The company appears to have made progress on the Navier-Stokes problem, one of the most famous unsolved questions in mathematics.
OpenAI claims its AI model solved an 80-year-old problemThe latest development follows a series of increasingly ambitious mathematical results involving AI.
OpenAI reportedly said an internal AI model generated a proof of roughly 100 pages in just a few days.
AdvertisementThe researchers' result has been verified, while OpenAI's alleged proof of the full Navier-Stokes problem has not been publicly disclosed.
According to the statement shared, the company became aware of the mathematicians' research and then moved rapidly to tackle the original Navier-Stokes problem.
OpenAI appears to have made a major claim about one of mathematics’ most famous unsolved problems, saying its reasoning AI generated a proof for the Navier-Stokes equations. But the proof remains private, while mathematicians involved in related research have questioned how OpenAI arrived at its result.
OpenAI's latest mathematical claim is drawing attention for a reason that goes well beyond the capabilities of its AI models. The company appears to have made progress on the Navier-Stokes problem, one of the most famous unsolved questions in mathematics. But while OpenAI's reported result could be significant, questions are already being raised about how the company arrived at it and whether researchers' earlier work played a role.
The controversy centres on a problem that has challenged mathematicians for generations. The Navier-Stokes equations describe how fluids such as air and water move, and mathematicians have yet to prove whether their solutions can always remain smooth or can instead develop singularities in finite time.
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The problem is one of the seven Millennium Prize Problems identified by the Clay Mathematics Institute. A complete solution carries a $1 million prize, putting Navier-Stokes among the most closely watched open questions in modern mathematics.
OpenAI claims its AI model solved an 80-year-old problem
The latest development follows a series of increasingly ambitious mathematical results involving AI. Earlier this year, OpenAI said one of its reasoning-focused models had independently produced a proof overturning a longstanding mathematical conjecture associated with Paul Erdős, a problem that had remained unresolved for decades.
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Now, attention has shifted to Navier-Stokes.
According to the account surrounding OpenAI's latest work, the company directed a large team and significant computing resources towards the problem after learning about progress made by mathematicians working on a closely related question. OpenAI reportedly said an internal AI model generated a proof of roughly 100 pages in just a few days.
There is, however, an important distinction between what has been independently established and what OpenAI is claiming.
Mathematicians Tristan Buckmaster and Levent Alpöge spent about a year studying a related version of the Navier-Stokes equations with the assistance of AI. Their work showed that a solution in the friction-free version of the equations can develop a singularity in finite time, a result often described as mathematical "blow-up".
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The researchers' result has been verified, while OpenAI's alleged proof of the full Navier-Stokes problem has not been publicly disclosed. That means outside mathematicians cannot yet examine the claimed solution or determine whether it actually resolves the Millennium Prize problem.
Mathematicians question OpenAI's claim, and accuse it of using their work
The dispute became more serious after Buckmaster publicly described his interactions with OpenAI.
According to the statement shared, the company became aware of the mathematicians' research and then moved rapidly to tackle the original Navier-Stokes problem. Buckmaster has questioned whether OpenAI's systems had been exposed to his private mathematical drafts, which he had been feeding into the company's tools during the year.
He also alleges that OpenAI initially portrayed its model as having been given the problem with little human assistance. During a subsequent conversation, however, he says the company would not clarify whether his private drafts had been part of the model's training or otherwise influenced the result.
Another point of contention was the authorship of the mathematicians' paper. Buckmaster says OpenAI asked him to remove Alpöge because his co-author works at Anthropic, a rival AI company.
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When Buckmaster indicated that he intended to speak publicly about the situation, he says he was told, “Why would you ruin your career?”
Buckmaster ultimately released his work publicly, despite describing it as early and unfinished, to establish a record of when the research had been produced.
The allegations do not, by themselves, establish that OpenAI copied or stole the mathematicians' work. That question cannot be independently settled without access to the company's claimed proof, relevant model records and the researchers' private material.
The most consequential part of OpenAI's Navier-Stokes claim remains unverified. If its model has genuinely produced a valid proof of the full problem, it could represent an extraordinary moment for both mathematics and AI. But until the proof is made available for scrutiny, questions over its origins are likely to remain just as important as the claimed breakthrough itself.
