Live from ICM 2026: What Is Math For in the Age of AI?

Artificial intelligence (AI) is increasingly involved in mathematics, with systems now capable of generating proofs, identifying connections between unrelated fields, and solving problems that have challenged mathematicians for years. This shift was highlighted at the International Congress of Mathematicians (ICM) 2026 in Philadelphia, where experts discussed AI's impact. For example, in 2024, an AI called AlphaProof achieved a silver medal at the International Mathematical Olympiad (IMO), a competition for high-school students solving six problems over two days. In 2025, a more advanced model, DeepThink, claimed a gold medal. These developments have sparked debates about AI's capabilities and its potential to reshape the creative and problem-solving aspects of mathematics, traditionally seen as human endeavors.

The International Mathematical Olympiad (IMO) is a prestigious competition where high-school students solve complex math problems over nine hours across two days. It has historically been a way to attract young talent to mathematics and develop problem-solving skills. Some mathematicians, like Ravi Vakil from Stanford University, participated in the IMO and excelled, while others, such as Akshay Venkatesh from the Institute for Advanced Study, did not. AI systems like AlphaProof and DeepThink have now matched or surpassed human performance in these competitions. However, Vakil and Venkatesh argue that the IMO's value lies not in competition but in fostering a mindset of mathematical thinking. They caution against overemphasizing competition, as it may discourage students who do not excel in such settings.

Paul Erdős, a prolific mathematician, posed thousands of unsolved problems in mathematics. Some of these, known as Erdős Problems, have remained open for decades. Recently, AI systems have begun solving these problems, including the Erdős unit distance conjecture, which was disproven by an AI model in 2026. This conjecture suggested a specific relationship between points in a plane, but the AI found a counterexample. The solution not only resolved this long-standing question but also inspired further progress in unrelated areas, such as the sum-product problem, which was solved by human mathematicians using techniques derived from the AI's work. These developments highlight AI's potential to accelerate mathematical discovery and open new avenues for research.

AI systems are generating a growing number of mathematical proofs, but many of these proofs may be incorrect or incomplete. This has created a new challenge for mathematicians: verifying AI-generated proofs. Some prominent mathematicians, like Terry Tao, have offered to referee these proofs, but the task is daunting. The sheer volume of AI-generated content could overwhelm journal systems and peer-review processes. Ravi Vakil noted that he receives numerous AI-generated proofs in his inbox but does not have the time or inclination to verify them. This raises concerns about the reliability of AI-generated mathematics and the sustainability of traditional peer-review systems in the face of this influx.

Mathematicians Akshay Venkatesh and Ravi Vakil argue that the essence of mathematics lies not just in proofs but in storytelling—the process of conveying ideas in a way that is engaging and understandable to others. Venkatesh describes mathematics as akin to exploring a landscape and crafting a narrative to explain discoveries. Vakil emphasizes that human understanding and the ability to communicate ideas effectively have always been central to mathematics. He cites examples like Paul Erdős and Martin Gardner, who advanced mathematics not through groundbreaking proofs but by inspiring others through storytelling. This perspective suggests that the value of mathematics may lie more in its ability to foster understanding and curiosity than in the proofs themselves.