Did AI solve the Navier-Stokes problem? OpenAI faces scrutiny
AI may have cracked a 90-year-old maths problem, but OpenAI’s Navier-Stokes claim faces scrutiny over the proof, data and who gets credit.
A 90-year-old maths problem may have met its match in AI. But OpenAI’s claimed breakthrough is already raising a second question: who gets credit when AI helps make a discovery?
The Navier-Stokes problem is known to be one of seven Millennium Prize Problems. OpenAI said on September 8 that an internal AI system had solved it. A valid solution carries a $1 million prize from the Clay Mathematics Institute. OpenAI, however, said it does not plan to claim the prize.
The claim would be historic if it survives mathematical scrutiny. For now, however, it remains a proposed solution rather than a formally accepted one.
The maths problem AI is trying to crack
The Navier-Stokes equations describe the movement of fluids such as water and air. They are fundamental to fluid dynamics and have applications ranging from weather modelling to aircraft design.
The Millennium Prize problem asks whether smooth three-dimensional solutions to these equations can remain smooth indefinitely, or whether they can develop a singularity in finite time. OpenAI says its proof demonstrates a finite-time singularity.
The company produced both an analytical proof and a formalised version in Lean, a system used to check mathematical proofs mechanically. The scale of the effort is also unusual. OpenAI says around 10,000 AI agents worked on the problem for 88 hours. Another model then formalised and verified the proof in Lean.
Inside OpenAI’s AI-powered proof
OpenAI says its agents worked across several Millennium Prize problems before focusing on Navier-Stokes. The effort began on September 1, after the company heard rumours that two Millennium Prize problems had been resolved.
The system reportedly reached the Navier-Stokes result on September 5. The formalisation and verification work followed on September 6. According to OpenAI, the final proof shows that an initially smooth fluid at rest can develop a singularity in finite time when a smooth force is applied.
Mathematicians need to independently examine that claim. A Lean-checked proof can verify the formal argument entered into the system, but the underlying mathematical assumptions and whether the result actually resolves Clay’s precise problem still require expert scrutiny.
A breakthrough comes with a credit dispute
Now, the claim quickly ran into a challenge from two mathematicians: NYU’s Tristan Buckmaster and Anthropic’s Levent Alpöge. Both Buckmaster and Alpöge had been working on related fluid-dynamics problems using AI tools, including OpenAI’s Codex and Anthropic’s Claude.
They published results involving finite-time blow-up for forced versions of several equations around the same time as OpenAI’s announcement. Buckmaster has alleged that OpenAI learned about their unpublished work and then moved quickly on a related Navier-Stokes result.
He also claimed that Sébastien Bubeck, an OpenAI researcher, proposed publication arrangements that would have left Alpöge off the authorship. OpenAI disputes that account. It says its researchers and agents did not see Alpöge and Buckmaster's work before it was publicly released and that no specific user data was accessed to solve the problem.
However, the ChatGPT maker acknowledged that it could not completely rule out de-identified data from their use of its products having indirectly contributed to model improvement. Bubeck has also denied asking for Alpöge to be removed.
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The proof still has to survive scrutiny
The mathematical question now goes beyond whether an AI can produce a convincing proof. Experts must establish whether the argument is correct and whether it actually satisfies the precise Navier-Stokes problem defined by Clay.
Clay’s rules require a proposed solution to be published in a qualifying outlet, remain published for at least two years and receive general acceptance from the global mathematics community before the institute considers awarding the prize.
That makes OpenAI’s announcement the beginning of the verification process, not the end. If the proof survives that process, it could become one of the most significant demonstrations yet of AI’s ability to contribute to advanced mathematics.