Chinese mathematicians Wang Hong and Deng Yu win Fields Medals in 2025.

No surprises, no twists—it was indeed Wang Hong and Deng Yu.

Just now, at the International Congress of Mathematicians (ICM) in Philadelphia, USA, the quadrennial Fields Medal list was announced, with China’s “twin stars” both included, marking a new milestone in Chinese mathematics.

Wang Hong, born in 1991 at age 35, has officially become the third woman in history to win the Fields Medal. Joining her in making history is her Peking University classmate from the 2007 cohort, Deng Yu.

Although Shing-Tung Yau won the award in 1982 and Terence Tao in 2006, Wang Hong and Deng Yu are the first Chinese mathematicians to win the highest honor in mathematics—and they did so simultaneously.

This is also a moment of glory for Peking University, the alma mater of Wang Hong and Deng Yu, adding another legend to the already celebrated story of Peking University’s golden generation of mathematicians.

A joke may therefore become widely known:

The best is the best; Peking University is double F.

Wang Hong and Deng Yu each solved a century-old mathematical problem.

As soon as the paper was posted on arXiv, the entire mathematics community sat up straight in their deathbed dreams: Wow! This is serious—something big is about to happen.

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After reviewing the papers by Wang Hong and Deng Yu, I also discovered that each of their collaborators is a student of Terence Tao.

Terence Tao, in 2006 at the age of thirty-one, took the stage at the International Congress of Mathematicians to become the second Chinese recipient of the Fields Medal after Shing-Tung Yau, and the only one in nearly two decades since.

Terence Tao particularly loves writing blogs. In 2014, he casually recorded his long-standing ideas on the Kakeya conjecture—a problem that had fascinated him since his doctoral studies—on his beloved blog, laying the groundwork for Wang Hong’s breakthrough.

The Kakeya conjecture is quite old.

In 1917, Japanese mathematician Kakeya Sōichi posed a seemingly naive question: What is the minimum area required to rotate a needle in a plane so that it points in every possible direction?

Reveal the answer: First, eliminate π.

Kakeya himself thought the answer should be π/8.

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However, 11 years later, the Soviet mathematician Besicovitch had a groundbreaking insight—he believed the problem was far more complex than it seemed.

There should exist a set of points in the plane with measure zero that contains unit-length line segments in every direction; by slightly modifying this construction, one obtains a region swept out by a short line segment rotating continuously through a full circle, with area that can be made arbitrarily small but has no minimum value.

This "null set" is extremely abstract—it cannot be drawn, and the only way to see it is to visit the mathematician's mind.

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The Kakeya set conjecture thus emerged: in n-dimensional Euclidean space, both the Hausdorff dimension and the Minkowski dimension of a Kakeya set are equal to n.

Nearly a century later, in 2025, Wang Hong and Joshua Zahl successfully proved the Kakeya set conjecture in three dimensions (n=3) in a 127-page paper.

After the paper was published, Terence Tao immediately updated his blog. He noted that although Wang Hong’s proof followed some of the directions he had previously envisioned, the 127 pages contained many highly ingenious innovations.

Mathematician Nets Katz, who worked with Terence Tao on the Kakeya conjecture, stated that Wang Hong’s paper doesn’t need the media to hype it up, because this achievement is truly once-in-a-century.

Another Fields Medalist, Yu Deng, has also studied the Kakeya conjecture. In a comment under a question about interesting counterexamples in mathematical research, he discussed this conjecture.

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At the end of his response, he let out a small sigh—

At the time, no one realized that this set also had a significant impact on the fate of harmonic analysis—though that’s another story entirely.

Clearly, Wang Hong is among the main characters in this “other story.”

Harmonic analysis, which Wang Hong has dedicated herself to, is a core tool for studying partial differential equations.

Partial differential equations are the core of Deng Yu’s research. At the top of his academic homepage, he sincerely writes: “I am interested in everything related to partial differential equations.”

Summer of 1900 in Paris. At the second International Congress of Mathematicians, 38-year-old Hilbert pulled out a sheet of paper listing 23 problems.

This paper, known as "Hilbert's Problems," has puzzled the mathematical community for over a century. Only half of the problems have been fully solved in that time.

Among the six questions, the sixth required mathematicians to ground physics in a rigorous axiomatic mathematical system.

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Perhaps because it sounded too difficult, Hilbert himself proposed a more specific entry point—

Physicists studying the different properties of gases must use different equations, ranging from Newtonian mechanics describing individual particles, to the Boltzmann equation describing the statistical behavior of large numbers of particles, to the fluid dynamics equations describing the fluid as a whole.

Can these equations be derived from one another?

In other words, is it possible that all the equations we've spent so many years working on are fundamentally the same?

Deng Yu and his collaborators Zaher Hani and Ma Xiao aim to prove the first part of this result. Specifically, they seek to show that, as the number of particles tends to infinity and the particle diameter tends to zero, the statistical behavior of the hard-sphere system strictly converges to the solution of the Boltzmann equation.

Sounds very engineering, but behind this question lies a rather philosophical existential inquiry—

Is time truly irreversible?

