OpenAI announced on September 8, 2026, that its multi-agent AI system addressed parts of the Navier-Stokes existence and smoothness problem. The system reportedly resolved two statements, labeled C and D, by constructing a proof involving a finite-time singularity scenario.
The computation involved approximately 10,000 AI agents running for about 88 hours, starting around September 1, 2026. These agents produced 2.7 million messages and 130 billion output tokens. OpenAI documented the findings in a 166-page report and verified the logic using the Lean software tool.
The company stated it is not seeking the $1 million prize offered by the Clay Mathematics Institute for solving the problem. The institute is currently reviewing the submission to determine if the proof holds for the unforced case, as current expert analysis suggests it may only apply to the forced formulation.
The announcement triggered a dispute involving NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge, who claimed OpenAI utilized their unpublished work. OpenAI denied borrowing data or prompts, while also addressing allegations regarding the exclusion of Alpöge from authorship discussions.
Harvard mathematics faculty are debating the implications of machine-generated proofs. While some acknowledge the efficiency of AI in formalizing solutions, others express concern that opaque reasoning provides correctness without mathematical insight, potentially limiting the ability of humans to build upon the results.
