The world’s most prestigious prize in mathematics has crowned four exceptional researchers this year, but it is the simultaneous recognition of two Chinese mathematicians that has emerged as the defining story of this year’s Fields Medals.
At the International Congress of Mathematicians (ICM) in Philadelphia on July 23, Hong Wang and Yu Deng became the first Chinese citizens to receive the honour.
Often described as the “Nobel Prize of Mathematics”, the Fields Medal is awarded every four years by the International Mathematical Union (IMU) to researchers under the age of 40 whose discoveries have significantly advanced the discipline.
Unlike the Nobel Prizes, which have no age restriction, the Fields Medal has traditionally recognised mathematicians early in their careers, celebrating both their existing contributions and their future potential to shape the field.
The 2026 awards came at a particularly interesting moment for mathematics. Rapid advances in artificial intelligence have heated up discussions about the future of mathematical discovery, with researchers debating whether AI could eventually surpass human capabilities in solving complex mathematical problems.
Against this backdrop, the latest Fields Medals celebrated achievements that required years of deep theoretical thinking and creativity — qualities that remain at the heart of fundamental mathematical research.
This year’s recipients are Hong Wang of New York University and the Institut des Hautes Études Scientifiques (IHES) in France, Yu Deng of the University of Chicago, John Pardon of Stony Brook University in the United States, and Jacob Tsimerman of the University of Toronto in Canada.
Their work spans harmonic analysis, geometric measure theory, partial differential equations, statistical mechanics, topology, algebraic geometry and analytic number theory, addressing questions that have challenged mathematicians for decades — and in some instances, for more than a century.
Each winner received a gold medal bearing the likeness of the ancient Greek mathematician Archimedes, along with prize money of 15,000 Canadian dollars.
Yet beyond the medal itself, the award represents one of the highest recognitions a mathematician can receive, often defining careers and highlighting breakthroughs that reshape entire branches of mathematics.
For China, however, the significance of the 2026 ceremony extends well beyond individual honours. While mathematicians of Chinese heritage have previously reached the pinnacle of the profession, Hong Wang and Yu Deng are the first citizens of the People’s Republic of China to be awarded the Fields Medal.
Why is the win being described as a historic milestone for China?
Before 2026, two mathematicians of Chinese descent had already secured the Fields Medal.
The first was Shing-Tung Yau, who won in 1982. Born in Shantou in China’s Guangdong province before growing up in Hong Kong, Yau later became a United States citizen.
His groundbreaking work transformed differential geometry by establishing the field of geometric analysis through the application of nonlinear partial differential equations. Among his greatest achievements was proving the Calabi conjecture, leading to mathematical structures now known as Calabi-Yau manifolds.
These geometric spaces would eventually become central to modern theoretical physics. They provide the mathematical framework used in superstring theory, where physicists attempt to reconcile quantum mechanics with gravity by describing the universe as existing in ten dimensions.
Yau also co-proved the Positive Mass Theorem alongside Richard Schoen, demonstrating that the total mass of an isolated physical system cannot be negative—an important result in Einstein’s theory of general relativity.
More than two decades later, another mathematician of Chinese heritage received the Fields Medal.
Terence Tao, born in Australia to parents who had emigrated from Hong Kong, won the prize in 2006 at just 31 years of age. Often described by colleagues as a “universal mathematician”, Tao has made influential contributions across numerous branches of mathematics rather than specialising in a single area.
Among his best-known achievements is the Green-Tao theorem, proved jointly with Ben Green in 2004. Their work demonstrated that prime numbers — long regarded as appearing almost randomly along the number line — contain arithmetic progressions of any desired length.
In simple terms, the research showed that sequences of evenly spaced prime numbers can continue indefinitely, overturning longstanding assumptions about the structure of prime numbers.
Beyond number theory, Tao’s research has influenced harmonic analysis, nonlinear Schrödinger equations, compressed sensing used in signal processing, and random matrix theory, making him one of the most versatile mathematicians of his generation.
Yet despite these remarkable accomplishments, neither Yau nor Tao was a Chinese citizen when receiving the Fields Medal. That is why this year’s awards represent such a watershed moment.
Hong Wang and Yu Deng became the first Chinese passport holders to receive mathematics’ highest honour, establishing a new chapter in the country’s scientific history.
For many years, China built an international reputation by producing outstanding performers at school-level competitions such as the International Mathematical Olympiad (IMO). Chinese students consistently dominated global rankings, demonstrating extraordinary talent at solving difficult mathematical problems under examination conditions.
However, success in mathematical competitions does not automatically translate into breakthroughs in original research.
Producing a Fields Medal winner requires a very different ecosystem — one capable of nurturing creativity, supporting long-term theoretical work and encouraging researchers to pursue problems whose solutions may take years or even decades to discover.
