OpenAI announced today that it has developed an AI-generated solution to one of mathematics’ most challenging problems: the 200-year-old Navier–Stokes equations, which describe the behavior of fluids such as water and air.
The announcement initially appeared to demonstrate AI’s potential to advance mathematical research. However, mathematician Tristan Buckmaster later challenged OpenAI’s account, saying the company accelerated its efforts after learning about progress he and another researcher had made on a related problem. Buckmaster also alleged that OpenAI attempted to influence how credit for the work was assigned.
The Navier–Stokes equations are among the Clay Mathematics Institute’s Millennium Prize Problems, a group of seven unsolved problems that each carry a $1 million prize.
Sébastien Bubeck, a mathematician and AI researcher at OpenAI, said during a press briefing that the company began training a new model with advanced mathematical reasoning capabilities on August 28.
After hearing rumors that Anthropic researchers were making progress on the Navier–Stokes problem, Bubeck said OpenAI committed additional resources to the challenge. More than 1,000 AI agents worked on the problem for over 50 hours before the system generated a proposed solution.
“I thought there had to be a mistake somewhere,” Bubeck said. “And on Sunday morning, we had the final solution, Lean formalized and all.” Lean is a programming language used to express and verify mathematical proofs formally.
OpenAI said that solving the problem required substantially more computing power than previous AI-driven mathematics projects. Mark Chen, the company’s head of research, estimated that the effort cost “in the millions of dollars.”
On Monday, New York University mathematician Buckmaster and Anthropic researcher Levent Alpöge shared documents describing significant progress on a problem related to the Navier–Stokes equations. The researchers said they used several AI models, including Claude and Codex, to support their work.
Buckmaster also published a statement alleging that he learned the previous week that OpenAI had become aware of his and Alpöge’s research and had begun directing substantial resources toward the problem. Buckmaster said he asked OpenAI leaders whether the company had accessed their Codex logs. He said OpenAI told him that the model “doesn’t look at user data,” but did not answer his questions about training practices. According to Buckmaster, OpenAI later offered several suggestions, including publishing a paper stating that an internal OpenAI model had solved the Navier–Stokes problem without naming Alpöge.
Buckmaster, Alpöge and Anthropic did not immediately respond to WIRED’s requests for comment.
During the briefing, Bubeck and other OpenAI executives denied reviewing the researchers’ Codex prompts or using them to guide the company’s work. “Whether it’s the researchers or the agents, we didn’t see any of their work until it was published last night,” he said.
“To be clear, we recognize the priority of Levent Alpöge and Tristan Buckmaster’s work on unforced Euler, and we have nothing but congratulations for this monumental achievement. We did not use their prompts or evidence to prompt our models or direct our agents,” Bubeck said.
OpenAI said it wanted to recognize Alpöge and Buckmaster’s work to date. However, Ven Chandrasekaran, a mathematician at OpenAI, emphasized that the company’s AI-generated solution differs significantly from the researchers’ approach.
The debate over who deserves credit for resolving one of mathematics’ most important open problems could continue for months or years. Similar disputes may become more common as AI systems play a larger role in mathematical discovery and proof development.
This is a developing story. Please check back for the latest information.
Source: www.wired.com