OpenAI claims Navier-Stokes solution; rival cries foul

OpenAI's announcement of a solution to the Navier-Stokes equation represents a significant claim in mathematics, a field where AI is increasingly playing a role. The company trained a model with advanced capabilities starting August 28, dedicating over 1,000 agents for more than 50 hours. The computing cost ran "in the millions of dollars," according to research head Mark Chen, highlighting the scale of such endeavors.

The controversy centers on allegations by mathematician Tristan Buckmaster, who, along with Anthropic researcher Levent Alpöge, posted documents claiming key advances in a related area. Buckmaster claims OpenAI became aware of their work and began dedicating resources to the problem, potentially influencing the outcome and credit. OpenAI's denial, including statements from researcher Sebastien Bubeck, acknowledges the pair's priority on unforced Euler but insists the company did not use their prompts or proofs.

The dispute underscores how AI's involvement in proofs could lead to more frequent conflicts over credit and methodology. The outcome may hinge on whether OpenAI's proof, formalized in the Lean programming language, is independently verified and whether Buckmaster's allegations are substantiated. For mathematicians, the episode could shape norms around data usage and collaboration with AI labs, making transparency and attribution critical as such partnerships evolve.