The achievements of Wang and Deng suggest that this transformation has now taken place.
Both mathematicians belonged to Peking University’s undergraduate cohort of 2007, one of China’s premier centres for mathematical education.
From there, they continued their academic journeys at internationally renowned institutions — Wang pursuing doctoral research at the Massachusetts Institute of Technology (MIT) and Deng at Princeton University—before establishing careers at leading universities abroad.
Their professional trajectories also demonstrate how contemporary mathematics has become an increasingly international enterprise. While their academic foundations were built in China, their research careers have flourished through collaboration across Europe and North America.
Wang currently teaches at New York University while also holding a position at France’s Institut des Hautes Études Scientifiques. Deng serves as a professor at the University of Chicago, where his work has earned global recognition in mathematical physics.
In lieu of her association with France, French President Emmanuel Macron also congratulated her in a phone call.
Félicitations à Hong Wang, lauréate de la Médaille Fields !Formée à l’École polytechnique, chercheuse à l’Institut des hautes études scientifiques, de Paris-Saclay, elle incarne l’excellence de notre recherche et de notre formation. Fierté.Choose France for science! pic.twitter.com/TWhccqAynZ— Emmanuel Macron (@EmmanuelMacron) July 23, 2026
Félicitations à Hong Wang, lauréate de la Médaille Fields !Formée à l’École polytechnique, chercheuse à l’Institut des hautes études scientifiques, de Paris-Saclay, elle incarne l’excellence de notre recherche et de notre formation. Fierté.Choose France for science! pic.twitter.com/TWhccqAynZ
The historic nature of Wang’s achievement extends even further. At just 35 years old, she has become only the third woman in the nearly ninety-year history of the Fields Medal to receive the award.
Since the prize was first established in 1936, female recipients have remained extraordinarily rare.
The breakthrough came only in 2014, when Iranian mathematician Maryam Mirzakhani became the first woman to receive the Fields Medal. Her work transformed understanding of geometry and dynamical systems before her untimely death from cancer in 2017.
Eight years later, Ukrainian mathematician Maryna Viazovska became the second female recipient after solving the sphere-packing problem in eight dimensions.
Hong Wang now joins that distinguished list as the third woman ever to receive mathematics’ highest honour.
What breakthroughs earned Hong Wang and Yu Deng the Fields Medal?
Although both Hong Wang and Yu Deng are now among the most celebrated mathematicians in the world, the problems that earned them the Fields Medal are anything but easy to explain.
Their research lies at the frontiers of modern mathematics, tackling questions that have resisted generations of experts and have implications extending far beyond the discipline itself.
One solved a century-old geometry puzzle that influences the study of waves and signals. The other established a rigorous mathematical bridge between the microscopic world of individual particles and the large-scale behaviour of gases — a problem that had remained unresolved since the nineteenth century.
Hong Wang: Solving one of geometry’s oldest puzzles
At 35, Hong Wang has established herself as one of the world’s foremost researchers in harmonic analysis and geometric measure theory.
She currently teaches at New York University while also serving at the Institut des Hautes Études Scientifiques (IHES) in France, one of Europe’s leading centres for advanced mathematical research.
Her Fields Medal citation recognises a body of work that transformed geometric measure theory, but its centrepiece is the solution to one of mathematics’ most famous unsolved questions — the three-dimensional Kakeya conjecture.
The origins of the problem stretch back more than a century. In 1917, Japanese mathematician Soichi Kakeya posed what appeared to be an innocent geometric question.
Imagine a straight line segment, or simply a pencil or needle. If it has to rotate through every possible direction while remaining inside a bounded region, what is the smallest possible region that can contain all of those movements?
The question sounds deceptively simple, but it quickly became one of the deepest puzzles in modern mathematics.
Explaining the problem in her own words, Wang told AFP, “In 1917, Kakeya asked a very simple question: if you rotate a pencil so as to turn it completely around, what is the smallest area it sweeps out?”
The original version considered movement on a flat two-dimensional surface. Over time, mathematicians realised that answering the same question in three-dimensional space was dramatically more difficult.
Instead of imagining a pencil rotating across a tabletop, researchers had to consider one floating freely in midair, capable of pointing in every possible direction.
The challenge was no longer about calculating an ordinary volume. It became a profound question concerning the geometric structure of space itself.
Mathematically, the Kakeya conjecture asks about the smallest possible region in n-dimensional space that contains a unit line segment oriented in every direction. More specifically, researchers sought to determine the dimensions such sets must possess.
For decades, mathematicians established partial results and developed increasingly sophisticated techniques, yet the complete three-dimensional problem remained unsolved.
