The 2026 International Congress of Mathematicians (ICM) opened in Philadelphia on the morning of July 23rd local time, with the International Mathematical Union officially announcing the winners of the 21st Fields Medal. Peking University's 2007 undergraduate alumni Wang Hong and Deng Yu both received the award, marking the first time Chinese mathematicians have won the Fields Medal.
The Fields Medal is awarded every four years to up to four scholars under 40 who have made outstanding contributions to mathematics, representing one of the highest honors in the field, often called the "Nobel Prize of Mathematics."
Wang Hong, in collaboration with Joshua Zahl, used a refined multi-scale inductive method to prove the three-dimensional Kakeya Conjecture, which had puzzled mathematicians for over a century. Additionally, Wang Hong, along with Larry Guth, Alex Iosevich, and Yu Meng Ou, achieved major breakthroughs on the two-dimensional Falconer distance problem, and with Ren Kaiyuan, completely solved the Furstenberg set conjecture.
Deng Yu, working with Zaher Hani and Ma Xiao, completed a rigorous derivation of the hard-sphere particle system to the Boltzmann equation over long time scales, establishing a derivation chain from Newtonian hard-sphere dynamics to the Boltzmann equation and then to the Navier-Stokes equations, achieving key progress on Hilbert's sixth problem.
As part of an established academic tradition, mathematicians invited to present at the ICM give either 1-hour or 45-minute talks. Fields Medal winners automatically become invited speakers, with their presentations representing the highest level of international mathematics.
The Beauty of Mathematics, Deep and Subtle
At the 2026 graduation ceremony of Peking University's School of Mathematical Sciences, Academician Tian Gang stated in his speech: "Take our alumni Wang Hong and Deng Yu as examples. Their recent breakthroughs on major mathematical problems are a vivid embodiment of the spirit of 'daring to be first.' This spirit is not just about being first, but about daring to venture into uncharted territories and challenge recognized major problems. It represents the courage to face difficulties and the perseverance for long-term commitment."
This spirit of exploration and the pursuit of simplicity and mathematical beauty come from Wang Hong and Deng Yu's long-term quest, attempts, and persistence, as well as their learning and accumulation at PKU's School of Mathematical Sciences.
The School of Mathematical Sciences has always emphasized exchange, encouraged independent exploration, and continuously expanded open international platforms, shifting from "knowledge instillation" to "thinking stimulation" in talent cultivation. Over the years, initiatives like special research reading seminars, special mathematics lectures, and undergraduate research have fostered a strong atmosphere for learning and enjoying mathematics, with many measures still in place today.
In 2008, after one year in the School of Earth and Space Sciences, Wang Hong transferred to the School of Mathematical Sciences. During her undergraduate studies, she conducted research under Wang Lizhong and completed her thesis "Classical Hodge Theory and Hodge Theory on Metric Spaces" under Liu Zhangju. Wang Hong was accustomed to "reading books and thinking in the library," and believed that mathematics learning requires ensuring basic study time, and on that basis, "resting enough before studying again."
Wang Hong's main research areas are harmonic analysis and geometric measure theory, making her the most outstanding mathematician in the new generation of harmonic analysis.
In June 2025, after proving the three-dimensional Kakeya conjecture, Wang Hong returned to her alma mater for a three-day lecture series, sharing the journey of solving this century-old problem. In 2023, on the 110th anniversary of PKU's mathematics discipline, Wang Hong returned to report during the alumni forum. When asked by students why she chose to delve into harmonic analysis, she replied: "If a problem is very attractive to me, it likely has the ability to attract others too. So there's no need to worry about producing a result that 'only I care about.'"
Now, as the tower of harmonic analysis is further strengthened and the peak of mathematical research is raised a bit higher, the spirit of mathematicians behind the Fields Medal remains deep and subtle, shining even more brightly through persistence and innovation.
For Deng Yu, the path to mathematics began in high school. In 2006, he won a gold medal at the International Mathematical Olympiad (IMO) and was admitted to PKU's School of Mathematical Sciences the following year, transferring to MIT two years later.
From Weiming Lake on the Yan campus to MIT, Princeton, and the University of Chicago, Deng Yu has always maintained a pure love for mathematical research. He enjoys collaborating with other scholars, discussing profound mathematical problems and broadening his research horizons. "Some initially unworkable key ideas were gradually refined through discussion."
Deng Yu's primary research field is partial differential equations (PDEs), with a long-term focus on probability theory in PDEs.
In 2018, when Fields Medalist Jean Bourgain passed away, Deng Yu wrote: "Will we ever, in our lifetime, see the back of our predecessors?"
The answer to this question subtly emerged when he and his collaborators completed key derivations for Hilbert's sixth problem, becoming increasingly clear through continuous exploration of multiple research questions.
