September 19, 2026
Mathematicians Cannot Give Up AI: OpenAI Gets a Navier-Stokes Solution in 88 Hours
On 8 September, OpenAI said that its internal model had produced an analytical proof that Navier-Stokes equations develop singularities in finite time. The solution was obtained in around 88 hours, with Lean verification taking another 17 hours. The agents sent 2,7 million messages and used around 130 billion output tokens.
WIRED describes the conflict: AI creates an existential risk for mathematics, yet researchers continue using it for its practical benefits.
A working compromise. Tristan Buckmaster worked on the problem with Codex and Claude. After his conflict with OpenAI, he continued using Codex to edit research papers and examine the proof's logical steps. OpenAI's investigation of 8 September confirmed that his prompts, submitted 2 months before publication, could not have influenced the result, including the training, and that his work with Levent Alpöge differed substantially from OpenAI's work.
The reproducible layer. OpenAI published Lean 4 formalizations of its Navier-Stokes and Euler results on GitHub. Building them requires Lean 4.34.0-rc2, Mathlib, and Lake, followed by `lake exe cache get` and `lake build`.
This is already a series. WIRED reported that Anthropic used Claude to prove 29 500 small theorems and formalize an existing proof of Fermat's theorem. In August, OpenAI reported progress on 10 long-standing mathematical problems.
Access is expanding. ChatGPT for Academic Researchers is expected to give 100 000 researchers free access to frontier models by 2027. The initial cohort includes 10 000 people, and an approved workspace includes up to 5 free seats for 12 months. Applications require research faculty or postdoctoral researcher status, an institution from the list, a paper from the past 3 years, and verification through SheerID.
Objections remain. More than 4 000 people signed the Leiden Declaration, 25 Fields Medal laureates joined an open letter, and more than 2 000 people affiliated with Caltech called for an AI mathematics hackathon to be paused.
By 2027, OpenAI plans to expand free access to frontier models to 100 000 researchers.
Source
