OpenAI Claims Solution to Navier‑Stokes Millennium Prize Problem Using AI

OpenAI announced that its artificial‑intelligence system has produced a proof that the Navier‑Stokes equations, which model fluid flow, can develop singularities, or “blow‑ups.” The claim, made after only a few days of AI work, would satisfy the Clay Mathematics Institute’s criteria for one of its six Millennium Prize Problems and could earn a $1 million award. The proof has not yet been peer‑reviewed, but it has been formalised into computer code that systematically checks the logic, giving confidence in its correctness. The announcement sparked controversy when researchers Tristan Buckmaster and Levent Alpöge, who had recently published a related solution to the Euler equations, alleged that their work was stored on OpenAI’s servers and that the company had received opaque responses. OpenAI denies any access to their research and insists its solution is distinct. The Clay Institute will conduct a deliberate, rigorous evaluation before deciding whether the prize should go to OpenAI or to the human researchers. If awarded to OpenAI, the cost of the AI effort—estimated at $15 million—would far exceed the prize money, raising questions about the commercial value of AI‑generated mathematics.