Mathematicians Debate What AI Proofs Really Mean at ICM 2026 Panel

Mathematicians are witnessing AI systems that can produce proofs, spot connections between distant fields and, in a few cases, solve problems that had stumped mathematicians for decades. That shift was the subject of a live recording of the podcast "The Joy of Why," taped at the International Congress of Mathematicians (ICM) in Philadelphia on July 26, 2026. Hosts Janna Levin and Steven Strogatz were joined by three mathematicians: Akshay Venkatesh of the Institute for Advanced Study, Ravi Vakil of Stanford University and president of the American Mathematical Society, and Alex Kontorovich of Rutgers University.

The panel discussed two recent AI milestones at the International Mathematical Olympiad (IMO), a competition in which high-school-aged students spend two days and nine hours solving six problems. At the 2024 Olympiad, an AI system called AlphaProof won a silver medal; in 2025, a more advanced model called DeepThink won gold.

Vakil, who competed in the Olympiad himself as a student, called the results "extremely interesting" and a genuine milestone, but cautioned against reading too much into them: "it did not represent superhuman intelligence or anything crazy like that," he said. He noted the AI system was not the highest scorer in the year it first appeared, though it improved in later years, and compared the achievement to how a student's first correct answer feels exciting because it shows they have learned to think, while a model repeating the feat becomes far less interesting each additional time.

Venkatesh said the achievements have reinforced an image of mathematics as a competition, which he called "not really how I see it" and "particularly unhelpful at the moment." He said he has "mixed feelings about how healthy" that competitive framing is. Vakil added that the framing "could be a danger" since some students are discouraged from pursuing mathematics after performing poorly in competitions — a reaction he called nonsensical, since competition results are not what determines whether someone is good at the field.