WASHINGTON: OpenAI has claimed that one of its unreleased artificial-intelligence models has solved the Navier-Stokes problem, one of the most famous unanswered questions in modern mathematics.
The company says its AI system reached the result within days after using millions of dollars’ worth of computing resources. However, the claim has already triggered debate among mathematicians and AI researchers, particularly over the originality of the approach and who should receive credit.
The Navier-Stokes problem is one of the seven Millennium Prize Problems, a collection of exceptionally difficult mathematical questions selected by the Clay Mathematics Institute. Each problem carries a $1 million prize for a valid solution.
Only one of the seven problems has been officially solved since the list was established in 2000.
What Is the Navier-Stokes Problem?
The Navier-Stokes equations are fundamental mathematical tools used to describe how fluids move. They help scientists and engineers understand the behaviour of substances such as water and air and have applications ranging from aircraft design and weather forecasting to modelling blood flow through the human body.
The Millennium Prize challenge focuses on whether smooth solutions to these equations always exist under certain conditions, or whether they can develop singularities in finite time.
OpenAI said its research indicates that the equations can indeed break down over time, which would address the central question posed by the Millennium Prize.
Mark Chen, OpenAI’s chief research officer, described the claimed result as a significant milestone for AI research and argued that such systems could potentially help tackle other longstanding scientific and mathematical questions.
However, the claim is not yet an officially recognised solution.
Why Mathematicians Must Verify the Claim
The Clay Mathematics Institute has strict requirements before a solution to a Millennium Prize Problem can be considered.
A proposed solution must first be published in a peer-reviewed mathematical journal. It must then survive at least two years of scrutiny and acceptance within the mathematical community before the institute will even establish a committee to consider whether the problem has been solved.
Professor Martin Bridson, president of the Clay Mathematics Institute, told AFP that the evaluation process is intentionally slow and designed to ensure that any claimed solution is subjected to rigorous examination.
This means OpenAI’s announcement is currently a claim rather than an officially verified solution.
OpenAI has also said it will not seek the $1 million prize if its work is eventually confirmed.
AI Agents Worked on the Problem
According to OpenAI, the project began in late August when researchers started training a new model that the company described as more capable than anything it had previously released publicly.
After reports circulated online that another AI system might have solved one of the Millennium problems, OpenAI reportedly directed its model to investigate all six problems that remain officially unsolved.
The Navier-Stokes problem quickly showed particular promise, leading OpenAI to devote substantial computing resources to the research.
OpenAI researcher Sebastien Bubeck said that at the final stage, around 10,000 AI agents were working simultaneously on the problem and exchanging information with one another.
The company said the computing costs were “emphatically in the millions of dollars,” with Bubeck estimating that the expenditure was roughly 1,000 times higher than what OpenAI had spent on some of its earlier mathematical results.
According to the company’s account, the AI agents produced their solution on Saturday, approximately 88 hours after the project began.
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Dispute Over Credit and Rival Research
The announcement also triggered a dispute over the origins of the approach used by OpenAI’s system.
Hours before OpenAI announced its result, mathematician Tristan Buckmaster of New York University and Levent Alpoge, a researcher at AI company Anthropic, published AI-assisted work involving three related equations.
Buckmaster subsequently said OpenAI began working on the problem after information about his research circulated online. He argued that OpenAI pursued an approach similar to one that he and Alpoge had spent months developing.
OpenAI researchers denied accessing the rival team’s work. Bubeck said the company did not use their prompts or proofs to guide its AI agents.
However, OpenAI later acknowledged that it could not completely rule out the possibility that de-identified data derived from users’ interactions with its products may have contributed to model improvements.
A Major Test for AI in Mathematics
The episode highlights both the growing capabilities of AI systems and the challenges they create for the mathematical community.
AI models are increasingly being used to assist researchers with difficult calculations, proofs and mathematical exploration. Yet a machine-generated result still has to meet the same standards of correctness, clarity and independent verification expected of human mathematical work.
For now, the Navier-Stokes problem remains officially unsolved.
OpenAI’s claim could ultimately represent a historic breakthrough if independent mathematicians confirm the proof. But until the work passes peer review and the lengthy verification process required by the Clay Mathematics Institute, the mathematical community will continue to treat it as a promising but unverified claim.
