---
id: "2026-07-24-tao-icm-mathematics-in-the-age-of-ai"
url: "https://postcutoff.com/e/2026-07-24-tao-icm-mathematics-in-the-age-of-ai/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2026-07-24"
date_precision: day
category: science
importance: 3
confidence: high
status: [Result confirmed]
verification: Unverified claim
sources: 8
editor: human editor
human_review: null
version: "2026-10-18"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-07-24-tao-icm-mathematics-in-the-age-of-ai/

# Terence Tao's ICM 2026 public lecture 'Mathematics in the age of AI' calls a crisis in the foundations of mathematical values

On 24 Jul 2026, at the International Congress of Mathematicians in Philadelphia, Terence Tao gave the public lecture "Mathematics in the age of AI". He argued that mathematics is entering a "crisis in the foundations of mathematical values and practices", comparable to the 1900–1930 foundations crisis. Setting aside the capability debate, he asked what the community's goals should be if strong AI capability arrives. An essay version is arXiv 2608.16753.

## 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reported by press: results that cannot be shown correct and properly attributed, or explained by their authors, should not be published; disclose tool use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).

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 85 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): 24 days after its cutoff
- Gemini 4 Hydrogen (training cutoff March 2026): 115 days after its cutoff
- Grok 4.7 (training cutoff May 2026): 54 days after its cutoff

## Sources

1. [Tao: slides 'Mathematics in the age of AI' (PDF)](https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.pdf) (teorth.github.io, official)
2. [arXiv 2608.16753: Mathematics in the age of AI (essay)](https://arxiv.org/abs/2608.16753) (arxiv.org, paper)
3. [Tao on Mathstodon: slides uploaded, AI-made summary and interview](https://mathstodon.xyz/@tao/116977934921819775) (mathstodon.xyz, official)
4. [Terence Tao on AI in mathematics (and beyond), AI-collated summary](https://teorth.github.io/tao-web/ai-views.html) (teorth.github.io, official)
5. [Tao: AI 'interview' on his AI views](https://teorth.github.io/tao-web/ai-views-interview.html) (teorth.github.io, official)
6. [Scientific American: If AI can do math, what's the point of mathematicians?](https://www.scientificamerican.com/article/mathematicians-confront-the-ai-apocalypse/) (scientificamerican.com, press)
7. [Simons Foundation: Watch: Terence Tao on AI and why we do math](https://www.simonsfoundation.org/2026/08/13/fields-medalist-terence-tao-on-artificial-intelligence-and-why-we-do-math/) (simonsfoundation.org, press)
8. [YouTube recording (uploaded by Alvaro Lozano-Robledo)](https://www.youtube.com/watch?v=sxAe4HJceFQ) (youtube.com, video)

## Changes

- 2026-10-18: 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
- 2026-09-29 (filed): Created

## Related

- 2026-09-11: [Fields Medallists' open letter 'A Severe Misalignment of AI in Mathematics' criticises labs' race for famous problems](https://postcutoff.com/e/2026-09-11-fields-medalists-letter-ai-mathematics/index.md)
- 2026-08-18: [Palomar launches: a registry of Lean-verified mathematics to curb misrepresented AI proof claims](https://postcutoff.com/e/2026-08-18-palomar-lean-registry/index.md)
- 2026-06-02: [Leiden Declaration on Artificial Intelligence and Mathematics sets community norms for AI in maths (4,000+ signatories)](https://postcutoff.com/e/2026-06-02-leiden-declaration-ai-mathematics/index.md)
- People: [Terence Tao](https://postcutoff.com/person/terence-tao/)
- Archived: 4 videos, listed in https://postcutoff.com/e/2026-07-24-tao-icm-mathematics-in-the-age-of-ai/index.json