In a recent article, mathematician Tristan Buckmaster of New York University disclosed that a confidential model, widely believed to be OpenAI’s next-generation Bel, has successfully tackled a Millennium Prize Problem: proving the finite-time blow-up of solutions to the Navier–Stokes equations under external force driving. Impressively, the model reportedly produced a rigorous 100-page mathematical proof manuscript, though Buckmaster has not yet had access to the full document.

Meanwhile, Buckmaster and Levent Alpöge announced that—with the aid of a large language model (LLM)—they have derived finite-time blow-up results for three types of fluid equations under smooth external forces. The related research paper and code have been made publicly available. Fields Medal recipient Terence Tao commended the breakthrough but noted that substantial technical hurdles remain before the Navier–Stokes equations can be considered fully resolved.

Buckmaster also revealed that his team’s research progress had been shared internally at OpenAI. During discussions, OpenAI requested the removal of Alpöge, an Anthropic employee, from the author list, sparking debate within the academic community.

As the story unfolds, the global research community eagerly awaits OpenAI’s official response and the release of the complete proof. If verified, this AI-driven achievement could stand as a landmark case of artificial intelligence independently pushing the frontiers of human knowledge.