OpenAI has announced that one of its experimental artificial intelligence models has solved the Navier-Stokes Millennium Prize problem, one of the most celebrated unsolved questions in mathematics. The result, if validated, would mark only the second time a Millennium Prize problem has been solved — the first being Russian mathematician Grigori Perelman's proof of the Poincaré conjecture in 2002. The announcement has electrified the mathematics community, while simultaneously triggering sharp debate over ethics, credit, and the role of AI in scientific research.

The Navier-Stokes equations, formulated around 200 years ago, describe the movement of fluids such as water and air. They underpin enormous swaths of modern science and engineering, yet a fundamental question about them has remained unanswered: can the equations produce a so-called "blow-up," where fluid speed becomes mathematically infinite? OpenAI's model found that yes, under certain conditions, such a blow-up is theoretically possible within the equations — even though it cannot occur in physical reality, since real fluids are made of discrete molecules rather than the continuous medium the equations assume. The seven Millennium Prize problems were selected in 2000 by the Clay Mathematics Institute, an American philanthropic body, each carrying a one-million-dollar reward for the first verified solution.

The path to the result was built on years of prior human work. Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa had spent roughly a year developing the conceptual foundation that OpenAI's system then extended, with Córdoba and Martínez-Zoroa asserting that without their ideas, the AI would not have reached a solution. OpenAI deployed a swarm of 10,000 AI agents running on its new experimental model, consuming an estimated 15 million dollars' worth of computing power over 88 hours, with verification requiring a further 17. According to OpenAI's own account, the push was accelerated by rumours that rival AI company Anthropic's researchers were close to solving two Millennium problems simultaneously — a race the company was determined to win ahead of both firms' planned stock market listings.

That competitive urgency has generated serious controversy. Mathematician Tristan Buckmaster of New York University, who had been pursuing a closely related line of work in collaboration with Anthropic staffer Levent Alpöge, says OpenAI approached him to discuss his research but declined to answer whether his unpublished work had influenced its model's output. He further alleges that OpenAI offered to collaborate with him on the condition that Alpöge's name be removed from the work, citing Alpöge's affiliation with Anthropic — a claim OpenAI denies. Separately, German mathematician Andreas Thom raised concerns that AI models may be absorbing unpublished human research and presenting it as AI-generated output. Prominent US-Australian mathematician Terence Tao has cautioned against using AI as a blunt instrument to extract solutions without building broader mathematical understanding, warning that if companies routinely race to exploit rumours of promising work, researchers may stop sharing ideas openly — eroding the collaborative foundations on which science depends.

The Millennium Prize rules require that at least two years pass after publication before a solution can be formally awarded, meaning the Navier-Stokes problem remains officially unsolved for now. The episode nonetheless signals a profound shift in how mathematics may be practised. Where the discipline has long been driven by individual insight and years of patient effort, AI is introducing a new variable: vast computational power guided by, but increasingly extending beyond, human ingenuity. Whether that represents liberation or disruption for mathematicians may depend on whether the industry can be trusted to handle their ideas responsibly.