Four mathematicians whose work covers areas like algebraic geometry and partial differential equations are the latest recipients of the Fields Medals, an award that is given out every four years to the brightest young researchers in the field.

This year’s recipients, announced on Thursday during the International Congress of Mathematics in Philadelphia, solved cutting-edge problems, including one that seemed like a simple puzzle of geometry and another that derived a fundamental equation that describes the motion of gases.

The medalists include two people who were born in China — Yu Deng, 37, a professor at the University of Chicago, and Hong Wang, 35, a professor at New York University and the Institute for Advanced Scientific Studies in France. This is the first time the cadre of Fields winners includes more than one Asian mathematician. Dr. Wang is also just the third woman to receive a Fields.

The other two medalists are Jacob Tsimerman, 38, a professor at the University of Toronto, and John Pardon, 37, a professor at Stony Brook University on Long Island.

The honor is accompanied by 15,000 Canadian dollars, or about $10,600, and a gold coin with the face of Archimedes, an ancient Greek mathematician.

The congress, which is the world’s largest and most prestigious gathering of mathematicians, comes as the field faces upheaval from artificial intelligence, which is quickly gaining skills that rival those of human mathematicians.

On Sunday, a mathematician reported that he and friends had disproved a conjecture that had first proposed in 1939. Using the Fable A.I. model from Anthropic, they found a counterexample while watching the World Cup final.

The counterexample was easily checked, leaving no doubt that the result was valid.

The congress will include talks about how A.I. and other tools like software that checks proofs are changing mathematics.

One of the Fields winners, Dr. Tsimerman, is even changing the focus of his research to studying the mathematical foundations of A.I. systems to better understand how they work and help avoid unintended consequences.

John Charles Fields, a Canadian mathematician, conceived of the medals in the 1920s, and the first medals were awarded in 1936. They are unusual among top academic honors in that they go to people who are still early in their careers, showcasing not only their accomplishments but also their promise.

To be eligible, a mathematician must be under the age of 40 on Jan. 1 of the year of the award. Because the medals are bestowed only once every four years, the Fields add prestige through rarity — which makes them somewhat akin to Olympic medals.

Another mathematics award, the Abel Prize, is modeled after the Nobel Prize and recognizes lifetime achievements.

The International Mathematical Union, which administers the Fields Medals, informed the recipients several months ago, but they were told to keep it secret until the official announcement on Thursday at the International Congress of Mathematicians, the world’s largest gathering of mathematicians.

The news leaked last week after hackers discovered the names, which had been poorly hidden on the website for the meeting.

“Some of my friends congratulated me, saying that they guessed maybe this is true and then they want to congratulate me,” Dr. Wang said. “But I didn’t give them any confirmation.”

John Pardon is a recipient of a Fields Medal, awarded to the top mathematicians under the age of 40. But he started at a much younger age. He published his first math research paper while he was in high school in North Carolina.

“My dad suggested I do a research project to submit to the Intel Science Talent Search,” Dr. Pardon, 37, said in an interview when he joined the faculty of Stony Brook University in 2022. “I find it easier to think visually and spatially, so geometry and topology come much more naturally to me, and I eventually settled on a very concrete geometry question.”

While he was an undergraduate student at Princeton University, he published more mathematical papers, including his first major result, which answered a question that Mikhael Gromov, a prominent Russian-French mathematician, had asked in 1983.

That problem was also geometric in nature and involved knots. For mathematicians, a knot can be thought of as a loop of rope that cannot be untangled without cutting the rope.

In essence, Dr. Gromov wondered whether all loops, no matter how tangled, could fit within a certain measure of how bendy the loop was. Dr. Pardon proved that they could not.

Math was not the only difficult class he took in college. He also became fluent in Mandarin Chinese.

“I was signing up for classes as a freshman in college, and I heard Chinese was pretty difficult, so I wanted a challenge,” Dr. Pardon said in a video shown on Thursday during the presentation of the Fields Medals.

The video shows him quizzing his sons, Alexandros and Andreas, on identifying Chinese characters plastered on their bedroom wall. “I talk to them in Chinese a lot,” he said. “We learn the characters. I read to them. I make them read to me.”

Once, he recalled, Alexandros turned to Andreas and asked whether their father was born in China.

Yakov Eliashberg, who was Dr. Pardon’s adviser when he was a doctoral student at Stanford University, said Dr. Pardon’s greatest achievement was not in proving any particular theorem. Rather, Dr. Eliashberg said, great scholars are those who figure out the mathematical landscape underpinning the problem.

“That’s his power,” Dr. Eliashberg said. “That’s what he was able to demonstrate again and again in different situations.”

Unlike most of the work that mathematicians do, the research of Yu Deng, 37, a professor of mathematics at the University of Chicago and one of the winners of this year’s Fields Medals, which recognizes mathematicians under the age of 40, directly addresses how the universe works.

The equations of physics generally fall into one of two categories.

Some equations, like Newton’s second law of motion, describe the behavior of individual particles — billiard balls bouncing off one another is one example. But it is impossible to calculate the precise interactions of billions or trillions of particles.

Other equations offer a statistical approximation of particles’ collective behavior.

Back in 1900, David Hilbert, a German mathematician, laid out what he regarded as the biggest unsolved problems in the field. No. 6 was broad and vague: deriving the laws of physics from the simplest axioms.

That is, how can the statistical behavior of the whole be calculated, ground up, from the motion of the individual particles? Dr. Hilbert offered a specific example: gases.

Mathematicians did manage to show how they could, through a progression of logic and calculation, derive the Boltzmann equation, which describes changes in the density of particles, from the basic laws of motion. The derivation was valid for only extremely short periods of time, so it was a start, but insufficient.

Dr. Deng, who grew up in Shenzhen, China, said he first became interested in partial differential equations when he was an undergraduate. He started his studies at Peking University before transferring to the Massachusetts Institute of Technology, where he graduated with a bachelor’s degree in mathematics.

But he put aside partial differential equations, because he did not feel there were enough mathematical tools to make progress with them. He returned to the subject around 2018, he said.

In 2021, Dr. Deng and Zaher Hani, a mathematician at the University of Michigan, came up with a full derivation of the wave kinetic equation, which describes phenomena like turbulence.

He then turned to the Boltzmann equation. “That was really kind of an analogue of what we just did in the last few years on this wave kinetic turbulence theory,” Dr. Deng said. “It was a major open problem.”

Dr. Deng, Dr. Hani and another mathematician, Xiao Ma, figured out how break up the big complex problem into smaller, manageable pieces. In 2024, they posted their solution to deriving the Boltzmann equation from Newton’s laws of motion.

In a follow-up paper last year, they claimed they had solved Hilbert’s sixth problem, at least for the Boltzmann equation.

“I’m very happy,” Dr. Deng said of the Fields Medal, “not just because of myself, but also because the field I’m representing is getting significant recognition.”