OpenAI announced on Tuesday that an artificial intelligence system had solved the Navier-Stokes existence and smoothness problem, a 200-year-old equation governing fluid dynamics that sits among the seven Clay Millennium Prize challenges, each carrying a $1 million reward.
The claim and the cost
Sebastien Bubeck, a mathematician and AI researcher at OpenAI, stated in a press briefing that the company began training a new model with advanced mathematical capabilities on August 28. Following reports that Anthropic was making progress on the same equation, OpenAI shifted resources toward the task. More than 1,000 agents worked on the problem for over 50 hours before finding a solution.
“I thought there must be a mistake somewhere,” Bubeck said. “And on Sunday morning we had the final solution, Lean-formalized and everything.” Lean is a programming language used to formalize mathematical proofs.
Mark Chen, head of research at OpenAI, noted that solving this problem required considerably more computing power than previous mathematical challenges. The cost ran into millions of dollars.
Academics say they were cut out
Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher at Anthropic, posted documents on Monday claiming key advances in an area relevant to the Navier-Stokes problem. The pair stated they used several AI models, including Claude and Codex, to complete their work.
Buckmaster said he learned last week that OpenAI had become aware of his and Alpöge’s progress and had started dedicating significant resources to the issue. He asked OpenAI leaders whether the company had accessed the pair’s Codex logs. He was told the model “didn’t look up user data” but claims the company did not respond to questions about training. Buckmaster then says OpenAI offered several proposals, including one where he could publish a paper announcing the Navier-Stokes problem had been solved by an internal OpenAI model but without Alpöge’s name included.
Buckmaster, Alpöge, and Anthropic did not immediately respond to WIRED’s request for comment.
OpenAI denies accessing their work
In the briefing, Bubeck and other OpenAI executives denied inspecting the pair’s Codex prompts to inform their own work. “We, whether it’s the researchers or the agents, did not see any of their work until it was released publicly last night,” he said.
“I want to be extremely clear that we recognize the priority of Levent Alpöge and Tristan Buckmaster’s work on unforced Euler, and we have nothing but congratulations to them on this monumental achievement that they have made. To be clear, we did not use their prompt or proof to prompt our models or direct our agents,” said Bubeck.
OpenAI said it wanted to recognise Alpöge and Buckmaster’s prior work. Ven Chandrasekaran, a mathematician at the company, also emphasised that their solution was significantly different in nature from the one produced by OpenAI’s model.
What it means
For researchers relying on AI to find proofs, this dispute highlights a friction point. If companies train models on data that includes unpublished work, or if they direct agents toward specific problems based on outside news, the line between independent discovery and derivative work blurs. As AI takes on more of the work involved with finding proofs, such fights could become more common.
