OpenAI claims huge maths breakthrough on a famed ‘Millennium Problem’

OpenAI claims to have solved one of the most challenging mathematical problems, known as the Navier-Stokes Millennium problem, using an AI model. This problem, which sits on the list of Millennium Prize Problems, offers a $1 million reward for a solution. The Navier-Stokes equations describe the movement of fluids in space, but they are not well understood and the Clay Mathematics Institute seeks to determine if they always work or if there are situations where they stop making sense.

OpenAI's groundbreaking discovery came after using 1,000 AI agents to find blow-ups in the Euler problem, a cousin of the Navier-Stokes problem, in just 50 hours. The same AI agents then took just 11 hours to extend the blow-ups to apply to the full Navier-Stokes problem. OpenAI did not disclose the specific AI model used, but stated that it was significantly more capable than its latest GPT-6 Astra model.

The discovery follows a series of shocking mathematical findings made by AI, including a recent crack of a decades-old conjecture by Paul Erdős and a counterexample to the Jacobian conjecture. However, OpenAI's announcement has sparked controversy, as it comes shortly after Tristan Buckmaster and Levent Alpöge at New York University and Anthropic had also cracked three significant problems considered "stepping stones" to the Navier-Stokes problem.

Buckmaster suggested that OpenAI acted unusually and opaquely when he approached them for clarification, claiming that OpenAI had used their work in their own solution without acknowledging it. OpenAI denied these allegations, stating that their model's proof is different from Buckmaster and Alpöge's and that no humans accessed their Codex model to see work in progress.

The Clay Mathematics Institute, which offers the Millennium Prize, will now determine the process for awarding the $1 million prize for this groundbreaking discovery.