OpenAI claims to have solved Navier Stokes’ math problem

OpenAI announced that it solved Navier Stokes’ 90-year-old mathematical problem in 88 hours using 10,000 agents and a new artificial intelligence model.

OpenAI, which developed the ChatGPT AI chatbot, said in a release published Tuesday that it is “sharing solutions” to problems related to fluid movement.

The company said it uses a “coordinating agent” system that leverages internal AI models.

“Agents had access to tools such as the ability to read from cached versions of the internet and the ability to execute code. Agents were subdivided into groups and able to communicate within groups,” OpenAI said. “The groups varied in size, and the group that drafted the Navier Stokes resolution had approximately 10,000 agents participating at the same time.”

“Agents reached a resolution on Saturday, September 5th, approximately 88 hours after the first agent was launched,” the company added.

Navier Stokes is one of seven Millennium Prize problems and is considered one of the most difficult mathematical problems of the early part of this century.

The Clay Mathematics Institute in Cambridge, Massachusetts, which created the bounty problem, has not yet commented on OpenAI’s proposed solution.

But OpenAI’s research raised questions from Tristan Buckmaster, a mathematics professor at New York University.

In a statement on his website, Buckmaster explained that he has been conducting “personal collaborations” on mathematical problems involving fellow mathematicians Levent Arposis and Navier Stokes, both of whom work at OpenAI’s rival Anthropic.

He said Alposi had received “information” that information about the pair’s progress had been passed to OpenAI. He said the tech giant’s path to a solution is similar to his own efforts, “not a direction you give a problem statement to a model and arrive at in a few days.”

Buckmaster also raised questions about whether the OpenAI models were trained on or had access to OpenAI’s Codex sessions. He said the mathematicians used several large-scale language models as part of their research.

“I want to be clear that I’m not making any claims. I haven’t seen any evidence of OpenAI. I don’t know what their model did or how they did it. I don’t know if our data was used,” Buckmaster added.

OpenAI said in a statement that the effort to solve Navier Stokes’ math problem began on September 1 after “hearing rumors” about progress on the puzzle, which was later found to be connected to Arposis and Buckmaster.

“We (researchers and agents) did not see their work by any means until they made it publicly available. In particular, we did not have access to specific user data to solve this problem. Although unlikely, we cannot rule out the possibility that anonymized data obtained from their use of our products could have helped improve our models,” the company added.

The Clay Mathematics Institute established Prize Problems in 2000, placing a $1 million prize on the solution to each problem.

“The award is designed to raise public awareness of the fact that the frontiers of mathematics are still open and that there are many important unsolved problems; it emphasizes the importance of striving to solve the deepest and most difficult problems, and aims to recognize achievements of historical scale in mathematics,” the institute said on its website.

Other problems include the Birch and Swinnerton-Dyer conjectures related to elliptic curves, and the Riemann conjecture related to prime numbers.