OpenAI said an internal AI model more capable than GPT-6 Astra produced a proof that 3D Navier-Stokes equations can develop a finite-time singularity, addressing a Millennium Prize Problem. The company said roughly 10,000 agents worked in parallel and the proof was verified using Lean.

OpenAI said that an internal model 'significantly more capable than GPT-6 Astra' had produced a proof showing that the three-dimensional Navier-Stokes equations can develop a singularity in finite time, tackling one of mathematics' seven unsolved Millennium Prize Problems. This problem has allegedly remained unresolved for 90 years.

How the breakthrough came together

The company said its effort began on September 1, after researchers heard rumours that two of the Millennium Prize problems had already been solved and turned its newest internal model toward the remaining ones. OpenAI executives told reporters the project consumed enormous computing resources, costing in the millions of dollars and involving roughly 10,000 agents working in parallel. The company later clarified that the effort began after hearing a rumour that it eventually traced back to Levent Alpoge, an Anthropic employee, and Tristan Buckmaster, a mathematics professor at NYU. OpenAI says the proof has been verified using the programming language Lean, which effectively guarantees its correctness.

A rival claim surfaces first