10,000 AIs Race for 88 Hours... OpenAI Claims to Have Solved a 100-Year Mathematical Enigma [Reading Science]

Solution Proposed for the Navier-Stokes Millennium Problem

If Verified, a ‘Historic Achievement’... Research Ethics and Credit Disputes Emerge

Has artificial intelligence (AI) solved one of the greatest modern mathematical conundrums that human mathematicians have failed to crack for decades?

OpenAI has proposed a solution to the Millennium Prize Problem regarding the Navier-Stokes equations, which describe the movement of fluids, using its next-generation AI model. About 10,000 AI agents simultaneously tackled the problem and produced a proof in just 88 hours. If the proof passes academic verification, it could be a historical case in which AI not only assists human research but directly solves an unsolved mathematical puzzle.

Visualization of fluid flow solving the Navier-Stokes equations released by OpenAI. It shows the process of a vortex spiraling inward at the center and stretching longitudinally along the axis. OpenAI stated that this process proves that a smooth fluid can form a singularity within a finite time. Provided by OpenAI

According to the scientific community on September 9, OpenAI announced on the 8th (local time) that its currently developing next-generation AI model has found a solution to the Navier-Stokes Millennium Problem. In addition to presenting an analytical proof, OpenAI also released a formalization of the result using Lean, a proof assistant system that allows computers to rigorously verify mathematical proofs.

The Navier-Stokes equations are the fundamental equations of fluid dynamics, describing how fluids like water or air move. The central issue was the inability to mathematically prove whether the flow of fluid, started smoothly in three-dimensional space, remains smooth over time or if a mathematical “singularity” can occur, where the solution breaks down.

Because of this, the Clay Mathematics Institute (CMI) in the United States chose this as one of the seven “Millennium Prize Problems” in mathematics in the year 2000. Solving the problem comes with a prize of 1 million dollars.

What OpenAI provided was a counterexample showing that under certain conditions, a singularity can actually occur. Specifically, it demonstrated that when vortices in a fluid with smooth external force spiral inward and stretch, a singularity can form within a finite time.

Professor Lee Joon-sang of Yonsei University’s Department of Mechanical Engineering explained, “Since cases allowing external force are included in the official problem statement, if this independently passes verification, it would be a very significant mathematical achievement.” He noted, however, “This does not mean the problem is solved for the case without external force, nor should it be interpreted as implying that the velocity in actual fluids becomes infinite.”

10,000 AIs Solved the Problem in Parallel Like ‘Mathematicians’

The scientific community has paid as much attention to the way AI solved the problem as to the result itself.

OpenAI used an unreleased next-generation model currently in training, forming multiple groups of AI agents to pursue different solution routes in parallel. The group tackling the Navier-Stokes problem consisted of about 10,000 AI agents, who found a solution 88 hours after beginning their first task.

This is different from the traditional approach of giving one AI a problem and waiting for an answer. Instead, many AIs explored different hypotheses and proof strategies in parallel, then consolidated promising results into a single proof.

Hanwoo Park, Dean of the College of Social Sciences at Yeungnam University, characterized this as an “Agent Academy,” saying, “Rather than AI becoming a genius mathematician alone, it’s as if a new research organization has been created, consisting of many AI researchers working in parallel.”

Simulation calculating the complex airflow around the UH-60 Black Hawk helicopter rotor using the Navier-Stokes equations. It shows the three-dimensional vortices and wake formed by the interaction of vortices created at the rotor tips. NASA is studying this complex fluid flow through computational fluid dynamics (CFD) calculations using supercomputers. Photo by Tim Sandstrom/NASA Ames

Professor Bae Hantaek of the Department of Mathematical Sciences at UNIST also commented, “The results announced by OpenAI mark a major turning point, showing that AI can accelerate complex mathematical research.”

However, it is premature to conclude that the Millennium Problem has been officially solved based solely on OpenAI’s announcement. The validity of the proof must be independently reviewed and accepted by the mathematical community.

Lim Sung-bin, professor of statistics at Korea University, stated, “If the proof is correct, it would mark a truly historic moment in mathematics,” but added, “For it to have genuine meaning in academia, we need to resolve the bottleneck that arises in human-led verification and translate the result into knowledge understandable to humans.”

Who Owns the Ideas? ... ‘Credit Disputes’ After AI Solves the Enigma

The research ethics surrounding this achievement have also sparked controversy.

Tristan Buckmaster, a mathematician at New York University, and Levent Alpoge, a researcher at AI company Anthropic, were conducting research closely related to the Navier-Stokes problem before OpenAI’s announcement. Controversy erupted after it was revealed that these researchers had used OpenAI's tools during their research, raising questions about whether their unpublished research data influenced OpenAI's model development or problem-solving efforts.

OpenAI stated that it did not directly access specific user data from those researchers to solve the problem. However, OpenAI acknowledged that it cannot completely rule out the possibility that anonymized data generated during their product use could have indirectly contributed to model improvement. OpenAI has also asserted that its proof and the two researchers’ approaches differ.

Arguments over the distribution of credit are also divided. Buckmaster’s side claims that OpenAI suggested omitting Alpoge’s name as a co-author, while OpenAI has given a different explanation, fueling the ongoing dispute.

Professor Bae remarked, “The controversies over the use of prior research data and credit allocation that have arisen around these results have sounded a serious alarm for the mathematics community,” emphasizing, “Discussions on AI research ethics, data sovereignty, and copyright systems are now necessary.”

As AI transitions from supporting researchers with calculations and literature searches to independently exploring hypotheses and proof pathways, new questions are emerging for science. If AI learns from researchers’ unpublished ideas and generates new discoveries, who owns those discoveries?

Professor Lim added, “AI-based scientific research is now a reality,” and said, “As it is only a matter of time before innovations in mathematics spread to other fields, this incident should stimulate multifaceted discussions on policy directions in the AI4Science field.”

This content was produced with the assistance of AI translation services.