OpenAI says it has made a breakthrough in advanced mathematics after using a new AI model and around 10,000 AI agents to tackle a decades-old problem involving the movement of fluids.
The ChatGPT maker said on Tuesday that its AI agents solved a difficult part of the Navier-Stokes equations in just 88 hours. The equations describe how fluids such as water and air move, but important parts of the problem have remained without a mathematical proof for about 90 years.
OpenAI described the result as a major milestone for AI and said it shows how quickly its mathematical capabilities are improving. However, the work has not yet been independently verified or accepted by the Clay Mathematics Institute, which oversees the Millennium Prize problems. A complete solution to one of those problems carries a $1 million prize.
The announcement has also caused controversy among mathematicians. Tristan Buckmaster, a mathematics professor at New York University, said he and Levent Alpöge, a mathematician at Anthropic, had also been working on the same problem using OpenAI’s Codex tool.
Buckmaster said that on September 3 he learned that information about their progress had reached OpenAI. He argued that OpenAI only began working on the Navier-Stokes problem after information about their research had reached the company. He also shared parts of emails exchanged with OpenAI about the issue.
Buckmaster said he had not yet studied OpenAI’s complete proof but decided to speak publicly because he believed the sequence of announcements could create a misleading impression about how the work had developed.
OpenAI described the work by Buckmaster and Alpöge as “remarkable” and said the two efforts happened concurrently. The company said it had not seen their work through any means before they released it publicly and that no user data was accessed during its Navier-Stokes research.
OpenAI did acknowledge that it could not completely rule out the possibility that de-identified data from use of its products had helped improve its models. However, it said the proofs produced by the two groups were significantly different and addressed different precise results.
According to OpenAI, it began training a new internal AI model at the end of August after discovering that it was particularly strong at advanced mathematics. Because the model was significantly more capable than its latest publicly released model, researchers decided to test it on several difficult mathematical problems.
The company said it heard rumours on September 1 that two Millennium Prize problems had been solved. It then assigned thousands of AI agents powered by the new internal model to work on some of the remaining problems.
By September 5, about 88 hours after the project began, the agents had produced a solution to the Navier-Stokes existence and smoothness problem.
The problem is closely connected to turbulence, a phenomenon that remains poorly understood. Although the AI reached its result in a relatively short period, the effort involved an enormous amount of computation. OpenAI said the agents exchanged nearly 3 million messages and generated around 130 billion output tokens while working on the problem.
Based on OpenAI’s own pricing for its most advanced models, the company estimated that an equivalent effort would have cost around $10 million.
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OpenAI said its result resolves two of the four statements required by the Millennium Prize problem. The company is not claiming the $1 million prize and said its purpose in publishing the work is to demonstrate the progress being made by its AI models.
