One of the highest honors in global mathematics, the Fields Medal — often described as the Nobel Prize of the field — has been bestowed upon four early-career mathematicians during the opening ceremony of the International Congress of Mathematicians in Philadelphia this Thursday. Awarded every four years by the International Mathematical Union to recognize groundbreaking work by researchers under the age of 40, the prize includes a 15,000 Canadian dollar (approximately 11,000 USD) cash award and a gold medallion engraved with the likeness of ancient Greek mathematician Archimedes. This year’s cohort of winners includes two Chinese citizens, Hong Wang and Yu Deng, one American scholar John Pardon, and Canadian mathematician Jacob Tsimerman.
Hong Wang, 35, who currently holds academic positions at institutions in both France and New York University in the United States, made history as only the third woman to claim the Fields Medal since the award was first established in 1936. She joins the ranks of just two other female recipients: Maryam Mirzakhani of Iran, who won in 2014, and Ukrainian mathematician Maryna Viazovska, who received the honor in 2022. Wang’s award-winning work centers on solving a century-old mathematical puzzle first posed by Japanese mathematician Soichi Kakeya in 1917. The problem, which became known as the Kakeya conjecture, asks a deceptively simple question: when a pencil is rotated a full 360 degrees, what is the smallest total area that the moving pencil sweeps out? Working alongside colleague Josh Zahl, Wang cracked the long-standing problem by extending analysis beyond the traditional two-dimensional plane into three-dimensional space. Wang explained the enduring appeal of the conjecture, noting that its underlying dynamic appears naturally across a vast range of unrelated mathematical fields, making its resolution relevant far beyond pure theory.
Yu Deng, the second Chinese recipient of this year’s award, currently teaches at the University of Chicago. His win underscores the rapidly growing global influence of Chinese mathematicians over the past several decades, a shift that has reshaped the international landscape of mathematical research. The United States, which holds the all-time record for the most Fields Medal winners, is represented this year by 37-year-old John Pardon, while 38-year-old Jacob Tsimerman completes the 2024 group of recipients. Tsimerman, a specialist in complex algebraic geometry and analytic number theory, traced his lifelong passion for mathematics back to a simple puzzle his grandfather shared with him as a child: a logic problem about toasting three slices of bread in a broken toaster that only toasts one side of each slot. When he worked out the elegant solution, he recalled thinking “That’s beautiful” — a moment that hooked him on mathematics for life.
This year’s International Congress of Mathematicians unfolds at a pivotal turning point for the field, as rapid advances in artificial intelligence are triggering widespread disruption and reevaluation of how mathematical research is conducted. In recent months, cutting-edge large AI models have stunned many leading mathematicians by demonstrating the ability to generate high-level, complex mathematical proofs, a development that opens promising new avenues for research but also raises pressing concerns. Back in June, a group of leading mathematics experts published the Leiden Declaration, a public statement outlining both scientific and ethical risks tied to growing AI integration in the field. The declaration calls for the urgent creation of standardized regulatory frameworks and safety safeguards to mitigate potential harms. Among the core risks outlined, the document notes that current AI-powered automated proof techniques often generate plausible-looking but ultimately unreliable or even fully incorrect mathematical arguments that can be extremely hard for even experts to distinguish from valid proofs. The statement also contextualizes these concerns within broader global debates, pointing out that AI’s rapid expansion carries overlapping risks related to unethical military applications, mass surveillance, political destabilization, and environmental harm tied to outsized energy consumption for large model training and operation.