OpenAI Claims AI Solved Millennium Problem on Fluid Equations

We present a solution to the existence and smoothness problem of the Navier-Stokes equations, one of the

Consensus

• OpenAI claims to have solved one of the seven Millennium Prize Problems.
• The problem concerns the existence and smoothness of solutions to the Navier-Stokes equations.
• The Navier-Stokes equations describe the motion of viscous fluids and gases.
• OpenAI used approximately 10,000 AI agents for 88 hours to solve the problem.
• The AI demonstrated that fluid flows can theoretically reach infinite velocity, forming a singularity.
• The solution was formally verified using the Lean proof language.
• OpenAI stated it will not claim the $1 million prize from the Clay Mathematics Institute.
• The company emphasized the achievement as a breakthrough in AI's scientific capabilities.

Points of divergence

• OpenAI began working on the problem on September 1, after hearing rumors that Tristan Bakmaster and Levant Alpège solved a version of the puzzle using Claude from Anthropic and Codex from OpenAI. — tg_varlamov_news
• Bakmaster asked OpenAI if its model was trained on the data from their project, and was told no. — tg_varlamov_news
• OpenAI used an internal model whose capabilities significantly exceed those of GPT-6 Astra. — vesti
• The internal model used by OpenAI significantly surpasses the capabilities of the latest GPT-6 Astra. — kommersant

Coverage (3 sources)

• OpenAI announced that its model solved the 'millennium problem' about Navier-Stokes equations. — Varlamov News
• AI model from OpenAI solved one of seven millennium problems — Вести
• OpenAI claims to have solved one of the 'Millennium Challenges' using AI — Коммерсантъ

Key entities

• OpenAI
• Peter Stokes
• Moscow
• Institute of Mathematics
• AI models
• Carol Clay