OpenAI and Navier–Stokes: Contested Offers and Academic Tensions

OpenAI claims to have found a solution to the Navier–Stokes problem, one of the seven Millennium Prize challenges, in 88 hours by mobilizing around 10,000 agents and tens of millions in computation. Mathematicians are contesting the methods, denouncing perceived unfair offers, retroactive credits, and conflicts involving a researcher employed at Anthropic.

Revised Credits and Suspicions of Conversation Use

Andreas Thom found himself at the center of a controversy following OpenAI's announcement of a mathematical result that heavily relied on work conducted with Gábor Kun. OpenAI subsequently discreetly modified its announcement to acknowledge this contribution, without publicly communicating this change. Thom described the episode as "not very pleasant." Allegations from Tristan Buckmaster led him to reconsider an open question: whether exchanges he had with ChatGPT regarding his research may have been used to improve models that solved the problem he was working on. Meanwhile, many mathematicians report observing OpenAI's progress with increasing concern, perceiving it as a well-funded intruder disrupting norms and balances.

Buckmaster Challenges Offers and the Exclusion of a Colleague

Tristan Buckmaster criticizes OpenAI for not clarifying whether its use of the Codex tool contributed to the recent results. OpenAI spokesperson Laurance Fauconnet asserts that his Codex queries from the past two months could not have influenced the system, including training, a position Buckmaster receives with skepticism. After learning that OpenAI was aware of his advancements and was rushing, Buckmaster says he had tense exchanges with Sébastien Bubeck. He claims that OpenAI offered him practically unlimited computation and the position of sole author of a paper announcing the breakthrough, provided he excluded Levent Alpöge, which he describes as a "bribe" and a request to "throw Levent under the bus." He says he refused, made his work public, and organized a "war room" with colleagues and lawyers, while questioning whether OpenAI had used his interactions with Codex.

OpenAI's Response and the Anthropic Question

Sébastien Bubeck refutes the description of threatening conversations and acknowledges having offered resources for Buckmaster to finish his own proof or take charge of writing OpenAI's. He adds that OpenAI has already established similar arrangements with other mathematicians, without naming them. Bubeck points to a friction point: the difficulty of integrating a researcher employed by Anthropic, namely Levent Alpöge, into an internal OpenAI project. While some details of the timeline are disputed, the parties agree on the general sequence and that Alpöge's involvement posed a problem for OpenAI.

What OpenAI Claims About Navier–Stokes

OpenAI presents the resolution of Navier–Stokes as one of its greatest successes. The company claims to have mobilized an advanced unpublished model, around 10,000 agents, and tens of millions of dollars in computation, achieving a solution in 88 hours. Navier–Stokes, which deals with fluid flow, was among the areas worked on by Tristan Buckmaster and Levent Alpöge, without complete proof at this stage. OpenAI explains that it embarked on this after learning that researchers were making progress on Millennium Prize problems.

The Race for Millennium Prize Problems and Its Tensions

Outlined by the Clay Mathematics Institute in 2000, the seven Millennium Prize problems are considered among the most formidable, each carrying a reward of $1 million. Only one, the Poincaré conjecture, has been solved in nearly a quarter of a century. For AI companies eager to demonstrate the performance of their models in mathematics, these challenges represent attractive targets. Buckmaster and others believe this explains the vigor of OpenAI's reaction when a rival company seemed involved. Buckmaster, marked by a previous collaboration with Google DeepMind, speaks of a tech obsession with grand problems and scoops, a fixation on prestige and being first, while asserting that he does not care about the prize itself. Andras Juhasz reminds us that mathematics is also a quest for beauty and discovery, often without immediate application. At the forefront, the plurality of approaches and the lineage of ideas matter as much as the resolution itself, a point on which Buckmaster sees a gap with Big Tech. OpenAI, which claims to have established itself in mathematics in recent years, presents its claim on Navier–Stokes as one of its greatest successes, which in other times many would have hailed as historic. However, mathematicians judge that OpenAI's motivations differ from those of the academic community.