OpenAI says its internal AI system solved the Navier–Stokes problem

OpenAI says an internal AI system has produced a solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The company detailed the result in OpenAI News on September 8, 2026, sharing both a mathematical paper and a Lean formalization.

The proof argues that a three-dimensional incompressible fluid can begin in a smooth state and develop a singularity in finite time, even while its total energy remains finite and the applied force stays smooth. In the proposed scenario, a vortex spirals inward and stretches lengthwise, causing fluid speeds to grow without bound. OpenAI says this establishes statements “C” and “D” in the Clay Mathematics Institute’s official formulation.

An AI-driven search

The effort began on September 1 after rumors that Millennium Prize problems had been solved. OpenAI deployed coordinating groups of agents with access to cached web information and code execution. The Navier–Stokes effort involved roughly 10,000 concurrent agents, which reached its result on September 5—about 88 hours after the wider effort began. Lean formalization and verification took another 17 hours using GPT-6 Astra.

Across all attempted problems, the agents exchanged 4.9 million messages and generated about 300 billion output tokens. The Navier–Stokes work accounted for 2.7 million messages and approximately 130 billion output tokens. OpenAI also says nearly 100 agents spent about 50 hours resolving a related Euler-equation regularity question.

For AI builders, the announcement points to a workflow beyond single-model prompting: large agent teams, specialized tools, cross-group synthesis through Codex, and machine-checked proof verification. The mathematical claim will still matter only if researchers independently scrutinize the paper and formalization, but the scale and structure of the reported process offer a notable example of AI-assisted research.

Source: OpenAI News