What century-old math problems did the first Chinese Fields Medalists solve?

Widely regarded as mathematics' highest honor, the Fields Medal has been awarded every four years by the International Mathematical Union since 1936 to recognize outstanding mathematicians under the age of 40.

At the 2026 International Congress of Mathematicians, which opened in Philadelphia, U.S., on July 23, Deng and Wang received the award alongside John Pardon of Stony Brook University and Jacob Tsimerman of the University of Toronto.

Deng and Wang are the first Chinese nationals to receive the Fields Medal, according to the South China Morning Post. Shing-Tung Yau, who won in 1982, and Terence Tao, who received the honor in 2006, are ethnic Chinese but held other citizenships at the time of their awards.

Yu Deng

Chinese mathematician Yu Deng. Photo courtesy of Clay Mathematics Institute

Deng, 37, a professor at the University of Chicago, was recognized for a breakthrough on Hilbert's Sixth Problem, one of the 23 famous mathematical challenges proposed by German mathematician David Hilbert in 1900.

The problem asks whether the microscopic motion of countless individual particles can be rigorously shown to produce the statistical laws that govern gases and other large-scale physical systems.

Earlier, Deng and University of Michigan mathematician Zaher Hani had shown how microscopic wave equations give rise to wave kinetic equations. They later realized the same mathematical framework might also apply to particles, even though the two systems are physically very different.

Working with Hani and Xiao Ma of the University of Michigan, the trio developed new mathematical techniques to bridge the gap between particle dynamics and statistical behavior. According to Quanta Magazine, they worked in secret because many research teams were pursuing the same goal, often working day and night and coming close to burnout.

By August 2024, they had completed a 200-page proof solving a major case of Hilbert's 124-year-old problem for long time scales. Their work rigorously showed how the microscopic motion of particles leads to the Boltzmann equation, a fundamental equation describing the statistical behavior of gases.

The paper took months for other mathematicians to digest. He and his collaborators subsequently revised the paper to make it easier to follow before its publication in the Annals of Mathematics, one of the world's most prestigious mathematics journals.

Hong Wang

Chinese mathematician Hong Wang. Photo courtesy of IHES

Wang, 35, a professor at New York University and France's Institut des Hautes Études Scientifiques, was honored for resolving the three-dimensional Kakeya conjecture, a geometric problem that had remained unsolved for more than a century, according to New York University.

She is the third woman among the 68 Fields Medal recipients since the prize was first awarded in 1936.

In 2025, Wang and collaborator Joshua Zahl published a 127-page paper proving the three-dimensional Kakeya conjecture.

The problem dates to 1917, when Japanese mathematician Soichi Kakeya asked how little area a needle needs to turn and point in every direction. Mathematicians later reformulated the question by studying "Kakeya sets," collections of lines pointing in every possible direction.

Researchers proved in the 1970s that two-dimensional Kakeya sets always have a Hausdorff dimension of two, a mathematical measure of an object's complexity. Extending that result to higher dimensions, however, remained an open challenge for decades.

Wang came across a 2014 blog post in which Terence Tao outlined a possible strategy developed with Rice University mathematician Nets Katz but never pursued. She later contacted Zahl, and the pair spent four years developing the proof, according to Quanta Magazine.

Wang and Zahl became the first to establish the exact Hausdorff dimension of three-dimensional Kakeya sets.

"The Kakeya conjecture was the first major obstacle to solving many other problems," Tao wrote in an IHES newsletter, adding that its resolution opens the restriction, Bochner-Riesz and arithmetic Kakeya conjectures.

Wang's breakthrough not only resolved a century-old mathematical problem but also introduced new analytical methods with potential applications in radar, remote sensing and signal processing, where understanding the interaction of wave packets is essential, as reported by CGTN.