OpenAI Claims to have Solved One of the "Millennium Problems"

San Francisco: Artificial intelligence research company OpenAI has claimed a major breakthrough in advanced mathematics, announcing that an unreleased internal AI system has solved the Navier–Stokes existence and smoothness problem—one of the world-famous "Millennium Problems" that has stumped mathematicians for nearly a century.

The announcement has sparked immense interest across the scientific community, alongside intense debate regarding independent verification, computing costs, and intellectual property disputes with rival researchers.

A Century-Old Fluid Mechanics Mystery

The Navier–Stokes equations describe how fluids—such as water, air, and blood—move and flow. While engineers and scientists rely heavily on these equations for everything from weather forecasting to aircraft design, theoretical mathematicians have long sought to understand whether the mathematical solutions remain smooth and well-behaved over time, or if they "blow up" under specific conditions with fluid speeds becoming infinite.

Established in 2000 by the Clay Mathematics Institute, the seven 'Millennium Prize Problems' represent some of the most difficult open challenges in mathematics, each carrying a $1 million award. Prior to OpenAI’s announcement, only one—the Poincare conjecture, solved by Russian mathematician Grigori Perelman in 2003—had been officially resolved.

According to OpenAI, its AI proof demonstrates that the equations do indeed break down under certain parameters.

Millions of Dollars and 10,000 Autonomous Agents

OpenAI disclosed that the project required an unprecedented concentration of automated computing power. The effort was spearheaded by an internal AI model significantly more advanced than its latest publicly available tools.

To tackle the problem, OpenAI deployed roughly 10,000 autonomous AI agents working in tandem. Over an 88-hour push, these systems exchanged nearly three million internal messages and generated approximately 130 billion tokens of code and mathematical proof. OpenAI estimates that the compute time required for the effort cost "emphatically in the millions of dollars," with estimates running as high as $10 million based on commercial API pricing.

Company representatives confirmed that OpenAI does not intend to claim the $1 million prize from the Clay Mathematics Institute.

Allegations and Credit Disputes

The milestone announcement was immediately accompanied by controversy regarding how OpenAI initiated its research.

New York University math professor Tristan Buckmaster and Anthropic researcher Levent Alpoge had been concurrently working on related aspects of the Navier–Stokes problem using OpenAI’s developer tools, such as Codex. Buckmaster publicly raised concerns, suggesting OpenAI launched its massive compute campaign only after learning of his team's preliminary progress, which was stored on OpenAI's servers, The Guardian reported.

OpenAI researchers strongly denied accessing the private research or using user prompts to guide their AI agents, asserting that their final proof differs significantly from Buckmaster and Alpoge's approach. However, the company acknowledged that it could not entirely rule out that de-identified telemetry or training data from usage of its commercial tools had indirectly influenced model capabilities.

Awaiting Peer Review

While OpenAI has published a technical paper detailing its proposed solution, the claim remains unverified by the global academic community.

Under official rules set by the Clay Mathematics Institute, any proposed solution to a Millennium Prize problem must be published in a peer-reviewed mathematics journal and withstand two full years of rigorous scrutiny by international experts before being formally recognized.

Mathematicians and computer scientists globally are now scrutinizing the generated proofs to determine whether the AI's complex output represents a true mathematical breakthrough or an intricate theoretical misstep.