OpenAI denies reading two mathematicians' Codex logs before racing them to Navier-Stokes

A mathematician mid-problem pastes a half-finished argument into a paid coding agent, because the agent handles Lean formalisation faster than he can by hand. Buckmaster and Alpoge say they used several models, including Claude and Codex, to reach the advances they posted ^[8]. Vendors tell themselves that unpublished, competitively sensitive work stays off their consumer surfaces. What users actually do is reach for whatever clears the next obstacle, and trust that the terms mean what they appear to mean.

Bubeck said neither the company's researchers nor its agents saw the pair's work before it went public, and that their prompt and proof were not used to prompt OpenAI models or direct its agents ^[12]. Buckmaster's account of asking about the Codex logs is that he was told the model "didn't look up user data", and that his questions about training went unanswered ^[10]. Lookup and training are different pipelines with different retention, so an answer about one does not answer the other.

What keeps either statement from closing the credit question is an employment fact. Bubeck says the accelerant was rumours that Anthropic was making progress toward Navier-Stokes ^[4]; Alpoge is a researcher at Anthropic ^[8]. The rumour OpenAI says it responded to and the work Buckmaster says it became aware of can be the same information travelling by two routes, and sincerity in a press briefing does not separate them.

More than 1,000 agents running for more than 50 hours is at least 50,000 agent-hours ^[5][16], and Mark Chen put the cost in the millions of dollars ^[7]. The Clay prize for the problem is $1 million ^[2], so the compute alone cost more than the prize pays out ^[17]. This was a demonstration, timed by a competitor's rumoured progress rather than by the mathematics.

The sourcing here carries a caveat: the proposals, including the one that would have carried Buckmaster's name on the announcement without Alpoge's, come from Buckmaster's own statement ^[11], and Wired reported that Buckmaster, Alpoge and Anthropic had not responded to its request for comment ^[15]. OpenAI says it recognises the pair's priority on unforced Euler ^[13], and its own mathematician, Ven Chandrasekaran, says the two solutions differ in nature ^[14].

For whoever decides on Monday which agent gets an unpublished result, the split worth making is between two things that usually get merged: whether the vendor's data commitment covers training on prompt content rather than only human access and retrieval, and whether the vendor is a plausible claimant for credit on that particular output. A vendor that only answers the retrieval half, and might publish the same result next month, is fine for boilerplate work; the unpublished work should go to whichever vendor puts the training answer in writing.