OpenAI says it solved Navier-Stokes in 88 hours

The announcement came on September 8, a day after two mathematicians published the advance that paved the way, and one of them was asked to stay off the paper.

What happened

On Tuesday, September 8, OpenAI announced that an unreleased internal model, more capable than GPT-6 Astra, proved that the three-dimensional Navier-Stokes equations can develop a singularity in finite time. It’s one of the seven Millennium Prize Problems the Clay Mathematics Institute set in 2000. Until now only one had been solved.
The result was produced by some 10,000 agents in parallel over 88 hours, at a cost the company put in the millions of dollars. OpenAI said it won’t claim the prize and that it started on September 1, after hearing rumors that Anthropic models had solved a bigger problem.
On Monday the 7th, mathematician Tristan Buckmaster of New York University posted on Mastodon a proof that the Euler equations, the simplified version, blow up. He did it with Levent Alpöge, a mathematician employed by Anthropic, after almost a year of work with public models from both companies.
In a document published alongside that proof, Buckmaster says OpenAI gave him two options: publish, and OpenAI would publish its own the next day, or sign a joint paper from which Alpöge was excluded because of his ties to Anthropic. OpenAI denied that its agents or employees accessed the transcripts.

Why it matters

The question of who solved the problem doesn’t have a company as its answer. The Euler advance belongs to two people with first and last names. The “OpenAI versus Anthropic” framing only holds if you accept that a mathematician’s employer weighs more than their work, which is exactly the criterion by which it was proposed to leave Alpöge off the byline.
Both proofs use the same approach, that of Diego Córdoba and Luis Martínez-Zoroa. It’s possible for two teams to get there separately, and it’s also possible for one to get there after hearing rumors about the other. Only one of the parties has the records to settle it.
For anyone doing research inside a vendor’s tool, the operational point is what gets logged. Buckmaster asked whether the agents had accessed his transcripts, and was told no. He asked whether the models had been trained on them and got no answer. That second question is the one that settles the matter, and it’s the one still unanswered.

The number

88 hours. What it took some 10,000 agents in parallel to produce the proof. Buckmaster and Alpöge had been at it for almost a year.

Context

The equations describe how fluids move, but nobody had proved whether they can break down and predict that a fluid reaches infinite velocity at a point, something that doesn’t happen in nature. Both proofs answer yes. The episode falls in a week when the conduct of frontier labs was already under discussion, after the public resignation of an Anthropic pretraining researcher.

What’s next

The proofs have to go through review by the mathematical community. OpenAI’s was formalized in Lean, which verifies the steps automatically but settles neither the statement nor the attribution. No timelines announced.
The Clay Mathematics Institute prize requires publication in a peer-reviewed journal and two years of general acceptance. OpenAI said it won’t claim it.
Anthropic hasn’t commented on the episode or on the proposal to exclude its employee from authorship.

Bottom line

Last week, Terence Tao wrote that these problems matter less for their solution than for what gets developed in trying to solve them, and that solving them prematurely and without transparency about the process may end up being negative for mathematics. He wrote it before the announcement.

OpenAI says it solved Navier-Stokes in 88 hours, and the problem is authorship