Accumulating Steps, Solving Century-Old Problems
"The tower of three immortal conjectures in harmonic analysis all stand on the Kakeya conjecture. If the Kakeya conjecture were disproved, the entire tower would collapse," stated Quanta Magazine.
The Kakeya Conjecture, also known as the Kakeya set conjecture, posits that in n-dimensional Euclidean space, any set containing a unit line segment in every direction has Hausdorff dimension and Minkowski dimension equal to n. It has long been a core problem in geometric measure theory, closely related to several key issues in harmonic analysis.
Wang Hong and Joshua Zahl have now proven the three-dimensional Kakeya conjecture.
"People understand the two-dimensional case of these Kakeya-related problems very well, but we lack the tools to study higher-dimensional problems. So I think this step was necessary; it had to be completed."
On February 24, 2025, Wang Hong and Zahl published the paper "Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions," proving that the Hausdorff and Minkowski dimensions of three-dimensional Kakeya sets are both 3, thus solving this more than century-old conjecture.
In the latest research, the two scholars adopted a new route, transforming the Kakeya set problem, which involves unit line segments in all directions, into a volume estimation problem for unions of δ-tubes (thin tubes) in space. By constructing a refined multi-scale inductive framework and analyzing the geometric structure and overlap of tubular sets at different scales, Wang Hong and Zahl deduced that both the Hausdorff and Minkowski dimensions of three-dimensional Kakeya sets equal 3.
In 1900, at the International Congress of Mathematicians in Paris, David Hilbert proposed 23 problems that later entered the history of mathematics. The sixth problem was particularly special, calling for the axiomatization of physics and the establishment of a rigorous mathematical foundation for the transition from microscopic laws to macroscopic equations.
This problem can be broken into two steps: deriving the Boltzmann equation from Newton's equations, and then deriving the fluid dynamics equations from the Boltzmann equation. The second step has been largely clarified, but progress on the first step had long stalled: how to derive time-irreversible thermodynamic systems from time-reversible Newtonian mechanical systems?
"Our two papers mainly focus on deriving the Boltzmann equation from interacting particle systems. In fact, the core ideas and proof framework essentially come from my previous series of papers with Hani, where we derived the wave kinetic equation (WKE) from the nonlinear Schrödinger (NLS) equation."
Facing extremely complex collision particle set structures, Deng Yu, Hani, and Ma Xiao decomposed particle collision patterns and designed cutting algorithms to break high-dimensional integrals into composites of basic integral operators, thereby establishing a rigorous derivation process.
Based on this, Deng Yu and collaborators published two important papers, completing the derivation from Newtonian hard-sphere dynamics to the Boltzmann equation, and then to the Navier-Stokes equations. In the gas model, they established a path from microscopic descriptions of individual particles to macroscopic descriptions of the gas.
PKU Mathematics, A Forest of Giants
Throughout the history of the ICM, an increasing number of scholars from PKU's School of Mathematical Sciences have appeared in the lecture hall.
In 2002, China hosted the 24th International Congress of Mathematicians (ICM-2002), the first time a developing country held the ICM. Academician Tian Gang was invited to give a 1-hour talk. PKU participated fully in the application, organization, and hosting of this congress, making outstanding contributions.
In 2018, two PKU faculty members, Xu Chenyang and Zhang Pingwen, along with six alumni from the School of Mathematical Sciences—He Xuhua, Jin Shi, Tang Tao, You Jiangong, Yun Zhiwei, and Zhang Wei—were invited as speakers at the 28th ICM.
In 2022, six PKU faculty members—Ding Jian, Dong Bin, E Weinan, Liu Yi, Zhang Zhifei, and Zhu Xiaohua—along with eight alumni from the School of Mathematical Sciences—Li Chi, Liu Gang, Wang Guozhen, Wang Lu, Xu Zhouli, Yu Bin, Zhou Xin, and Zhu Xinwen—were invited as speakers at the 29th ICM.
In 2026, PKU's 2007 undergraduate alumni Wang Hong and Deng Yu won the Fields Medal, marking a historic moment. Four PKU faculty members—Chen Songxi, Sun Xin, Xie Junyi, and Yuan Xinyi—along with ten alumni from the School of Mathematical Sciences—Deng Yu, Lin Lin, Lu Jianfeng, Shen Junliang, Tang Yunqing, Wang Hong, Xu Feng, Zhang Ruixiang, Zhu Yongchang, and Zhuang Ziquan—were invited as speakers at the 30th ICM.
Like spring breezes nurturing peaches and plums, the forest of giants grows. PKU mathematics and Chinese mathematics are forging a path with Chinese characteristics, Chinese style, and Chinese spirit.