OpenAI says it solved the 90-year-old Navier–Stokes mathematics problem in 88 hours, using 10,000 agents and a new artificial intelligence model.
In a release published Tuesday, OpenAI — the company behind the ChatGPT AI chatbot — said it was "sharing a solution" to the problem, which relates to how fluids move.
It said it used a system of "coordinating agents" powered by its internal AI model.
"The agents had access to tools such as the ability to read from a cached version of the internet and the ability to run code. Agents were subdivided into groups with the ability to communicate within the group," OpenAI said. "The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents."
"The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched," the company added.
Navier–Stokes is one of seven Millennium Prize Problems, considered to be among the most difficult mathematical problems at the start of this century.
The Clay Mathematics Institute of Cambridge, Massachusetts, which founded the Prize Problems, has not yet commented on OpenAI's proposed solution.
Mathematician pushes back
OpenAI's work drew questions from Tristan Buckmaster, a professor of mathematics at New York University, however.
In a statement on his website, Buckmaster explained that he had been working with fellow mathematician Levent Alpöge, who works at OpenAI rival Anthropic, in a "personal collaboration" on math problems including Navier–Stokes.
He said Alpöge received "tips" that information about the pair's progress had been passed to OpenAI. He said the tech giant's route to the solution was similar to their own work, which is "not the direction one arrives at in a few days by giving a model the problem statement."
Buckmaster also raised questions over whether OpenAI models had been trained on, or had access to, their sessions in OpenAI's Codex. He said the mathematicians had used several large language models as part of their work.
"I would like to be clear about what I am not claiming. I have not seen OpenAI's proof. I do not know what their model did, or how. I do not know whether our data was used," Buckmaster added.
In its statement, OpenAI said its effort to solve the Navier–Stokes mathematics problem began on Sept. 1 after "hearing a rumor" about progress on the puzzle that it later found out related to Alpöge and Buckmaster.
"We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models," the company added.
Millennium Prize Problems
The Clay Mathematics Institute established the Prize Problems in 2000, putting up a $1 million prize for the solution of each problem.
"The Prizes were conceived ... to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude," the institute says on its website.
Other problems include the Birch and Swinnerton-Dyer Conjecture, which relates to elliptic curves, and the Riemann Hypothesis, which relates to prime numbers.
