deng and his collaborators cracked a longstanding problem within the overarching effort to mathematically connect the equations governing the motion of gases from the smallest to the largest scales. The award also recognizes Deng’s research on the equations that govern wave dynamics that laid the foundation for this historic result. “Yu’s beautiful and original work resolves a fundamental problem in mathematical physics that goes back to Hilbert more than a century ago,” said Frank Calegari, professor and chair of UChicago’s Mathematics Department. “It also introduces powerful new methods that will shape future research. This is a landmark achievement.” Deng is the 11th current or former UChicago mathematician to become a Fields Medalist. "This is a great honor for me—an important recognition for my works with collaborators and for the field that I am representing," said Deng. A pattern of problem-solving Deng’s mathematical roots run deep. He grew up in Shenzhen, China, where his computer programmer father would take him hiking, giving him little questions in combinatorics—the branch of mathematics focused on counting—to solve along the way. In his youth, Deng displayed a gift for problem-solving, excelling in both math competitions and tournaments of Go, an ancient Chinese strategy game played with black and white stones on a grid. Deng said he entertained the idea of becoming a professional Go player before devoting himself to academia. In 2006, at 16 years old, he represented China at the International Mathematical Olympiad and won a gold medal. “At that time, I realized, okay, so maybe I do have some talent in math,” said Deng. The following year, he was admitted to Peking University, later transferring to MIT, where he became a Putnam Fellow in the 2010 William Lowell Putnam Mathematical Competition. Deng earned a bachelor’s degree in mathematics in 2011, followed by a Ph.D. from Princeton University in 2015. He joined UChicago in 2024. The breakthrough that earned Deng the Fields Medal, however, had unexpected beginnings. While he was spending a semester at Brown University’s Institute for Computational and Experimental Research in Mathematics in 2021, a thought came to him while in a Korean fried chicken stall in Providence, Rhode Island. Deng wasn’t thinking about a new project, but in a moment of chicken-fueled insight, he hit on an idea: a way to solve complex problems by breaking them into smaller, more manageable pieces. This laid the foundation for his eventual resolution to Hilbert’s sixth problem—a challenge to ground physics in rigorous mathematics. A way to understand nature Deng works on analysis of partial differential equations, or PDEs, as a way of understanding nature. A differential equation describes how something evolves: an ordinary differential equation might describe how a falling object speeds up due to gravity, but a partial differential equation handles questions with more than one dimension, such as how temperature spreads across both space and time. Deng’s work involves PDEs connected to probability. “There is a lot of randomness in this world,” he said, “and we need a mathematical way to capture it.” Prior to turning his attention to Hilbert’s sixth, Deng’s focus was using PDEs to study wave turbulence, looking at how energy spreads through systems of waves, like those found on the surface of the ocean or waves in quantum systems. This work proved to be vital to his award-winning breakthrough. His goal was to mathematically prove that energy spreads predictably, despite the tendency of waves to influence each other, shaping and changing future activity. Statistical predictions work by averaging across large numbers to determine what is typical . This can only work if the elements work independently. When waves build relationships with other waves, they are no longer acting alone, and it is not possible to determine how a typical wave behaves; you can’t make predictions if you don’t know what typically happens. Deng and his collaborator Zaher Hani, a professor of mathematics at the University of Michigan, accounted for those behavior-changing interactions by constructing a mathematical ledger that could capture every possible pattern. These patterns range from interactions where waves meet and then continue on their separate ways, to encounters that form such a strong, behavior-affecting relationship that a feedback loop forms. For extremely short time periods, the most strongly correlated, disruptive interactions were negligible, and the predictability of wave turbulence mathematically held. However, with more time comes more frequent and complex interactions, and more opportunity to forge shared histories. The team needed a way to prove that the math held over longer periods. It was in that chicken stall that a thought occurred to Deng: “What if we try to divide long time intervals into short time intervals?” That is, what if they could cut up those interaction histories into shorter, more manageable segments? Deng and Hani developed an algorithm that cuts up the complex patterns. The segments, representing smaller periods of time along the interaction record, still add up, but the entries are now small enough to manage statistically. What their results showed was that even over long time periods, the impact of those coupled interactions is negligible; averaging is possible; and statistical predictability holds. Bolstered by this success, Deng set his sights on a new—yet very old—problem to solve. Hilbert’s challenge One mission often associated with Hilbert’s sixth problem is bridging the equations describing the behavior of gases at the smallest, middle, and largest scales. The motion of individual gas particles is described by Newtonian mechanics. The likelihood of finding particles in certain places at certain speeds is described by the Boltzmann equation. The behavior of gas as a continuous medium is described by the Navier-Stokes equations. The ultimate goal is to show that each set of equations logically leads to the next. The link between the middle and largest scales had already been established. But the link between the smallest to the middle scales, Newtonian to Boltzmann equations, was still elusive. Ludwig Boltzmann believed his equation, developed in 1872, followed from Newton’s laws, but only if the particles don’t collide repeatedly—they must move independently. Proving that assumption mathematically was the challenge. In 1975, mathematician Oscar Lanford showed this proof, but only for very short time periods. Over longer periods of time, particles have more opportunities to collide more than once. There needed to be a way to analyze an impossibly large number of collision patterns. Deng and Hani realized that their research on wave turbulence could translate to particle collisions where repeated interactions build shared histories that threaten a particle’s independence. This makes it harder to statistically predict the behavior of the group at the middle scale from the motion of its individual members at the smallest scale. At a conference in 2023, Deng and Hani met Xiao Ma, a recent graduate from Princeton who studied under Deng’s former advisor, Alexandru Ionescu. “We realized that he's very good in these fields,” said Deng, “so we invited him into the project.” Particles behave very differently than waves, so the trio had to incorporate those differences, but they were able to use the same approach: a ledger to record every possible collision history—whether a particle pair had collided once or 100 times, for instance—and a cutting algorithm to break down the most complex histories into manageable pieces. They started with an easier scenario: gas in an infinite amount of space, where particles have room to disperse and eventually stop colliding all together. They then moved on to gases in a box, where the particles are increasingly more likely to re-collide, creating more complicated patterns. They found that, while particle re-collisions happen, especially inside a bounded box where particles have plenty of opportunity to meet repeatedly, the impact of re-collisions on the overall independence of the system was negligible. Deng and his team mathematically proved Boltzmann’s assumption and completed the chain. Hilbert’s sixth problem, at least in this specific case, was resolved, and a new methodology for analyzing complex interactions was introduced. Deng, Hani, and Ma revealed their proof in 2025. As for what’s next: “There are many things I am interested in,” said, Deng, “including long-time propagation of randomness in PDEs, and general critical problems in statistical physics.” In addition to the 2026 Fields Medal, Deng has received the Gold Medal of the International Congress of Chinese Mathematicians, a Clay Mathematics Institute Research Award, and the Leonard Eisenbud Prize for Mathematics and Physics from the American Mathematical Society. He has also received a Porter Ogden Jacobus Fellowship, a Sloan Research Fellowship, an ICBS Frontiers of Science Award, an MCA (Mathematical Council of the Americas) Prize, an Oberwolfach Prize, and an Antonio Ambrosetti Medal. “Yu’s extraordinary achievement adds to the University’s and the Division’s long tradition of innovative, foundational mathematics,” said Ka Yee C. Lee, dean of the Physical Sciences Division. “This richly deserved distinction recognizes Yu’s accomplishments in bridging across mathematics and physics, and his promise of shaping the course of mathematical inquiry.”