OpenAI says it has made a major breakthrough in solving a 90-year-old mathematical problem using a new artificial intelligence model and about 10,000 AI agents.
The ChatGPT developer said on Tuesday that the AI agents solved a longstanding problem linked to the Navier-Stokes equations in about 88 hours.
The equations are used to describe how fluids move and are central to understanding turbulence, a phenomenon that remains difficult to fully explain.
Important aspects of the Navier-Stokes problem have remained unresolved for about 90 years, making it one of the major unsolved problems in mathematics.
OpenAI described its result as a “milestone” and said it demonstrated the rapid improvement of AI systems in advanced mathematical reasoning.
However, the claimed solution has not been independently verified or accepted by the Clay Mathematics Institute, the US-based organisation behind the $1 million Millennium Prize for solving major mathematical problems.
The claim has also triggered controversy after New York University mathematics professor Tristan Buckmaster alleged that information about his work with mathematician Levent Alpöge, who works at OpenAI rival Anthropic, may have reached OpenAI before the company announced its result.
Buckmaster said he and Alpöge had been using OpenAI’s Codex tool while working on the same problem.
He claimed that on September 3, he learned that information about their progress had been passed to OpenAI.
OpenAI published its Navier-Stokes work hours later.
Buckmaster said he had not yet examined OpenAI’s full proof but felt compelled to publicly explain the circumstances surrounding the development.
OpenAI, however, denied accessing the researchers’ work and said it had not seen any of it until it was publicly released.
The company also said no user data was accessed during its work on the Navier-Stokes problem.
“While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models,” OpenAI said, adding that its proofs differed significantly from the researchers’ work.
According to OpenAI, it began training a new internal AI model at the end of August after noticing that it was particularly capable in mathematics.
The company said it later deployed thousands of AI agents using the model to tackle some of the remaining major mathematical problems after hearing rumours that two Millennium Prize problems had been solved.
By September 5, about 88 hours after assigning 10,000 AI agents to the task, OpenAI said the system had produced a solution to the Navier-Stokes existence and smoothness problem.
The company said the agents exchanged nearly three million messages and generated about 130 billion output tokens during the effort.
Based on OpenAI’s own pricing for its most advanced models, the computing effort would have cost about $10 million.
Despite the breakthrough claim, OpenAI said its result resolved only two of the four statements required by the Millennium Prize problem.
The company also said it was not seeking the $1 million prize.
“Our goal in releasing this result is to report on the substantial progress of our AI models,” OpenAI said.
The company said the work was intended to demonstrate the growing capabilities of AI rather than claim the Millennium Prize.
