OpenAI Claims Its AI Solved the Navier-Stokes Millennium Prize Problem

OpenAI says an unreleased internal AI model has produced a solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems announced in 2000.

The company says the 165-page proof demonstrates that a smooth three-dimensional fluid flow can develop a finite-time singularity, although the problem remains officially unsolved.

OpenAI’s proof creates a finite-time singularity

The Navier–Stokes problem asks whether smooth three-dimensional fluid flows can always remain smooth or whether their velocity can become unbounded within a finite amount of time.

OpenAI says its proof constructs a three-dimensional incompressible fluid that initially starts at rest.

A smooth external force then causes a vortex to spiral inward, stretch, and accelerate until the fluid’s velocity becomes unbounded.

According to OpenAI, the total kinetic energy remains finite during the process.

The company says the construction satisfies statements C and D of the official Millennium Prize formulation, showing that smooth Navier–Stokes solutions can break down under the specified conditions.

The model is more capable than GPT-6 Astra

OpenAI says the internal model behind the proof is significantly more capable than GPT-6 Astra.

According to the company, the unreleased system has achieved unprecedented results across its internal benchmarks.

Training began on August 28 and remains ongoing.

Around 10,000 AI agents worked on Navier-Stokes

OpenAI used swarms of AI agents to work on several Millennium Prize Problems at the same time.

Around 10,000 concurrent agents reportedly worked on the Navier-Stokes problem.

The agents reached the proposed solution after roughly 88 hours, according to OpenAI.

GPT-6 Astra then spent another 17 hours formalizing and verifying the proof in Lean.

The effort produced billions of AI-generated tokens

The scale of the project was substantial.

OpenAI says the Navier-Stokes effort involved around 2.7 million messages, roughly 130 billion output tokens, and about 10,000 concurrent AI agents.

The numbers highlight how heavily OpenAI relied on parallel agent workloads rather than a single model working through the problem sequentially.

Navier-Stokes is still officially unsolved

Despite OpenAI’s announcement, the Clay Mathematics Institute still lists the Navier-Stokes existence and smoothness problem as unsolved.

A proposed solution must satisfy several requirements before it can receive official recognition.

The work must appear in a qualifying publication, remain published for at least two years, and gain general acceptance within the mathematics community.

Only after those conditions are met can the institute consider recognizing the solution as resolving the Millennium Prize Problem.

OpenAI says it will not claim the $1 million prize

OpenAI says it does not intend to claim the $1 million prize associated with solving the problem.

Instead, the company says it published the result to demonstrate how quickly its frontier AI systems are advancing.

The announcement also comes as OpenAI pushes further into large-scale agent systems. Recent reports suggested that GPT-6 Astra can spawn large numbers of agents and use local CPU resources.

OpenAI has also recently expanded its generative AI lineup with ChatGPT Images 2.5.