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Morning Edition · Wednesday, September 9, 2026Published at 2:20 AM EDT · New York
OpenAI Claims an Internal Model Resolved Navier-Stokes, and Mathematicians Are Contesting It
The company says roughly 10,000 parallel agents worked 88 hours to produce a finite-time singularity proof formalized in Lean, while the Clay Mathematics Institute still lists the problem as open.
OpenAI said on September 8 that an unreleased internal system, one it describes as more capable than the GPT-6 Astra model it previewed five days earlier, produced a solution to the Navier-Stokes Millennium Prize Problem. The company published a writeup together with a formal proof in Lean, the proof assistant that mechanically checks each logical step. The claimed result is a finite-time singularity: a smooth fluid flow that breaks down after a finite interval. The Clay Mathematics Institute problem admits either a regularity proof or a demonstration that solutions can fail, so a verified blowup construction would settle it.
The production details are what practitioners should note. Reporting on the announcement puts the run at about 88 hours with as many as 10,000 agents in parallel and a 165-page writeup, a scale of computation closer to a sustained research campaign than a single chat session. Telegram channel AI Post carried the same figures to Russian and English-language AI audiences within hours.
Two things are disputed. First, status: the Clay Mathematics Institute continues to list Navier-Stokes among its unsolved problems, and independent mathematicians have not yet published a confirmation that the released Lean artifact compiles and proves the stated theorem. Second, credit. Tristan Buckmaster of New York University and Levent Alpöge of Anthropic released Lean-verified blowup proofs for related fluid systems, and Buckmaster has alleged that private Codex-session work may have been visible to OpenAI researchers. OpenAI says it finished its own Lean verification on September 6 without accessing that work, and Sébastien Bubeck of OpenAI called the allegations false and inflammatory.
The unusual feature of this dispute is that one half of it is decidable. Originality claims are a matter of testimony, but a Lean file either type-checks under the standard axioms or it does not, and any mathematician with the artifact can run that check.
Veracity: Plausible
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