OpenAI announced September 8 that its AI agents had found a solution to the Navier–Stokes Millennium Prize problem. The company released a proof writeup and computer-checkable version, putting a potential milestone for AI in mathematics before outside researchers.
The problem, in plain English: The equations describe how liquids and gases move. The mathematical challenge asks whether an initially smooth flow can develop a singularity, where the equations' predicted behavior stops remaining smooth. Clay lists it among its Millennium Prize problems.
OpenAI says it constructed a case in which fluid speeds grow without limit in a finite time, despite the fluid's finite energy. Its result includes an applied force. That would identify a limit of the mathematical model; it does not mean real water can move infinitely fast.
The AI work involved more than asking a chatbot a question. OpenAI says its researchers directed groups of agents using an internal model more capable than GPT-6 Astra. It has posted Lean files for checking the mathematical arguments.
Keep the significance in proportion: Chris Combs cautioned on X that sweeping claims about having solved Navier–Stokes overstate a result concerning a specific mathematical scenario.
In a public statement, Tristan Buckmaster described related Euler-equation research with Levent Alpöge and questioned OpenAI's handling of credit. Buckmaster also raised questions about model training, while explicitly saying he did not know whether their data was used.
In its response, OpenAI recognized the pair's priority on their Euler result and said its own proofs differ. It denied accessing their unpublished work to solve the problem, while saying it could not rule out model improvements from de-identified usage data. Those accounts leave questions about credit and research-data use unresolved.
What remains open: As of September 8, Clay's problem page still labeled Navier–Stokes unsolved. The release gives researchers a proposed proof to scrutinize; Still in the Loop has not independently established its correctness.