Four mathematicians have been awarded the Fields Medal, one of the highest honors in mathematics, recognizing significant advances across a range of fields including algebraic geometry and partial differential equations. The medals were announced on July 23 at the International Congress of Mathematics held in Philadelphia, an event that takes place once every four years.
This year’s recipients include Yu Deng, 37, a professor at the University of Chicago; Hong Wang, 35, a professor at New York University and the Institut des Hautes Études Scientifiques in France; Jacob Tsimerman, 38, a professor at the University of Toronto; and John Pardon, 37, a professor at Stony Brook University in New York. For the first time, more than one Asian mathematician received the award, with Dr. Deng and Dr. Wang both born in China. Dr. Wang also became only the third woman ever to receive the medal since its inception in 1936.
The Fields Medal celebrates young mathematicians under the age of 40 who have made outstanding contributions and show exceptional promise for future work. Each medal is accompanied by 15,000 Canadian dollars (approximately $10,600) and a gold coin bearing the likeness of Archimedes.
Yu Deng’s research, rooted in partial differential equations, addresses core questions about the fundamental laws of physics. His recent work involves deriving the Boltzmann equation, which describes particle density changes in gases, from Newton’s laws of motion—advancing a longstanding mathematical challenge known as Hilbert’s sixth problem. Dr. Deng and collaborators produced a rigorous derivation that extends earlier partial results, marking a significant breakthrough in kinetic theory.
Hong Wang’s work focuses on a complex geometric problem known as the Kakeya conjecture, which involves analyzing the minimal area swept by rotating needles in three-dimensional space. Alongside Joshua Zahl, Dr. Wang demonstrated that the fractal dimension of these needle sets in three dimensions is exactly three, resolving a question that has persisted for decades. Her proof represents a major milestone in harmonic analysis, a branch of mathematics related to the study of oscillatory behaviors.
Jacob Tsimerman, who was born in Kazan, Russia, and emigrated with his family to Israel and later Canada, is recognized for his contributions to number theory, including work on the André-Oort conjecture. He is known for investigating solutions to diophantine equations—polynomial equations where integer solutions are sought—a field rich with historical problems and implications for other areas like string theory. Dr. Tsimerman is now shifting his research toward the mathematical foundations of artificial intelligence, aiming to deepen understanding of large language models that power systems such as ChatGPT, while also expressing concern about the potential societal risks posed by AI technologies.
John Pardon’s achievements lie in geometry and topology, particularly in problems involving knots—loops that cannot be untangled without cutting. Early in his career, he resolved a problem posed by Mikhael Gromov in 1983 concerning the geometry of knots and the limits of their “bendiness.” Dr. Pardon’s work has been noted for its insight into the underlying mathematical structures behind complex spatial problems. Beyond mathematics, he has pursued fluency in Mandarin and maintains an active role in raising his children bilingually.
The International Congress of Mathematics this year also highlighted the increasing impact of artificial intelligence on the discipline. Recent developments demonstrate that AI models can assist in disproving longstanding conjectures and accelerating mathematical research, prompting discussions on how these tools may shape the future of mathematics.
The Fields Medals, established by Canadian mathematician John Charles Fields in the 1920s and first awarded in 1936, continue to stand as a prestigious accolade for young mathematicians, emphasizing both their achievements to date and the potential for groundbreaking discoveries ahead.