OpenAI announced on Tuesday that it used a new internal artificial intelligence model and roughly 10,000 AI agents to solve a notoriously difficult mathematics problem in just 88 hours, a feat the company called a milestone in AI capability. The problem, part of the Navier-Stokes equations concerning how fluids move, has lacked a complete proof for 90 years. However, the claim has already sparked controversy over research ethics and the timing of OpenAI's work.

What Is the Navier-Stokes Problem and Why Does It Matter?

The Navier-Stokes equations describe how fluids behave, from water flowing through pipes to air moving around aircraft wings. The specific problem OpenAI tackled, called the Navier-Stokes existence and smoothness problem, sits at the heart of turbulence, a phenomenon scientists still don't fully understand. The Clay Mathematics Institute, a U.S.-based organization, has offered a $1 million Millennium Prize to anyone who can solve it.

OpenAI's solution addressed two out of four required statements in the proof demanded by the prize. The company stated it does not intend to claim the $1 million prize for this result. Instead, OpenAI framed the achievement as evidence that its AI models are improving rapidly and can tackle complex mathematical problems that have stumped human researchers for decades.

How Did OpenAI's AI Agents Solve the Problem?

In late August, OpenAI began training a new internal AI model that showed exceptional ability at mathematics. The model remains proprietary and is not yet available to the public, but the company described it as "significantly more capable" than its most recent public release. After hearing rumors on September 1 that two Millennium Prize problems had been resolved, OpenAI decided to deploy thousands of AI agents trained on this new model to work on remaining unsolved problems.

The scale of the computational effort was enormous. Over roughly 88 hours, the 10,000 AI agents exchanged nearly 3 million messages and used 130 billion output tokens, or individual lines of text and code that an AI model produces in answers. Based on OpenAI's own pricing for its most advanced models, this effort would have cost approximately $10 million.

Steps to Understanding AI's Role in Mathematical Discovery

• Autonomous Problem-Solving: AI agents work somewhat independently to tackle mathematical problems, exchanging information and refining solutions without constant human direction, demonstrating a new approach to research.
• Computational Scale: The sheer volume of processing power required, including 130 billion output tokens and thousands of coordinated agents, shows how AI breakthroughs often depend on massive computational resources rather than algorithmic innovation alone.
• Verification and Validation: OpenAI's solution has not yet been independently verified or publicly accepted by the Clay Mathematics Institute, highlighting that AI-generated proofs require human expert review before they can be considered definitive.

What's the Controversy About Research Ethics?

The announcement has drawn sharp criticism from the academic community. Tristan Buckmaster, a mathematics professor at New York University, stated that he and Levent Alpöge, a mathematician at OpenAI rival Anthropic, had also been working toward solutions for the Navier-Stokes problem. Buckmaster said that on September 3, he learned that "information about our progress had been passed to OpenAI." He claimed OpenAI did not begin working on the problem until after his team's progress reached the company.

Buckmaster, a mathematics professor at New York University

"I was told, when, and what was proposed to me...because the alternative is to let a sequence of announcements say something I know to be false," Buckmaster stated, explaining why he felt compelled to go public with his concerns about OpenAI's timing and methods.

Tristan Buckmaster, Mathematics Professor at New York University

OpenAI responded by congratulating the "concurrent work" of Buckmaster and Alpöge, calling it "remarkable." The company denied seeing any of their work through improper means and stated that no user data was accessed in its own research. However, OpenAI acknowledged a potential gray area: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." The company added that its proofs differ significantly from Buckmaster and Alpöge's work and that the precise results proved are different.

What Does This Achievement Mean for AI's Future?

OpenAI's claim represents a significant moment in AI development, demonstrating that large-scale AI systems can now tackle problems at the frontier of human mathematical knowledge. The company framed the result as evidence of rapid progress in its AI models. Yet the controversy surrounding the announcement raises important questions about how AI companies should conduct research, share information with the academic community, and claim credit for breakthroughs.

The fact that OpenAI's solution has not yet been independently verified or accepted by the Clay Mathematics Institute also underscores a critical limitation: AI-generated proofs, no matter how sophisticated the system that produced them, still require human expert validation before they can be considered authoritative. This suggests that while AI can accelerate mathematical discovery, human mathematicians remain essential to confirming and understanding the results.