OpenAI claims to have solved a major Millennium Prize Problem, but the announcement is overshadowed by allegations that the company failed to credit two researchers for their foundational work.

OpenAI announced that its AI agents have solved the Navier–Stokes existence and smoothness problem, one of seven prestigious Millennium Prize Problems. The achievement has sparked controversy following accusations that the company utilized and failed to credit work by NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge. OpenAI has denied these claims, stating that its internal models reached the solution independently.

The Dispute Over Attribution

Buckmaster, who recently posted a proof regarding a simplified version of the Navier–Stokes equations, alleged that OpenAI employees offered him a choice: either wait for OpenAI to publish its own solution or collaborate on a paper that would exclude Alpöge due to his employment at Anthropic. Buckmaster also questioned whether OpenAI's models had been trained on transcripts of his and Alpöge's previous work with AI tools, a claim OpenAI denied. OpenAI's chief research officer, Mark Chen, maintained that no employees or agents accessed the researchers' private transcripts.

Resource Disparity in Mathematics

The solution to the Navier–Stokes problem was achieved by OpenAI using approximately 10,000 simultaneous AI agents at a cost of millions of dollars. This contrasts with the human-led approach, where Buckmaster and Alpöge spent nearly a year working on the problem. Experts, including UCLA mathematician Terence Tao, have expressed concern that the rapid, private, and resource-intensive nature of AI-driven mathematical discovery may bypass the collaborative, iterative processes that historically drive the field forward.