OpenAI claims that a new internal AI model, working through around 10,000 autonomous AI agents, made significant progress on a years-old mathematics problem in just 88 hours.
The company said Tuesday that the agents tackled the Navier-Stokes existence and smoothness problem, which concerns equations describing how fluids move and is closely connected to the still poorly understood phenomenon of turbulence.
Strong mathematical abilities
OpenAI started training the new model at the end of August and discovered that it showed unusually strong mathematical skills.
After hearing on September 1 that two Millennium Prize problems may have been solved, the company assigned thousands of agents running the model to several difficult mathematics challenges.
By September 5, roughly 88 hours later, the system had produced a proposed solution addressing part of the Navier-Stokes problem.
The agents exchanged nearly 3 million messages and generated about 130 billion output tokens while working on Navier-Stokes alone.
Based on OpenAI’s pricing for output from its most advanced models, a comparable workload could cost roughly $10 million.
No independent verification of results
OpenAI called the result a milestone, showing how rapidly AI capabilities are enhancing.
However, the proof has not yet received independent verification or formal acceptance from the Clay Mathematics Institute, which oversees the Millennium Prize Problems.
The Navier-Stokes challenge carries a $1 million prize, but OpenAI said its result addresses only two of the four statements required by the prize.
The company said it is publishing the work to show progress in its AI models and does not intend to claim the Millennium Prize.
Tristan Buckmaster raises questions about OpenAI’s timing
The statement also ignited criticism from New York University mathematics professor Tristan Buckmaster.
Buckmaster said he and the Anthropic mathematician Levent Alpöge had also been working on the problem using OpenAI’s Codex.
According to Buckmaster, he learned on September 3 that information about their progress had been passed to OpenAI. He claimed OpenAI only began working on Navier-Stokes after learning about their research.
Buckmaster said he had not yet reviewed OpenAI’s complete proof but released emails and details about the timeline because he believed the public record needed clarification.
OpenAI appraised Buckmaster and Alpöge on what they called their “remarkable” concurrent work.
The company said it had not accessed or seen their research before it became public and that no user data was used directly in its Navier-Stokes effort.
OpenAI further said that it could not completely reject the possibility that de-identified data from their use of its products had earlier contributed to improving its models but said the two proofs and the exact results they establish differ significantly.
