OpenAI says an experimental AI system solved a roughly 90-year-old mathematics problem in 88 hours, but the claimed breakthrough has sparked a dispute over research credit and the possible influence of customer data.
The Navier-Stokes equations describe how fluids move, from blood through arteries to air over airplane wings. The equations date to the 19th century, but since Jean Leray’s foundational work in 1934, mathematicians have debated whether initially smooth three-dimensional fluid motion can develop a finite-time singularity, with speeds growing without bound. The Clay Mathematics Institute offered $1 million in 2000 for proof either way.
OpenAI claims its internal system, which it describes as significantly more capable than GPT-6 Astra, proved that an initially smooth fluid can develop a finite-time singularity under smooth external forcing. Approximately 10,000 concurrent AI agents generated 130 billion output tokens over 88 hours. One outside expert estimated that comparable computing resources would cost about $6 million at retail rates, exceeding the problem’s $1 million prize, which OpenAI does not plan to claim.
The friction: A credit dispute clouds the breakthrough
NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working on related fluid dynamics problems using OpenAI’s Codex tool. On Sept. 3, Buckmaster emailed OpenAI to clarify that he and Alpöge had related work they planned to publish shortly after rumors about their progress began circulating.
According to Buckmaster, OpenAI then offered him sole authorship on a Navier-Stokes solution — but only if Alpöge’s name was removed. OpenAI researcher Sébastien Bubeck denied this on social media. Buckmaster also alleges Bubeck said: “Why would you ruin your career?” when Buckmaster threatened to make their interactions public.
OpenAI says it launched its effort after hearing “rumors that two Millennium Prize problems had been resolved.” The company acknowledged it “cannot rule out that de-identified data derived from their usage of our products helped improve our models.”
An uncomfortable precedent
The episode reveals a problem science hasn’t confronted: what happens when the company providing AI research tools can also mobilize vastly more resources to compete with its own users?
For independent mathematicians, the resource disparity is stark. University of Michigan’s Karthik Duraisamy, per Science, estimates the OpenAI effort would cost about $6 million at retail rates, far beyond what most academics can access.
Yet Columbia University mathematician Michael Harris worries about something else: “It convinces decision makers that human mathematicians are obsolete, and it convinces young people that their passion for mathematics has no future.”
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What this means for business
OpenAI’s approach — using one AI system to generate a proposed solution and another process to verify it — illustrates the value of independently checking high-stakes AI output. Businesses can apply a similar principle to proposals, contracts and technical documents, although automated reviews should support rather than replace qualified human sign-off.
The limitations are equally important. Lean is specialized mathematical software rather than a general-purpose business validation tool, and OpenAI’s system used approximately 10,000 concurrent agents. For IT leaders, the practical takeaway is to establish independent verification, human oversight and clear policies governing whether proprietary work submitted to AI tools can be used for model improvement.
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