At the 2026 International Congress of Mathematicians (ICM), where Wang Hong and Deng Yu were awarded the Fields Medal, 2006 Fields Medalist Terence Tao delivered a sobering speech titled 'Mathematics in the Age of AI.' He warned that mathematics is facing a 'century crisis'—not about logical foundations like the early 20th century, but about values and practices.
The Working Hypothesis: Assume AI Wins
Tao proposed a working hypothesis: assume AI can soon complete a significant portion of research-level mathematics at reasonable cost and quality. He cited the First Proof benchmark, where AI solved 7 out of 10 novel research problems at a cost of $10–$1000 per problem. This, he argued, shifts the debate from 'Can AI do math?' to 'What is mathematics for?'
The KPI Trap: Goodhart's Law
Tao invoked Goodhart's Law: 'When a measure becomes a target, it ceases to be a good measure.' He illustrated how AI optimization could decouple traditionally aligned goals of mathematics—solving problems, developing theory, building community, and educating the next generation. He traced five revisions of the goal 'solve problems':
- Version 1: Solve as many open problems as possible. Flaw: yields many false proofs (e.g., of the Riemann Hypothesis).
- Version 2: Solve and verify correctness. Flaw: AI-generated proofs may be verified by Lean but incomprehensible to humans. Already, dozens of AI-generated proofs on Erdős' problem site lack human verification.
- Version 3: Solve, verify, and communicate clearly. Flaw: AI writing is grammatically perfect but glosses over difficulties, robbing readers of the struggle that is part of mathematical learning.
- Version 4: Solve, verify, communicate, and be accepted by the community. Flaw: Community acceptance is slow and cannot be optimized by authors alone.
- Version 5: All the above, plus canonization into textbooks. This is the slowest step but the most valuable, as it builds the foundation AI now exploits.
From Proof Scarcity to Proof Glut
Tao coined the term 'proof indigestion' to describe the impedance mismatch between AI's rapid generation and the slow human processes of verification, communication, and canonization. He declared: 'Mathematics will move from an era of proof scarcity to an era of proof glut.' This undermines the entire cultural and reward system built on the rarity of proofs.
Proposed Solutions
Tao endorsed the Leiden Declaration on AI and Mathematics (June 2026), emphasizing:
- Disclosure of AI use: To avoid a culture of hidden AI usage.
- Reduce weight on 'first to solve,' increase weight on 'digestion': Communication, publication, and canonization become the scarce skills.
- Human responsibility for correctness and attribution: Even when AI is used.
His personal rule: 'If the author cannot convincingly demonstrate they can give a clear, expert-level, correct, and properly attributed talk on the result, then the result should not be published.' In education and hiring, AI should be strictly limited; in other areas, mathematicians must define the rules proactively.
Tao concluded by calling for an open, honest discussion about AI capabilities and mathematical values, akin to the foundational crisis a century ago that ultimately strengthened the discipline. He humorously noted that his slides used AI for text completion and chart generation, but all dashes were human-generated.