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

Key Takeaways:

• Yu Deng has earned the Fields Medal for his role in placing the laws of physics on a rigorous mathematical footing.
• His work addresses a component of David Hilbert’s sixth problem, bridging key equations in physics.
• Deng’s method involves cutting long chains of interactions into shorter segments, making them manageable for statistical predictions.
• He and his collaborators proved that repeated collisions do not disrupt the overall independence of particles, resolving a core assumption of the Boltzmann equation.
• Deng’s achievement continues the University of Chicago’s legacy of producing Fields Medalists, marking him as the 11th so honored.

A Historic Honor

University of Chicago mathematics professor Yu Deng has been awarded the Fields Medal, often regarded as the highest accolade in mathematics. “On behalf of the whole University of Chicago community, I offer warm congratulations to Professor Deng,” said UChicago President Paul Alivisatos, praising Deng for “solving a problem that puzzled generations of scholars.”

Hilbert’s Legacy

Deng’s recognition stems from his solution to one of a group of problems outlined by the German mathematician David Hilbert at the 1900 International Congress of Mathematicians. Hilbert’s sixth problem seeks a rigorous connection among the equations describing gas motion at different scales, spanning from the smallest particle interactions to large-scale fluid behavior.

The Breakthrough Method

Trained in partial differential equations (PDEs) and probability, Deng began his research exploring wave turbulence—analyzing how energy propagates through systems of waves. In one moment of insight, while dining at a Korean fried chicken stall, he realized how to split long-term interactions into shorter segments. This approach enabled him to track even the most intricate patterns that waves (and later particles) can form, proving that statistical predictions remain valid despite repeated behavior-changing collisions.

Proving Boltzmann’s Assumption

Deng’s success in wave turbulence laid the groundwork for tackling Hilbert’s sixth problem. In the late 19th century, Ludwig Boltzmann proposed an equation for predicting the distribution of gas particles, assuming they rarely collided repeatedly. Although mathematician Oscar Lanford proved the theory viable for short time spans in 1975, no one could confirm its validity over longer intervals—until Deng, along with collaborators Zaher Hani and Xiao Ma, extended the proof. Their work shows that even for extended durations or confined spaces, successive collisions do not undermine the overall statistical independence of particles.

Deng’s Roots and Academic Path

Growing up in Shenzhen, China, Deng developed a passion for problem-solving early. He excelled at math competitions and was even a talented Go player. After winning gold at the International Mathematical Olympiad, he went on to study at Peking University, transferred to MIT, and later earned his Ph.D. from Princeton University. He joined the University of Chicago in 2024 and has now become the 11th current or former UChicago mathematician to earn the Fields Medal.

Looking Ahead

Having answered a piece of Hilbert’s sixth problem, Deng and his collaborators continue to explore challenges in PDEs and statistical physics. “There are many things I am interested in,” he said, highlighting the long-term propagation of randomness in physics as a next step. Alongside the Fields Medal, Deng has also received the Gold Medal of the International Congress of Chinese Mathematicians, a Clay Mathematics Institute Research Award, and other significant honors. As Ka Yee C. Lee, dean of the Physical Sciences Division, affirmed, “This richly deserved distinction recognizes Yu’s accomplishments in bridging across mathematics and physics, and his promise of shaping the course of mathematical inquiry.”