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OpenAI Says Its AI Solved Navier-Stokes, but Mathematicians See Little Human Understanding

OpenAI says its AI solved the Navier-Stokes problem, a Millennium Prize question, but mathematicians say its 166-page proof is technically correct yet hard to read and offers little human understanding.

AI News Feed · 2026-09-22 19:29

James Maynard, a mathematician at the University of Oxford, said, "So far it's been very difficult to really extract any human understanding from this new AI proof." Javier Gómez-Serrano, a mathematician at Brown University who uses AI in his own research, said, "The paper is not written for humans." He said he believes the proof could help advance the field after "some serious re-writing," but "as of today, the paper doesn't teach us much."

The problem concerns a set of equations used to describe fluid flow, known as the Navier-Stokes equations. Tristan Buckmaster, a mathematician at New York University, said the equations are used every day across physics and engineering. Researchers do not fully understand at a fundamental level why they work. Buckmaster said deeper insights into Navier-Stokes would likely yield "a new toolkit to understand complicated solutions to fluids," which could lead to better models of turbulence in fluids and lift in aircraft.

Mathematicians had been looking for scenarios in which the equations "broke down," or stopped working. Describing such scenarios became one of the $1 million Millennium Prize Problems established in 2000 by the Clay Mathematics Institute. Martin Hairer, a mathematician at EPFL in Lausanne, Switzerland, said the community could sense it was getting close. "Among the seven Millennium Problems … Everyone agreed that this would be the next one that got solved," he said.

OpenAI's announcement came as human mathematicians were closing in on a solution. Buckmaster and his collaborator Levent Alpöge at Anthropic were among those inching closer to finding a scenario where the equations stopped working, using AI tools including OpenAI's chatbot. OpenAI then wrote that on Tuesday, September 1, it heard rumors that two Millennium Prize problems had been resolved. "Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems," the company wrote.

OpenAI said it marshalled some 10,000 AI agents to work on the Navier-Stokes problem. The agents worked for 88 hours and used around 130 billion output tokens, or units of text and characters generated by the model. According to OpenAI's pricing for its most advanced publicly available model, the solution cost the company somewhere around $6 million to $10 million to compute. Overall, the company said it used 300 billion tokens, closer to $15 million to $20 million, while looking for solutions.

The announcement sparked controversy after Buckmaster issued a public statement describing how the company had approached him. According to Buckmaster, OpenAI said it would put him on their paper if he dropped Alpöge, his collaborator at rival company Anthropic. Buckmaster told NPR he believes OpenAI was tipped off to the approach he and Alpöge were using to try to find the solution to Navier-Stokes.

Maynard, who signed a statement by 25 winners of the Fields Medal, said the episode could have demonstrated the power of collaboration between humans and AI. The statement, published September 11, decried "misaligned goals" between the AI companies and the mathematics community. "Unfortunately, because of the decisions of humans involved, it became this scrappy, messy battle," Maynard said.

OpenAI had framed the work in broad terms. "A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity," the company wrote. But mathematicians contacted by NPR said that while AI has exploded onto the math scene over the past six months, and large language models appear for the first time capable of producing real results that could lead to new mathematical discoveries, few see OpenAI's announcement as an example of how AI and mathematicians can work together.

Editor's Summary

OpenAI announced that its AI solved the Navier-Stokes problem, a Millennium Prize question in fluid dynamics, but mathematicians say the 166-page proof is technically correct yet difficult to read and has not yet produced much human understanding. The company used roughly 10,000 AI agents for 88 hours at a cost of about $6 million to $10 million, according to OpenAI pricing cited by NPR News. A dispute over OpenAI's approach to a competing researcher, along with a Fields Medal winners' statement criticizing "misaligned goals," has added controversy to the result.