OpenAI says it has solved one of the seven Millennium Prize Problems in mathematics. The problem concerns the Navier–Stokes equations, the standard model of how fluids move. OpenAI announced on 8 September that it generated a proof showing these equations can break down. Its researchers say some fluids starting out normally reach infinite speed in finite time. That is physically impossible, so the equations may not always mirror reality. OpenAI posted a preprint on its website rather than in a journal. It had been testing a prototype model on all six unsolved Millennium Problems. It narrowed focus on 1 September after rumours of rival work using Anthropic models. Two mathematicians published a zero-viscosity result on 7 September using Claude, Codex and Astra. A Caltech group released a similar result the same day using a specialised neural network.

• $1 million Millennium Prize
• 1,000 agents, 50 hours on simpler case
• 10,000 agents on full problem
• 7 Millennium Prize Problems