The focal point of the week was the September 15 panel discussion titled “AI in Mathematical Research,” moderated by Tony Feng of UC Berkeley and Google DeepMind. The panelists included Fields Medalists Peter Scholze and Jacob Tsimerman, along with Michael Harris of Columbia University and Geordie Williamson of the University of Sydney. Rather than presenting a united front, the panel surfaced sharply divergent positions on how the mathematical community should respond to the rapid encroachment of machine intelligence into a discipline that has, for centuries, prized human insight, proof and understanding above all else. The onstage discussion, organizers noted, became the starting point for countless conversations among participants throughout the remainder of the week.

Scholze delivered one of the most pointed assessments of the entire Forum. “AI wants to accelerate everything, and I don’t see any inherent value in acceleration at all,” he said. His argument cut against the prevailing narrative that faster discovery is automatically better discovery. Scholze contended that even in the absence of AI, mathematics is already advancing so quickly that genuinely understanding its progress has become a bottleneck in its own right. In a field where a single landmark proof, such as his own work on perfectoid spaces, can take the community years to absorb and verify, the prospect of machine-generated conjectures and proofs arriving at an even greater pace raises an uncomfortable possibility: a mathematics that grows faster than any human, or even the collective of humans, can comprehend it.

Jessica Fintzen and Albrecht Schmidt, Scientific Co-Chairs of the Heidelberg Laureate Forum Foundation, reflected on the range of views the panel exposed. According to the co-chairs, the discussion spanned everything from embracing the use of AI, to cautioning against supporting companies whose values might not be aligned with those of the mathematical community, to trying to pinpoint what mathematics should really be about. They emphasized that the onstage debate addressed many questions that the mathematical and broader community must face, and that it served as a catalyst for conversations among HLF participants throughout the week. That framing captured the spirit of the Forum itself: not a search for consensus, but a structured confrontation with a technological shift whose consequences no one in the room claimed to fully predict.

Those questions extended well beyond the single panel. In a Spark Talk on “AI Safety and Mathematics,” Tsimerman, who received this year’s Fields Medal, argued that societies manage real risks by looking at them clearly and steering away from bad outcomes, not by ignoring them. His position framed AI safety not as a reason for disengagement but as a discipline in its own right, one in which mathematicians have a distinctive role to play. Torsten Hoefler, recipient of the 2024 ACM Prize in Computing, posed the question “Can We Build an AI Scientist?” and offered a prediction with sweeping implications: “everything that is verifiable will be automated.” For a discipline built on verification, that forecast lands with particular force, suggesting that the parts of mathematical work reducible to formal checking may eventually belong entirely to machines, leaving humans the tasks of conjecture, taste and interpretation.

Fields Medalist Martin Hairer presented “First Proof,” an initiative designed to measure how useful AI genuinely is to mathematical research by giving it the kinds of problems that talented mathematicians would actually work on. The approach addresses a persistent weakness in public claims about AI capability, where benchmarks often fail to correspond to the difficulty and texture of real research mathematics. By testing systems against problems of genuine current interest, Hairer’s framework aims to replace anecdote and hype with calibrated evidence, offering the community a way to track whether machine assistance is becoming a practical tool for working mathematicians or remains confined to well-trodden territory.

While AI dominated the conversation, the Forum also confronted a second technological threat with a very different character. Charles H. Bennett and Gilles Brassard, recipients of the 2025 ACM A.M. Turing Award for their pioneering role in the quantum revolution in computer science, delivered a joint lecture titled “The Quantum Information Revolution from Wiesner to Turing.” Brassard issued a caution that the quantum threat to today’s public-key cryptography is widely misunderstood. The danger, he explained, does not begin when a large quantum computer finally appears. Because encrypted data can be harvested now and decrypted later, adversaries need only record today’s traffic and wait. As he put it, “if a quantum computer arrives tomorrow, then my data is gone today.” The warning underscores why the migration to post-quantum cryptographic standards is treated by security researchers as an urgent present-day task rather than a distant concern.

Questions of trust in computation also ran through the program. Yael Tauman Kalai, recipient of the 2022 ACM Prize in Computing, took up a problem that grows more pressing as computation is increasingly outsourced to untrusted servers and, increasingly, to AI systems: when a massive computation is performed remotely, how can anyone be sure the result is correct? Her lecture presented succinct cryptographic proofs, compact certificates that are quick to check even for computations that are prohibitively expensive to rerun, as one answer. The technique connects directly to the week’s AI debates, since verifiable computation offers a potential safeguard for a future in which machine-generated results must be trusted at scale.

The scientific program showcased the breadth of both disciplines. Shayan Oveis Gharan, recipient of the 2026 IMU Abacus Medal, lectured on the polynomial paradigm and its applications in algorithms. Yu Deng, a 2026 Fields Medalist, gave a Spark Talk addressing critical problems in statistical physics and partial differential equations. Efim Zelmanov, Fields Medalist in 1994, opened the final day with a sweeping look at 200 years of abstract algebra. Nobel laureate Brian P. Schmidt, whose Nobel Prize in Physics recognized the discovery of the universe’s accelerating expansion, delivered this year’s Lindau Lecture, “The State of the Universe,” tracing how scientists came to understand that the cosmos is expanding. Attendees also watched livestreams marking the 100th birthday of Jean-Pierre Serre, the first recipient of the Abel Prize, including a lecture by Pierre Deligne in Serre’s honor and a talk by Serre himself from the celebrations in Paris.

The next generation made its own mark on the week. Dorothee Bär, Germany’s Federal Minister of Research, Technology and Space, addressed the Opening Ceremony by video, praising the Forum as a place where knowledge that cannot be learned from a paper passes in person from one generation to the next, and closing with an appeal: “Mathematics has outlived every border ever drawn around it. Please keep it that way.” The young researchers carried that spirit into the Forum’s first-ever Un-Conference on the final day, a bottom-up format for which participants had pitched and voted on discussion topics throughout the week. The results confirmed that the laureates’ concerns were widely shared: many sessions dealt with AI, including its impact on academia, how to reshape education in the age of AI, and technofascism and Silicon Valley ideology, while others took up the role of mathematics and computer science for society and the value of pure mathematics. The entire scientific program is available on the HLF’s YouTube channel, with in-depth coverage on the HLFF Blog, and journalists can register for accreditation for the 14th Forum in 2027 from March onwards. What the week made plain is that the debate over AI in mathematics is no longer a speculative exercise; it is a live argument being conducted at the very top of the discipline, and the outcome will shape how human knowledge itself is made.

Subject of Research: Debates on artificial intelligence in mathematical research at the 13th Heidelberg Laureate Forum

Article Title: Leading mathematicians and computer scientists weigh AI's growing role in mathematics at the 13th Heidelberg Laureate Forum

Article References: Leading mathematicians and computer scientists weigh AI's growing role in mathematics at the 13th Heidelberg Laureate Forum. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: Heidelberg Laureate Forum, artificial intelligence, mathematics, Fields Medal, Peter Scholze, quantum cryptography, post-quantum security, verifiable computation, AI safety, Turing Award, young researchers, Un-Conference