OpenAI claims to have solved complex mathematical puzzle

OpenAI has claimed to have solved a mathematical problem that had remained unresolved for nearly a century. The company said it has found a solution to the "Navier-Stokes" problem, one of the seven "Millennium Prize Problems" declared by the Clay Mathematics Institute.

However, the claim has sparked controversy. Tristan Buckmaster, a professor at New York University, has said that OpenAI began working rapidly upon learning that he and Anthropic researcher Levent Alpoge were close to solving a related form of the problem. He fears that data from their incomplete research may have been used in the AI model. OpenAI denied the allegation, but later proposed a joint announcement acknowledging the two researchers' priority on related (but different) work.

OpenAI said its new, unreleased internal AI model — more powerful than GPT-6 Astra — reached the solution in 88 hours using around 10,000 AI agents. The proof was subsequently verified in the "Lean" programming language.

The Navier-Stokes equations describe the motion of fluids. OpenAI's proof shows that under certain conditions, smooth three-dimensional fluid flow can break down — where, despite finite energy, a vortex can progressively contract and accelerate to reach infinite speed.