Fields Medalist Terence Tao delivered a speech at the ICM conference, warning that mathematics is facing a foundational crisis driven by AI. He proposed a working assumption that AI will soon handle a significant portion of research-level math tasks at reasonable cost, and argued that this could decouple mathematics' traditionally aligned goals, leading to a crisis of values and practices.
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Fields Medalist Terence Tao proposed at the 2026 International Congress of Mathematicians that AI may usher mathematics from an era of 'proof scarcity' into one of 'proof abundance,' where the true bottleneck is no longer producing proofs but verifying, interpreting, and digesting them.
In his ICM 2026 talk, Tao proposed the 'AI capability hypothesis': future AI could perform some research-level mathematics at acceptable cost and under a degree of human supervision. He explicitly stated he did not intend to judge whether the hypothesis holds, but asked the audience to accept it as a working assumption—if AI soon takes on a significant portion of research-level mathematics, how should the mathematical community respond?
As background, Tao cited the First Proof benchmark from late May. Under controlled conditions, four AI systems successfully solved 7 out of 10 never-before-seen problems, with at least one solution per problem reaching the level of an academic journal publication, at a computational cost of roughly $10 to $1,000 per problem. However, the benchmark also exposed AI limitations: it still makes simple errors like citation mistakes and insufficient explanations. Tao cautioned that many public cases of AI mathematical ability suffer from reporting bias, with key variables such as compute investment, human involvement, and failure cases often not fully disclosed.
Tao invoked Goodhart's law to note that when 'solving more problems' becomes the optimization target, it ceases to be a good metric. He laid out a five-level progression around 'when is a mathematical problem truly solved': from solving an open problem, to verification, interpretation, peer acceptance, and finally integration into the shared knowledge base. AI can greatly increase production efficiency at the front end of the knowledge chain, but cannot automatically expand the back end, leading to 'proof indigestion'—mathematics may move from an era of proof scarcity to one of proof abundance.
This judgment continues Tao's thinking in recent years. In 2023 he predicted that by 2026 AI might become a trustworthy collaborator; in June 2026 he proposed the concept of 'Big Mathematics,' breaking complex research into distributed human-machine collaborative tasks. This talk pushes the thinking further to the new bottleneck of verifying, understanding, and digesting proofs.
Tao pointed out that AI-generated text dwells too long on simple parts and glosses over difficult or novel parts, rarely actively explaining connections to existing literature. Excessive polish masks genuinely instructive ideas. He cited Thurston's 1994 argument: the true measure of mathematics is whether it enables people to understand and think about mathematics more clearly and effectively.
Based on this, Tao made several suggestions: disclosing AI use should become the norm in academic writing; evaluation systems should reduce emphasis on being 'first to solve' a problem and give more recognition to interpretation, verification, and knowledge integration work. If an author cannot produce a clear, accurate, and well-cited expert-level report on research results, the results should not be directly published.
In April 2026, Tao told Nature that the 'job requirements for mathematicians are changing.' This year's Fields Medalist Jakob Zimmermann announced he would join OpenAI at the end of August to work on AI safety; Levent Alpöge, who earlier used Claude Fable 5 to discover a counterexample to the Jacobian conjecture, is Zimmermann's student and has now joined Anthropic. This reflects that future mathematicians may no longer just produce proofs, but design verification systems, interpret machine results, and help shape new rules for human-machine collaboration.
After the talk, Tao had AI gather over 100 of his past posts, interviews, and videos, summarize his views, and then had the AI 'interview' him in reverse, asking for sharper questions. The AI's questions included: Does collaborating with multiple AI companies lend credibility to industry hype? Is the automatic verifiability of mathematics just a special case? Does promoting large-scale mathematics projects accelerate 'proof abundance'? Tao responded that large-scale projects would focus on 'long-tail' problems that have lacked attention, avoiding competition with young mathematicians; determining when a proof is 'digested' requires new norms from journals and publishing systems.
This article is primarily based on Tao's 52-page slide presentation from ICM 2026; the talk video has not yet been released. First Proof benchmark results come from the official report; the Jacobian conjecture counterexample has independent formal verification. Tao's self-interview experiment was publicly shared on Mastodon. All inferences are based on clearly stated sources.
AI is changing the workflow and evaluation system of mathematical research. In the future, mathematicians' core skills may shift from proving theorems to posing questions, understanding proofs, and organizing knowledge. The mathematical community needs to redesign journal review, education systems, and career incentives to meet the challenges of the 'proof abundance' era.
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