OpenAI Says 1,000 AI Agents Produced a Navier-Stokes Solution

OpenAI says an internal AI system produced a solution to the Navier-Stokes problem, a major open question about how fluids move. The company says the proof was formalized in Lean, but its announcement has been met with allegations about how the work began and who should receive credit.

A claimed answer to a famous equation

The Navier-Stokes equations describe the movement of fluids including water and air. A solution would address one of seven Clay Millennium Problems, each tied to a $1 million prize. OpenAI says its proof shows the equations can sometimes “blow up,” implying infinite fluid speed at some points.

Lean is a programming language used to write formal mathematical proofs. OpenAI said it started training a model with advanced math capabilities on August 28, then assigned substantially more computing power to Navier-Stokes after rumors of progress at Anthropic.

Parallel work became a credit dispute

Tristan Buckmaster and Levent Alpöge posted documents describing advances relevant to Navier-Stokes. They said they used several AI models, including Claude and Codex. Buckmaster alleged that OpenAI learned of their progress, then devoted significant resources to the problem.

The competing accounts

• Buckmaster also alleged that OpenAI proposed a publication arrangement that would announce an internal OpenAI solution without Alpöge’s name.
• OpenAI executives denied inspecting the pair’s Codex prompts or using their prompts or proof to direct its models and agents.
• OpenAI recognized Buckmaster and Alpöge’s priority on their unforced Euler result, while saying its own solution differed significantly in nature.

Scientific American reported that OpenAI’s full Navier-Stokes proof follows a method similar to the other mathematicians’ approach and was developed over the weekend, according to Bubeck. Sorting out the differences between the proofs will likely take further examination by mathematicians.