You said it's irreversible, but the Newtonian laws governing all particles that make up this world are reversible—there is no distinction between past and future for a single particle.

But you said it’s reversible… you said… even you don’t believe what you’re saying.

Boltzmann's explanation was that even though individual particles are time-reversible, all collisions between particles lead to irreversible gas diffusion.

In August 2024, Deng Yu and his collaborators Zaher Hani and Ma Xiao published a paper deriving the Boltzmann equation for a specific gas model from the Newtonian dynamics of a hard-sphere system.

This result essentially confirms that Boltzmann's intuition was correct.

Dripping water penetrates stone—not the work of a single day; skillfully solving problems—born of a lifetime of thought.

Getting here hasn't been easy.

In 2001, Deng Yu was admitted to the junior high school division of Shenzhen Advanced Middle School through a summer camp, scoring over 70 points and ranking 12th.

At the time, Shenzhen Advanced High School was a newly established institution with subpar student quality overall. The principal personally visited Feng Yuefeng, a young teacher from the Mathematics Department of Guangzhou University, three times to invite him aboard, hoping to improve and elevate the students’ academic standards.

Therefore, Deng Yu's academic performance upon enrollment was not particularly outstanding, and there is still a long way to go before he can compete at a national level.

However, starting from the eighth grade, Feng Yuefeng began to feel something was off—Deng Yu was off; many of the competition problems he created could only be solved by Deng Yu, and not only that, but he solved them exceptionally well, with clear originality.

Could this kid really be a genius? Overjoyed, Feng Yuefeng began inviting the boy to his home every weekend to tutor him for free—a practice that continued for five years.

Bole successfully identified a talented horse. Deng Yu demonstrated exceptional enthusiasm and focus in his studies, scoring more than 60 points higher than other students on every high school exam.

In 2006, Deng Yu won a gold medal at the national winter camp with a perfect score, then represented China to win a gold medal at the International Mathematical Olympiad, and was subsequently admitted to Peking University without taking the entrance exam.

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Feng Yuefeng later evaluated this winter camp gold medal as follows: “Deng Yu won every possible award at this highest-level competition”—the only perfect score nationwide that year, the only student to solve the number theory problem, and one of only two “Special Prizes” awarded in twenty years for elegant solutions.

That same year, Deng Yu began using the username "Nine-Point Circle" to discuss mathematics and Go on forums, earning him the nickname "Light God."

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Perhaps because his replies on Tieba were casual and calm, someone once compared him to Liu Zhiyu—“I am an extreme realist,” Deng Yu, who had already transferred to MIT, replied at the time.

The following dialogue is excerpted from Yan Xiaochuan’s “Interview Notes of a MIT Student”: Yan: Deng Shen, where do you think the quality of life is better—Peking University or MIT? Deng Shen: Definitely Peking University. Here at MIT, the food is terrible—those cold sandwiches and such; just looking at them makes me feel uneasy. Yan: What about other aspects, like going out for fun? Deng Shen: I find this side of America pretty boring. When I have free time and want to go out for a walk, I just stroll along the riverbank. There’s only this small stretch of path here that’s suitable for walking, so I keep repeating the same route…

Yan: It sounds so tough being abroad—why did you come to the U.S. to study? Deng: Mathematics research in China hasn’t reached this level yet. I want to do cutting-edge research in the U.S., strive to make my own contributions and achieve breakthroughs in certain areas, and then bring those results back to China. That way, my students in the future won’t need to go abroad to learn the best mathematics.

Then again, Deng Yu’s Zhihu account may be even more widely known than the rumor that Deng Yu won the Fields Medal.

and 111 posts under the account.

And the excellent yuri works he recommended (struck through).

And the couple he ships (crossed out).

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After the list of Phi Awards was revealed, his follower count surged, and the comment section was mostly filled with this style of comment (· x ·)

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Even before the list was exposed, it wasn't much better.

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A quick glance at Deng Yu’s 111 posts on Zhihu can be broadly categorized into four types: mathematical and academic answers, yuri work introductions and analyses, go life-and-death problem introductions and analyses, and reflections on social values such as gender equality.

A crude classification may offer a glimpse into the young mathematician's mental landscape.

One could say he is a mathematician living in poetry, novels, and anime.

Deng Yu once provided a very vivid illustration of this in an answer he wrote on Zhihu.

Question: "What are some other无情对 (paradoxical couplets) like 'Amphetamine, thus have I heard'?"

Answer: "Once served in the Southern Palace for the former master, now inspired by Nishikigi Maki."

He loves reading poetry and identifies himself with Du Fu’s lines: “Or gazing at kingfishers on orchid sprouts, yet failing to seize whales in the azure deep.” What we do is merely flutter like kingfishers above the orchids, not swallow the vast ocean like whales.

He loves watching dramas; during a meeting, he angrily typed out a response to a question claiming that "women cannot carry serious-themed protagonists."

Starting with “I just don’t understand,” they then enthusiastically listed characters such as Daikō Miko, the surgeon from Doctor X; the entire female cast of Red Carnation; the team from Criminal Investigation Unit 6; and the American TV series Monk.

