NEW YORK (VINnews) — OpenAI says an artificial intelligence system has solved one of the most famous unsolved problems in mathematics, producing a proof of a finite-time “blow-up” in the equations used to describe the motion of fluids such as water and air.

The company announced on Tuesday that an internal AI system had solved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute. Each problem carries a $1 million prize for a mathematically valid solution.

The claim, however, has immediately generated controversy, according to a Guardian report. While OpenAI describes the result as a major mathematical breakthrough, outside mathematicians will need to examine the proof in detail before the result can be regarded as an established solution to the Millennium Problem.

The Navier–Stokes equations have been used for more than a century to model fluid motion, including the behavior of water, air and other liquids and gases. They are fundamental to fields ranging from physics and engineering to meteorology.

The central mathematical question is whether smooth, physically reasonable starting conditions can always produce smooth solutions that remain well behaved over time or whether the equations can develop a singularity in finite time.

OpenAI says its system found a scenario in which the equations “blow up”: the velocity of the modeled fluid becomes mathematically infinite in finite time.

That would answer the Clay Institute’s question in the direction of breakdown, rather than proving that smooth solutions always exist. The institute’s official formulation specifically allows a solution to the problem by proving that a singularity can occur under the prescribed conditions.

OpenAI published a technical paper alongside its announcement, including a formalized version of the proof. The result is now expected to undergo intense scrutiny from mathematicians.

Nature described the announcement as the first time a computer had reportedly produced a solution to a truly major open problem in mathematics, while emphasizing that the work must still be evaluated by experts.

OpenAI said it began concentrating its resources on the problem after hearing reports that mathematicians were making progress on it. The company deployed approximately 10,000 autonomous AI agents working simultaneously on different aspects of the problem. According to OpenAI, the system produced its solution after approximately 88 hours of work.

The internal system used for the effort was more powerful than OpenAI’s latest publicly released GPT-6 Astra model.

A separate GPT-6 Astra system subsequently spent about 17 hours verifying the proposed solution, according to OpenAI.

The scale of the computation reportedly cost millions of dollars, illustrating the enormous computing resources increasingly being devoted to AI-assisted mathematical research.

OpenAI researcher Sebastien Bubeck described the result as “a spectacular culmination of the arc we have seen over the past 12 months.”

The company said the work was intended not merely as a demonstration but as evidence of how rapidly AI systems are beginning to contribute to fundamental scientific research.

“A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity,” OpenAI researchers wrote.

The announcement was quickly overshadowed by an unusual dispute involving mathematician Tristan Buckmaster, a professor at New York University, and Levent Alpöge, a mathematician at Anthropic. Buckmaster and Alpöge had been working on related Navier–Stokes questions using AI tools, including Anthropic’s Claude as well as OpenAI’s Codex and Astra models.

The two researchers published their own work on Monday, shortly before OpenAI announced its result. Their research addressed a related version of the problem and also produced a finite-time singularity, although under different assumptions from the full problem OpenAI says it solved.

Buckmaster subsequently raised concerns about the timing of OpenAI’s effort and whether information from his and Alpöge’s work could have influenced the company’s system.In a statement published on his website, Buckmaster wrote:

“I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything.”

His concern was heightened because drafts of the researchers’ work had been entered into OpenAI’s Codex, the company’s AI coding platform. OpenAI strongly denies that its researchers accessed the pair’s unpublished work.

“We did not see any of their work until they released it publicly last night,” Bubeck said, adding that OpenAI’s proof and the researchers’ proof differ significantly.

OpenAI nevertheless acknowledged that it could not completely exclude the possibility that de-identified data derived from users’ interactions with its products may have contributed indirectly to model training. The company said no specific user data was accessed in order to solve the problem.

The dispute has raised broader questions about intellectual property, attribution and the use of researchers’ work in training increasingly powerful AI systems.

The claimed breakthrough comes amid a rapid expansion of AI’s role in mathematical research. OpenAI has reported other mathematical advances in recent months, while Google DeepMind has demonstrated AI systems capable of solving difficult problems at near-human competition levels. Anthropic has also been using its models to explore major mathematical questions.

The Navier–Stokes claim is potentially far more significant, however, because it concerns one of the six Millennium Prize Problems that remained unsolved after the Clay Mathematics Institute established the list in 2000. Only one of the original seven problems, the Poincaré conjecture, had previously been officially solved.

Mathematicians have nevertheless cautioned against treating the announcement as the end of the story. A computer-generated proof must still be understood, checked and accepted by the mathematical community.

The Clay Mathematics Institute’s prize is awarded only for a solution that meets its formal requirements and undergoes the required mathematical scrutiny. OpenAI said it does not intend to claim the $1 million prize.

If the proof survives independent examination, the achievement could mark a historic moment—not simply because an AI system solved a problem that resisted mathematicians for decades, but because it would demonstrate that AI can generate genuinely new mathematical knowledge rather than merely assist humans in applying known techniques.

For now, however, the crucial question is no longer whether an AI can produce a proposed solution. It is whether mathematicians can independently verify that the solution is correct.