OpenAI says 10,000 agents solved a $1 million math problem

OpenAI mathematicians announced a claimed solution to the Navier-Stokes existence and smoothness problem on September 8. Quanta reports that an unreleased internal model ran about ten thousand agents for eighty-eight hours. The agents produced a proof that a smooth three-dimensional fluid can develop a singularity in finite time under a smooth external force. Another OpenAI model then spent about seventeen hours converting the result into Lean. Lean checks whether each formal step follows from the stated rules.

The result addresses the forced versions labeled C and D in the official Millennium Prize problem. Quanta reports that the agents exchanged almost five million messages. OpenAI estimated the compute cost at several million dollars. The result would show that smooth forces can drive the equations to a point where the modeled fluid stops behaving smoothly. It does not mean that a real fluid reaches infinite speed.

Another group published related work hours earlier. New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge released Lean-checked proofs for three-dimensional Euler and other fluid equations. They built on years of work by Diego Córdoba and Luis Martínez-Zoroa. Buckmaster says OpenAI learned that the group was close to a major result before it began its sprint. OpenAI says rumors prompted the work, but denies using the group's private proofs or prompts.

OpenAI still owns the central claim, which Quanta reported. Lean confirms the logic that was encoded, but people must still check whether that statement matches the intended problem. Buckmaster says he has not seen OpenAI's proof and does not accuse the company of using his data. The two sides still disagree about the timeline.

OpenAI says its system did more than formalize a proof written by people. The company says the system developed the mathematical argument and then converted it into a formal proof. If outside reviewers uphold the result, models can do more than fill gaps in existing proofs. They can produce work at the edge of research mathematics.

The scale could change who can compete. Ten thousand agents can test many routes at once, while most mathematicians cannot spend several million dollars on compute. The credit dispute shows the cost of that speed. Rumors, private model sessions and pressure to publish can make it harder to tell who supplied a key idea before the usual review begins.

First, independent mathematicians need the full argument, the Lean files and a list of dependencies. They need to confirm that the formal statement matches the Millennium Prize question and that no hidden assumption changes the result.

The credit dispute needs a dated account from OpenAI, along with public prompts or run records. Reviewers could then compare its proof with the Córdoba and Martínez-Zoroa program. The Clay Mathematics Institute's response will matter only after mathematicians have had time to inspect the work.