Many experts came to regard it as one of the defining challenges of harmonic analysis. Working alongside Joshua Zahl, Wang finally resolved this longstanding question.
Their proof demonstrated that three-dimensional Kakeya sets necessarily possess both Hausdorff dimension and Minkowski dimension equal to the surrounding three-dimensional space.
Although highly technical, this result effectively answered the central conjecture that had frustrated researchers for generations. The significance of the breakthrough extends well beyond one isolated problem.
Kakeya sets appear naturally in harmonic analysis, geometric measure theory and Fourier analysis — branches of mathematics that examine how complicated functions and wave-like phenomena behave.
These ideas, in turn, influence numerous scientific disciplines. Wave propagation, signal analysis, imaging techniques and partial differential equations all depend upon mathematical tools connected, directly or indirectly, to harmonic analysis.
That is why solving the Kakeya conjecture has implications extending beyond pure mathematics. It unlocks progress on several related questions, including the famous Fourier restriction conjectures, while providing researchers with entirely new methods for studying the geometry of high-dimensional spaces.
Reflecting on why the problem has fascinated mathematicians for more than one hundred years, Wang told AFP, “If this conjecture fascinates people so much, it is because this kind of phenomenon shows up naturally in problems from very different fields.”
Yu Deng: Connecting microscopic particles to the visible world
While Hong Wang’s work focused on geometry, Yu Deng’s research tackled one of the most fundamental questions in mathematical physics.
How do countless microscopic particles moving according to simple physical laws collectively produce the behaviour we observe in gases, liquids and other large-scale systems?
Scientists have understood many aspects of this relationship for well over a century. The Boltzmann equation, introduced in 1872, has long served as one of the central mathematical tools for describing how gases evolve over time.
Physicists have successfully applied the equation to explain a vast range of phenomena involving gases and fluids.
Yet one crucial question remained unresolved. Could this equation be derived rigorously from the deterministic laws governing the motion of individual particles?
For generations, mathematicians struggled to establish this connection.
The microscopic world follows Newtonian mechanics, where particles collide according to precise physical laws. The macroscopic world, however, is described statistically, treating enormous collections of particles through probabilities and averages.
Building an exact mathematical bridge between these two descriptions proved extraordinarily difficult. Yu Deng’s work finally provided that bridge.
Together with collaborators, he established a mathematically rigorous derivation of the Boltzmann equation from Newtonian mechanics involving colliding hard spheres.
Instead of beginning with gases as continuous substances, Deng effectively constructed the theory from individual particle interactions, showing precisely how microscopic collisions give rise to the large-scale behaviour described by kinetic theory.
The achievement answered a narrowly formulated aspect of one of mathematics’ historic challenges.
In 1900, German mathematician David Hilbert presented his famous list of twenty-three unsolved problems that would guide mathematical research throughout the twentieth century.
Hilbert’s Sixth Problem called for the axiomatization of physics — the development of rigorous mathematical foundations for physical theories.
Although physicists had used statistical mechanics successfully for decades, proving exactly how microscopic mechanics generates macroscopic equations remained one of its outstanding challenges.
Deng’s work resolved an important formulation of that problem. His research therefore strengthens the mathematical foundations of statistical mechanics while providing new tools for understanding complex physical systems.
Its implications extend to fields concerned with gases, fluids and kinetic behaviour, illustrating once again how highly abstract mathematics can deepen scientific understanding of the physical universe.
Who are John Pardon and Jacob Tsimerman?
The other two Fields Medallists also solved landmark problems across several branches of mathematics.
John Pardon, 37, of Stony Brook University, was recognised for major advances in topology and geometry.
Among his achievements is resolving long-standing questions about knots wrapped around torus-shaped objects and proving the MNOP conjecture, which connects geometry with mathematical structures appearing in quantum string theory.
Reflecting on the unpredictable impact of mathematical discoveries, Pardon told AFP, “It’s hard to know at the time how much significance a given solution will have.”
He added, “Certainly, finding the solution was not proportional to the interest it’s generated.”
Jacob Tsimerman, 38, of the University of Toronto, was honoured for pioneering work in algebraic geometry and analytic number theory.
By introducing tools from mathematical logic — particularly o-minimality — into algebraic geometry, he has helped address several major open problems, including important progress related to the Hodge conjecture, one of mathematics’ seven Millennium Prize Problems.
Tsimerman has often spoken about how his fascination with mathematics began with a childhood puzzle posed by his grandfather.
“It was a little puzzle about a toaster. If you have a toaster but it’s broken, so both slots only toast one side of the bread, and you have three pieces of bread that you want to fully toast both sides of, how many times must you use the toaster?” he recalled to AFP.
After discovering the solution, he remembered thinking, “I was like, ‘That’s beautiful,’ and I was basically hooked.”
