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Terence Tao's Long Response to OpenAI's Navier-Stokes Claim

After OpenAI claimed to solve the Navier-Stokes equations, Terence Tao warned that AI cracking open problems too early could harm mathematics, then posted a long, widely-shared thread analyzing the result, praised by François Chollet.

2026-09-08 ~ 2026-09-09 · 2 episodes · 8 posts

Episode 1 · Terence Tao warns premature AI solutions could harm mathematics (2026-09-08, 5 posts)

Terence Tao suggested that if AI cracks key open problems in mathematics too early, it could backfire on the progress of the entire field, prompting follow-up discussion from multiple authors.

Confirmed

  • Tao used the global regularity problem for the incompressible Navier-Stokes equations (and the corresponding Euler equations problem) as an example: the intermediate theories and methods a mathematical field grows on emerge from the human process of tackling hard problems. If AI skips these intermediate steps and delivers answers directly, subsequent research loses its foundation.
  • @ValerioCapraro relayed Tao's view: pure mathematics poses hard problems not just for the answers themselves, but because the human process of solving them drives the field forward. AI opaquely "solving" these problems prematurely would contaminate that process and could even have a net negative impact on mathematics' overall progress. He said he has followed Tao for 20 years and considers his thinking exceptionally clear.
  • @qberthet offered another mental model: mathematical knowledge resembles "islands of knowledge" — the bigger the island, the longer its boundary with the unknown. Mathematics is thus not a field that can be exhausted; any new result brings new questions.
  • @tak3sh8 pointed out a limitation of AI problem-solving: people who solve problems with AI often don't truly understand them the way those who grind for months or even years do, making it hard to pose the right and productive next question — possibly the core reason AI accelerates problem-solving yet struggles to accelerate mathematical progress. He also asked: if AI solved Navier-Stokes and left behind a large Lean formalized proof, what would the next interesting question be?

Why it matters

  • This debate touches the core question of the AI era: does the value of mathematics lie in the answers themselves, or in the theories and methods accumulated through human problem-solving? If AI solves problems en masse by "skipping grades," disciplines traditionally organized around hard problems as their engine may need restructuring.

Episode 2 · Terence Tao's long response to AI's Navier-Stokes claim earns Chollet's praise (2026-09-09, 3 posts)

Terence Tao posted an insightful long thread responding to OpenAI's Navier-Stokes announcement, which François Chollet recommended; the discussion also touched on whether other fields would benefit if human-driven frontier math fades.