The Fields Medal, the world’s most prestigious award in mathematics, was presented Thursday in Philadelphia to four researchers under the age of 40 who have made significant contributions to diverse areas of the field. This year’s recipients are Yu Deng, John Pardon, Jacob Tsimerman, and Hong Wang, whose work spans from physics equations to the geometry of knots and higher-dimensional shapes.
Yu Deng, a University of Chicago professor, was recognized for his rigorous derivation of the Boltzmann equation, a fundamental formula in statistical mechanics describing the behavior of gases. Deng and collaborators extended earlier partial results to validate the equation’s applicability over arbitrarily long time periods, addressing a longstanding challenge in linking microscopic particle dynamics with macroscopic fluid behavior.
John Pardon, a professor at Stony Brook University, solved a long-standing problem about the distortion of knots—an attribute quantifying how convoluted a knot is. His work demonstrated the existence of complicated knots that maintain a minimum distortion regardless of how they are manipulated, resolving a question about the limits of simplification for certain knot types.
Jacob Tsimerman, from the University of Toronto, made notable advances in algebraic geometry, a branch of mathematics focused on solving equations that describe geometric shapes. His research involved transforming complex shapes by systematically adding points without altering their core structure, offering new tools for fields such as string theory in physics.
Hong Wang, a New York University professor and the third woman ever to win the Fields Medal, achieved a breakthrough in a problem involving Kakeya sets—geometric constructs related to the minimal area necessary to rotate a needle in space. Building on work from the 1970s, Wang and her collaborator resolved the three-dimensional case of the Kakeya conjecture, which had resisted proof for decades.
The Fields Medal, awarded every four years, is distinct in limiting recipients to mathematicians under 40, a rule intended to both honor significant accomplishments and encourage future contributions. Since its inception 90 years ago, the award has been given to 68 individuals, with only three women among them.
This year’s ceremony comes amid growing discussion about the influence of artificial intelligence (AI) on mathematics. Recent advances in AI have enabled systems to solve complex problems and assist in verifying mathematical proofs, prompting questions about the future role of human researchers. Tsimerman expressed that AI could soon outperform humans in mathematical reasoning, signaling a transformative period for the discipline. Deng, however, emphasized an ongoing collaboration between humans and AI in research efforts.
AI models have reportedly contributed to disproving mathematical conjectures recently, as noted by Levent Alpöge, a researcher at Anthropic, who used AI to challenge assumptions regarding multidimensional space transformations. Experts anticipate that AI will increasingly become integrated into mathematicians’ workflows by helping digest literature, synthesize arguments, and accelerate problem-solving.
The next Fields Medal awards are scheduled for 2030, by which time the integration of AI tools in mathematical research is expected to be further developed, though exactly how remains uncertain.