OpenAI's 10,000-Agent Navier-Stokes Proof Draws a Credit Fight

OpenAI said on September 8 that an internal AI system had produced a proof that the Navier-Stokes equations, which govern fluid motion, can develop a singularity in finite time — a point where they stop describing anything physical. The company published a 166-page manuscript and a formalization in Lean, the language mathematicians use to check proofs mechanically, and said it does not intend to claim the $1 million Millennium Prize attached to the problem.

By OpenAI's own account, roughly 10,000 agents ran about 88 hours from September 1 and consumed an estimated 130 billion output tokens, driven by an unreleased model the company calls significantly more capable than GPT-6 Astra; another 17 hours went into the Lean work. Sebastien Bubeck, who led the effort, told reporters on September 8 that OpenAI began training a new mathematics model on August 28 and committed heavy resources to Navier-Stokes after reading rumors that Anthropic was making progress on it. None of those figures has been independently audited.

The rumors pointed at Levent Alpöge, a mathematician at Anthropic working on the problem in his spare time with Tristan Buckmaster of NYU. Building on work by Diego Córdoba and Luis Martínez-Zoroa, and using commercial AI models as assistants, the pair proved finite-time blowup under smooth forcing for the incompressible porous medium, Boussinesq and three-dimensional Euler equations — neighbors of Navier-Stokes, not the Millennium problem itself — and posted their drafts late on September 7, hours before OpenAI's announcement. Buckmaster says he contacted OpenAI on September 3, and that on a September 6 call Bubeck told him OpenAI already had the same approach and offered two options: publish first and let OpenAI follow a day later with the full result, or pursue the prize on condition that he credit OpenAI and drop Alpöge over his Anthropic affiliation. Buckmaster also asked whether the model had seen the drafts the pair fed into Codex. OpenAI says it "did not see any of their work through any means until they released it publicly," and that his Codex prompts could not have influenced the system.

The stake for readers is less the prize money than whether AI labs can be trusted in open research, and whether what is typed into a commercial coding assistant stays private. Terence Tao, who called the Alpöge-Buckmaster argument a remarkable achievement on his blog on September 7, has written that solving such problems is "only a proxy goal for the primary goal of developing mathematical understanding and insight," and warned that strip-mining open problems could destroy the ecosystem from which the next generation of techniques and mathematicians would emerge.

What comes next is slow. OpenAI's proof is machine-checked but not refereed, and no one outside the company has confirmed that the formalized statement matches the Millennium formulation, which the Clay Mathematics Institute still lists as unsolved. Clay's rules require publication in a qualifying outlet, at least two years to pass and general acceptance in the global mathematics community. Quanta Magazine reported that parties to the September calls give differing accounts; they have not been reconciled.

Disclosure: NewUJ's editorial process uses Anthropic's Claude models.