OpenAI faces competing claims around maths breakthrough

OpenAI has become embroiled in a public spat with a mathematician who had been working with a researcher from its arch-rival Anthropic, after the ChatGPT maker announced it had solved one of the biggest problems in the field.

OpenAI on Tuesday announced that an unreleased internal model had solved the Navier-Stokes equation, a complex mathematical question that carries a $1mn prize.

However, the achievement has been met with claims of foul play by a New York University mathematician, Tristan Buckmaster, who had been working on related research with Levent Alpöge, a mathematician at Anthropic.

Chief executive Sam Altman defended OpenAI on Tuesday as the controversy escalated, saying the lab had been threatened with “unfounded accusations of plagiarism”.

The dispute over the mathematics breakthrough demonstrates the increasing abilities of AI systems but also underscores how the fierce rivalry between OpenAI and Anthropic has spilled out into unexpected controversies.

The mathematics furore began after OpenAI in a blog post on Tuesday said it had reached a solution to Navier-Stokes — one of seven Millennium Prize problems set out by the Clay Mathematics Institute as some of the “most difficult” in the discipline.

OpenAI said it had been training a new internal model since the end of August, with “unprecedented performance” in mathematics. It said it was inspired to use the model to try to solve all the unresolved Millennium problems — each carrying a $1mn prize — after hearing “rumours” that Anthropic had cracked some of them at the beginning of September.

The company said it later learnt that the rumours related to Alpöge and Buckmaster. After completing its project, OpenAI said it reached out to both of them “to offer a concurrent release of our results and to recognise their priority in a joint announcement”.

Yet Buckmaster’s account sharply conflicts with this version of events. The New York University professor on Tuesday claimed OpenAI raced to beat him and rival Anthropic by using their existing approach and throwing considerable computing resources at the problem.

Labs and AI users are widely grappling with a shortage of computing power and the increasing cost of running advanced models. OpenAI said it spent millions of dollars on its effort to crack the problem.

Buckmaster and Alpöge on Tuesday announced three proofs regarding problems seen as a milestone closely linked to Navier-Stokes, including a breakthrough involving the Euler equation.

The pair used multiple models including tools from Google DeepMind, Anthropic and OpenAI. Buckmaster argued their work and the way they approached the problem laid the foundations for solving the Navier-Stokes.

Buckmaster said he and Alpöge, working in a personal capacity, had “quietly chosen to attack” the problem using an approach introduced in previous academic work. “Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement,” he said.

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He described conversations with OpenAI researcher Sébastien Bubeck, who he claims asked twice to remove Alpöge’s name from the proof because of his employment at Anthropic. Bubeck denies this characterisation.

The conversations became acrimonious after Buckmaster told Bubeck he would go public about the dispute, according to the professor’s account.

Altman said, in a post on X, that OpenAI would have “greatly preferred coordination” and “did not rush to publish even though the other team wasn’t communicating with us”.

“When we learned that they had Euler but not Navier-Stokes, we offered to let them go first, to suggest that they should be the ones to get the prize, and optionally for Tristan [Buckmaster] to be the lead author on a rewrite of the OpenAI proof,” Altman added.

He said it felt “challenging” to extend the same offer to Alpöge, the Anthropic employee, “who was not willing to talk or coordinate with us anyway”. But OpenAI was “open to other solutions”, he added.

Anthropic did not respond to a request for comment.

Alpöge said in a post on X that he “actually woulda been pumped to collaborate on this” but was deterred after OpenAI offered to share the prize with Buckmaster if he removed the credit for his collaborator.

“[It was] pretty wacky, unstrategic, and unnecessary,” he added.

Both researchers suggested that because they had used OpenAI’s tools, data from the work might have informed how the lab’s model approached the problem.

OpenAI said “no specific user data was accessed in order to solve this problem” but that it could not “rule out that de-identified data derived from their usage of our products helped improve our models⁠”. It added that its proofs and results differ from the work completed by Alpöge and Buckmaster.