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OpenAI's 10,000 AI Agents Crack a Millennium Problem—and Spark Debate

In a stunning announcement on September 8, OpenAI revealed that its undisclosed internal AI model—far more powerful than the recently released GPT-6 Astra—has successfully cracked the Navier-Stokes existence and smoothness problem. This is one of the seven Millennium Prize Problems, a set of challenges that have stumped mathematicians for nearly a century. The breakthrough, achieved by a swarm of 10,000 AI agents working together for 88 hours, has sent ripples through the scientific community.

But the excitement is tinged with controversy. Just a day earlier, New York University mathematician Tristan Buckmaster and Anthropic researcher Levant Alpoge had published related work on fluid equations. Buckmaster now questions whether OpenAI merely redirected its efforts after learning of their progress, and he worries that his research data stored in OpenAI's Codex might have been used without permission. OpenAI denies any misuse, but admits that anonymized data from its products could have indirectly improved the model.

A Proof Born from Collaboration

The Navier-Stokes problem asks whether a smooth, stationary fluid can suddenly develop a singularity—a point where velocity becomes infinite—within a finite time. OpenAI's AI agents designed a clever "vortex" that rotates and stretches inward, maintaining finite energy while leading to such a singularity. The proof, which addresses the "C" and "D" scenarios of the official problem statement, was then formally verified using the Lean programming language, a task completed by GPT-6 Astra in about 17 hours.

OpenAI researcher Sébastien Bubeck called this an "amazing peak" in the trajectory of AI capabilities over the past year. The achievement is indeed remarkable, but it also raises profound questions about the future of mathematical discovery.

Terence Tao's Mixed Feelings

Mathematician Terence Tao, known for his own contributions to the field, compared such problems to a "lighthouse" that attracts scientists' efforts. He praised the AI's achievement but also voiced a warning: if AI can solve the most difficult problems without deep human involvement, it might weaken our collective understanding of mathematics. After all, the journey of solving a problem often teaches us as much as the solution itself.

The computational cost of this feat is estimated to be between $15 million and $22.5 million (roughly 101 to 151 million yuan). Interestingly, OpenAI has stated that it does not intend to claim the $1 million prize (about 6.7 million yuan) offered by the Clay Mathematics Institute. That decision, perhaps, is a nod to the collaborative nature of the achievement—or a recognition that the real value lies elsewhere.

The Broader Implications

This event is not isolated. Last month, Anthropic announced that its internal research model, Claude, made significant progress on the Riemann Hypothesis, raising the lower bound of the zero point ratio on the critical line from 41.6% to 67.2%. These developments suggest that AI is increasingly capable of tackling problems that have resisted human effort for decades.

But as AI takes on more of the heavy lifting, we must ask ourselves: What does it mean for human mathematicians? Will we become mere spectators, or will we find new ways to collaborate with these digital minds? The answer likely lies in a balanced approach, where AI serves as a tool to augment human creativity rather than replace it.

For now, the mathematical community is left to ponder the implications of a proof generated by machines. It's a moment of triumph and trepidation, a glimpse into a future where the boundaries between human and artificial intelligence become ever more blurred.

Key Points

  • OpenAI's internal AI model solved the Navier-Stokes existence and smoothness problem, a Millennium Prize Problem.
  • The proof was generated by 10,000 AI agents in 88 hours and formally verified in 17 hours.
  • The achievement has sparked controversy over research priority and data usage.
  • Terence Tao praised the breakthrough but warned about the potential loss of human understanding.
  • OpenAI declined the $1 million prize, and the computational cost is estimated at $15-22.5 million.