OpenAI has spent recent years pushing into ever more difficult areas of mathematics, and this week claimed one of its most significant results to date: a solution to a legendary Millennium Prize problem. Under ordinary circumstances, such a breakthrough would be greeted as a historic achievement. Instead, many within the mathematics community have responded with growing disquiet.
To numerous researchers, the company resembles less an enthusiastic newcomer than an exceptionally well-funded outsider, moving into problems that scholars have devoted their careers to studying, with limited regard for established norms or for those affected by its progress. Underpinning that concern is a belief that OpenAI approaches mathematics with a different motivation. Where mathematicians seek to advance the field, the company appears focused on winning.
More than a dozen mathematicians shared their views this week, among them Tristan Buckmaster and Andreas Thom, both connected to the recent controversies surrounding the company’s work. Even those doubtful of the most serious accusations described a discipline unsettled by the firm’s conduct and uncertain about its next steps.
Disputes Over the Navier-Stokes Proof
Buckmaster has questioned whether OpenAI adequately explained if work he carried out through its tool Codex may have contributed to its recent results. An OpenAI spokesperson firmly rejected the suggestion, stating: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.” Buckmaster remained sceptical, saying that given the company’s behaviour, such statements should be treated with considerable caution.
The dispute arose after a rumour that some researchers were making progress on Millennium Prize problems. OpenAI decided to test whether one of its advanced, unreleased models could make headway on the same ground. According to the company, it deployed roughly 10,000 agents, spent tens of millions of dollars on computing resources and took just 88 hours to reach a solution to the Navier-Stokes problem, which concerns the flow of fluids.
Competing Researchers and Contested Events
OpenAI also identified those it was competing against: Buckmaster, a professor at NYU, and Levent Alpöge, a researcher at rival firm Anthropic. Among several lines of enquiry, the pair had been pursuing Navier-Stokes but had not yet completed a proof. Some details of what followed are strongly disputed, though both sides broadly agree on the basic sequence of events. Alpöge’s involvement presented a difficulty for OpenAI, despite his description of the work as a “personal collaboration” independent of his role at Anthropic.
Buckmaster said he contacted OpenAI after learning the company was aware of their progress and was racing towards its own solution. He said discussions with OpenAI researcher Sébastien Bubeck became contentious and, in his view, threatening. The company offered him a path forward, one that excluded Alpöge, and Buckmaster said he was offered practically unlimited computing resources.
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