Terence Tao warns AI-cracked math problems could pollute and stall mathematical progress
量子位 · wechat · 2026-09-05
Terence Tao published a long-form warning that AI solving math problems too quickly, in black-box fashion, could "pollute" the value of major open problems.
Using the Navier–Stokes global regularity problem as an example:
- Process matters more than answers: past "failures" attacking such problems produced foundational results like Leray–Hopf weak solutions, Prodi–Serrin partial regularity, and the Beale–Kato–Majda blow-up criterion. Tao's own failed attempts unexpectedly connected fluid computation, Turing universality, and symplectic topology.
- The problem fits an AI pipeline: a consensus strategy exists — self-similar ansatz, numerical verification, stability proof, residual checking — which ML simulation + interval arithmetic + formal proofs + LLM-proposed ansätze + human guidance could plausibly complete.
- The risk: an autonomous AI harness solving the problem inside a company, with the process hidden from the public and the proof beyond human comprehension, would yield a solved problem but almost no new mathematics. In the worst case, AI's impact on math could turn net negative.
He also quipped about a hypothetical scenario where GPT-6 announced pushing the twin-prime gap bound from 246 to 186 (with Anthropic and Axiom at 188 and 212), days after Oxford's Julia Stadlmann published her analysis narrowing it to 240 on Aug 31 — luckily before the problem was "polluted".
Related event: Rumors Claim Claude Solved Navier-Stokes; Terence Tao Responds(9 posts)→
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