Terence Tao’s ICM 2026 public lecture ‘Mathematics in the age of AI’ calls a crisis in the foundations of mathematical values
Result confirmed
The takeaway
On 24 Jul 2026, at the International Congress of Mathematicians in Philadelphia, Terence Tao gave the public lecture “Mathematics in the age of AI”.
Status
- Claim
Result confirmed
- Our reporting
- High confidence
- Verification
- Unverified claim
- Importance
- 3 of 5
- Last verified
- 18 October 2026
Your AI and this story
- GPT-6 Astra85 days after its cutoff
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None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 24 days before it.
Key facts
- Venue: ICM 2026 public lecture, Pennsylvania Convention Center, Philadelphia, 24 Jul 2026 (7:15 pm)
- Frames an ‘AI Capability Conjecture’ (weak vs strong forms) and conditions on it being true, then asks the orthogonal ‘Goals and Values Question’
- Uses problem-solving as a case study: from ‘solve as many unsolved problems as possible’ to results that are verified, clearly communicated, digested and incorporated into the definitive theory
- Recommendation reported by press: results that cannot be shown correct and properly attributed, or explained by their authors, should not be published; disclose tool use
- Slide footnote: ‘All em-dashes in these slides were human-generated.’
- Essay: arXiv 2608.16753 (17 Aug 2026, 12 pages, submitted to the ICM 2026 Proceedings)
- Tao also published an AI-collated summary of his AI views and an AI-conducted ‘hard hitting’ interview of himself
What happened
Tao’s public lecture at the quadrennial ICM compared the present moment to the early-20th-century crisis in foundations. That crisis ended with a rigorous, standardized framework. Tao said the community now needs to codify its values in the same way. He deliberately did not argue about which AI capabilities are real. He treated a “reasonably strong” capability conjecture as a working hypothesis and asked what mathematicians actually want. Press described the lecture as more foreboding than his earlier comments.
Why it matters
It was the most prominent framing of AI-and-mathematics at the field’s main quadrennial event. It came just before the wave of AI results (Astra’s ten advances, Navier–Stokes) and the community statements that followed (Fields Medallists’ letter, Palomar, SAIR).
Sources
8 sources from 6 sites. Numbers match the chips in the text.
8 sources: 5 primary, 2 press, 1 reaction
Primary
- Tao: slides ‘Mathematics in the age of AI’ (PDF)teorth.github.io, official
- arXiv 2608.16753: Mathematics in the age of AI (essay)arxiv.org, paper
- Tao on Mathstodon: slides uploaded, AI-made summary and interviewmathstodon.xyz, official
- Terence Tao on AI in mathematics (and beyond), AI-collated summaryteorth.github.io, official
- Tao: AI ‘interview’ on his AI viewsteorth.github.io, official
Press
- Scientific American: If AI can do math, what’s the point of mathematicians?scientificamerican.com, press
- Simons Foundation: Watch: Terence Tao on AI and why we do mathsimonsfoundation.org, press
Reactions
- YouTube recording (uploaded by Alvaro Lozano-Robledo)youtube.com, video
Changes
- Videos added (ipam-terence-tao-integrated-explicit-analytic-number-theory-network, big-think-terence-tao-6-essential-concepts-of-math), from Tao’s Oct 17 post on recent talks
- Filed
