Mathematicians Tristan Buckmaster and Levent Alpoge published three preprints on September 6, 2025, addressing the Navier-Stokes existence and smoothness problem. They utilized large language models, including Claude, Codex, GPT-5.6 Sol, and Astra, to advance the work of Diego Cordoba and Luis Martinez-Zoroa.
The research was conducted independently of their employers. The team used the Lean system for verification, which concluded on August 22. The publication was accelerated following a leak regarding their progress, which reached OpenAI, prompting a meeting with OpenAI's VP of Research, Sebastien Bubeck, on September 6.
Bubeck claimed that an internal OpenAI model had independently solved the Navier-Stokes equations with smooth force. He proposed that the mathematicians publish their work on Euler equations while OpenAI released its own findings, or that Buckmaster publish alone while excluding Alpoge, who is affiliated with Anthropic.
During the discussions, Bubeck questioned Buckmaster's professional future and suggested that Alpoge's employment at Anthropic complicated the situation. Buckmaster refused the terms and disclosed the pressure he faced. As of the report, the Navier-Stokes problem remains officially unsolved by the Clay Mathematics Institute.