Finally, the phrase “It is not that I cannot, but that I will not!” expresses a pure and unambiguous disagreement.

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This broad range of interests is also reflected in his research pursuits—“Geometry, analysis, and physics are never separable at any time,” Deng Yu wrote several years ago while still an undergraduate.

Broadly explore, transcend disciplinary boundaries, and always seek connections.

He viewed mathematics as "an idealization of the physical world," which may offer insight into why he was so drawn to Hilbert's sixth problem.

Unlike Deng Yu, Wang Hong, born in 1991 in Pingle County, Guilin, Guangxi, has never received any professional competition training.

However, at age five, she had already memorized her first-grade Chinese textbook inside and out. She started elementary school directly in second grade. At age ten, she skipped sixth grade entirely. At thirteen, she entered Guilin High School as a freshman and often read extracurricular books in class. In 2007, at age sixteen, Wang Hong enrolled at Peking University.

However, a score of 653 is not among the highest. With a score that fell short, she initially chose the School of Earth and Space Sciences.

The report described the interview meeting with the girl as follows: “As we arrived at a shaded grove on campus, a girl in a white pleated blouse and purple plaid skirt walked toward us with light, graceful steps.”

At the end of the article on Wang Hong’s learning methodology, it was written: “It is said that Peking University will hold a department-transfer exam next April, and Wang Hong has already begun previewing Peking University’s mathematics textbooks. This intelligent and eager-to-learn young girl is once again spreading her wings toward a new dream…”

This ellipsis attempts to convey a sense of imagination, but Wang Hong had no intention of leaving anyone in suspense.

In the autumn of 2008, this intelligent and eager young girl transferred into the Department of Mathematics through self-study—the same year that Deng Yu was enrolled.

At Peking University’s School of Mathematical Sciences, the foremost of the four “madhouses,” there’s a saying: “Some students who scored perfect marks on the Gaokao math exam foolishly choose to enroll in Peking University’s Department of Mathematics.”

At the time, Peking University’s 2007 mathematics cohort was considered a gathering of geniuses, hailed as China’s new golden generation of mathematicians following the class of 2000. Wang Hong was not among the most prominent students in that group.

She is not tall and appears slender, but is actually an athletic and cheerful person. Her classmate Sun Xin recalled, “I often saw her dressed in sportswear,” and loved playing table tennis.

She has loved all kinds of sports since childhood and would play whatever was available—

I played table tennis when I was at Peking University, then went to France where there was no table tennis, so I took up fencing. During the pandemic, when neither table tennis nor fencing was available, I took online taekwondo classes.

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Exercise and mathematics form the main focus of Wang Hong’s life. She exercises four to five hours per week, but the time she spends on mathematics is harder to quantify.

“It’s hard to measure how much time I spend on math, because sometimes I just daydream about it while walking, but other times I rest and do something else when I’m tired,” she said.

Perhaps due to the difficulty of mathematical research or the highly competitive environment, she once doubted whether she was suited for studying mathematics.

I never received training like competition-based programs, so my earlier understanding of math was simply reading books on my own—supplementary texts, pondering the problems, and reflecting. I found that much of undergraduate studies, and even much afterward, was much the same: sitting in the library, reading books, and thinking through problems. I can’t really describe my feelings about math—I didn’t experience any major shock or dramatic turning point—but I always felt like I was struggling, so I didn’t overthink it; just surviving was good enough (laugh).

While studying for her master’s in France, she switched to architecture and worked at an architectural firm in Paris. Later, it became well known that she returned to the ivory tower of mathematics.

This skepticism accompanied her throughout her academic life: “Doubt is my primary driving force; if I stop questioning my reasoning, I become careless, and errors immediately appear.”

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Perhaps mathematics is precisely the kind of thing that makes you suffer and struggle, yet still refuse to let go of your love for it. For Wang Hong, it may have been the same.

However, Wang Hong chose to accept this unsettling doubt:

Obstacles aren't always visible, but they exist in perceptions and in societal expectations of young girls. I hope my experience encourages more young women to pursue pure mathematics—to not fear doubt, and not fear years without obvious results.

It is June 24, 2025, in Beijing.

Wang Hong wore a sheer white blouse and black trousers, holding a cup of Dongfang Shuye jasmine tea. The audience below was filled with elderly mathematical giants.

At Tsinghua, Shing-Tung Yau, the first Chinese-born Fields Medalist, opened the event with unstinting praise for her.

On the day Wang Hong returned to Peking University’s School of Mathematical Sciences to explain the Kakeya conjecture, the second floor of Zhihua Building was packed.

So crowded was it that all the chairs from every classroom on this floor were taken by people attending the lecture.

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After the lecture, her one-square-meter stage was surrounded by people eager to ask questions or exchange ideas.

Some observant students noticed a man wearing a white-striped shirt—he had been present every day during Wang Hong’s lectures.

He leaned down, listened closely, almost pressing his face against Wang Hong’s laptop screen.

This person is Wei Dongyi. One finger points to the problem on the screen as he asks a question, while his other hand still clutches the opened bottle of mineral water.

This article is from the WeChat public account "Quantum Bit" (ID: QbitAI), authored by Cheng Qian.