OpenAI's 88-hour Navier-Stokes run leaves provenance in the vendor's own logs

Buckmaster wrote that the line of attack originates with Diego Cordoba and Luis Martinez-Zoroa, who spent years building forced blow-ups using rough forcing, and said he thought Martinez-Zoroa should be awarded a Fields Medal.

Buckmaster says he and Alpoge kept their draft proofs inside OpenAI Codex sessions, that when he asked whether OpenAI's model might have been trained on that data he got no answer, and that he is not claiming it happened, only that the question went unanswered.

Buckmaster emailed a mathematician at OpenAI on Thursday, September 3rd, to avoid confusion, emphasising the work with Alpoge was a personal collaboration not supported by Anthropic or NYU; the answer was warm and even offered OpenAI compute.

The calls came on Sunday, September 6; Buckmaster says Sebastien Bubeck came on, the two sides had a couple of conversations that afternoon, and Alpoge was not on the line.

Buckmaster says he was told an internal OpenAI model had yielded a roughly 100-page proof of forced Navier-Stokes blow-up using smooth forcing along "options c and d" in Charles Fefferman's formal statement of the problem, the narrow route he and Alpoge had secretly selected and that nearly no one else was following.

Over the weekend before OpenAI's Tuesday announcement, rumours swirled that Anthropic was on the cusp of announcing that one of its AI models had cracked a Millennium Prize Problem.

The Millennium Prize Problems are seven mathematical challenges selected in 2000 by the Clay Mathematics Institute, which offers a $1 million prize for the first correct solution to each.

Buckmaster, of New York University's Courant Institute, says he and Alpoge used Anthropic's Claude and OpenAI's Codex powered by the GPT-5.6 Sol model, and used OpenAI's Astra model to help audit and write up results but not for the mathematical reasoning and calculations.

Buckmaster says he and Alpoge worked for most of a year making only slow progress, but made rapid progress from mid-August onwards with help from several AI models.

OpenAI deployed around 10,000 agents of an as-yet unreleased powerful model on Aug. 28 and solved the problem within 88 hours, proving the equations sometimes break down under extreme conditions.

Buckmaster says Bubeck told Alpoge that "very little human input" went into the OpenAI result.

Buckmaster wrote that it emerged an entire team had been working on the problem, that this was one of a number of things tried, that work had started on the unforced problem, that the team first set the model on easier problems including Euler, that even the prompt shown to him had been written by prompting Codex, and that an insane amount of compute had been used.

Buckmaster alleges Bubeck twice pushed to remove Alpoge as an author due to his Anthropic ties, and once asked him, "Why would you ruin your career?"

OpenAI denied the allegations; Bubeck called the claims "false and inflammatory" in a post on X, said he had entered the debate following academic norms, promised a more complete response, and denied using the mathematicians' prompts or proofs.

Sam Altman posted that he spent much of the weekend talking with the team who did the work, that Bubeck and everyone else acted with integrity and generosity throughout, and that OpenAI initially believed the other team had also solved the problem and wanted to collaborate on a joint release.

Roughly 10,000 agents running for 88 hours is about 880,000 agent-hours, or close to a hundred agent-years of continuous work.

An 88-hour run beginning on August 28 completes around August 31 or September 1, two to three days before Buckmaster's September 3 email to OpenAI.

If the OpenAI result holds up, it would be only the second Millennium problem ever solved, and the first credited to an AI company.