OpenAI, the company behind ChatGPT, announced Tuesday that it has used a new artificial intelligence model and approximately 10,000 AI agents to solve a complex mathematics problem that has remained unsolved for 90 years. The problem is related to the Navier-Stokes equations, which describe the motion of fluids, and has been a persistent challenge in the field.
According to OpenAI, the AI model, trained in late August, demonstrated a strong aptitude for mathematical tasks. Researchers then directed a swarm of AI bots, powered by this new model, to tackle some of the most difficult mathematical problems. Within 88 hours, by September 5, the AI had generated a solution to the Navier–Stokes existence and smoothness problem, a key aspect of fluid dynamics and turbulence.
The effort involved significant computational resources, with the AI bots exchanging nearly 3 million messages and processing 130 billion output tokens on the Navier-Stokes problem alone. OpenAI estimated the cost of such an endeavor, based on its own pricing for advanced models, to be around $10 million.
OpenAI stated that its solution addresses two of the four required statements for a proof sought by the Clay Mathematics Institute's Millennium Prize, which offers $1 million for solutions to certain mathematical challenges. However, the company emphasized that its primary goal in releasing the results is to showcase the advancements in AI models and that it does not intend to claim the prize.
The announcement has quickly generated controversy within the mathematics community. Tristan Buckmaster, a mathematics professor at New York University, alleged that he and Levent Alpöge, a mathematician at OpenAI rival Anthropic, were also working on solutions to the same problem using OpenAI's Codex tool. Buckmaster claimed that information about their progress was shared with OpenAI on September 3, shortly before the company's public announcement.
Buckmaster stated that OpenAI did not begin its work on the Navier-Stokes equations until after receiving information about his and Alpöge's efforts. He expressed concern over the timing and methodology of OpenAI's approach, although he had not yet reviewed the company's full proof. Buckmaster felt compelled to speak out to prevent a potentially misleading narrative.
OpenAI acknowledged the concurrent work of Buckmaster and Alpöge, calling it "remarkable." The company asserted that it had not accessed any of their work prior to its public release and denied accessing user data for its research on the Navier-Stokes problem. While OpenAI could not definitively rule out that de-identified data from user interactions might have contributed to model improvements, it stressed that its proofs differ significantly from any other purported solutions.