Terence Tao responds to Navier-Stokes AI rumor with warning against benchmark-driven math races

量子位 · wechat · 2026-09-06

After rumors that Claude cracked the Navier-Stokes millennium problem, Terence Tao published a long response: he wasn't involved and doesn't know the details, but used the moment to warn against AI benchmark culture in mathematics.

The trigger: Mathematician Julia Stadlmann posted a 34-page paper pushing the bounded prime gap from 246 down to 240 — the first progress in 12 years — after two years of work with no AI tools. Hearing OpenAI was about to publish on the same problem, she rushed to upload, saying she can't compete with corporate compute. Within days, Claude Opus 5.1 claimed 260, Axiom Math 220, and GPT-6 Astra 186 (unverified).
The thought experiment: Tao imagined benchmark-driven AI labs existing in 2005 — they'd swarm GPY's method, saturate the problem, leave no papers, no textbook material, no Maynard sieve; in that timeline Zhang Yitang is still washing dishes.
Core argument: Citing Goodhart's law, he argues optimizing a single metric doesn't advance mathematical understanding; the real opportunity cost is turning fruitful problems into viral marketing material. He isn't anti-AI (the collaborative Erdős problems project is his positive example) but opposes skipping human understanding, peer review, and expert collaboration purely to hit a benchmark number.
Context: Tao has proposed restricting certain math problems from automated solvers, and the IMU-backed Leiden Declaration warns AI-generated proofs threaten verifiability. His suggestion to AI companies: race to announce new mathematical insight, not solved open problems.

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Terence Tao responds to Navier-Stokes AI rumor with warning against benchmark-driven math races

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