OpenAI has announced a significant breakthrough in mathematics by providing a solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000. The problem, which has puzzled mathematicians for nearly 90 years, concerns the behavior of fluid dynamics described by the Navier-Stokes equations. According to the announcement, an internal OpenAI system has produced an analytical proof and a formalization in Lean, demonstrating that an initially smooth fluid can develop a singularity in finite time. This finding resolves the problem by establishing statement “C” and “D” in the official Millennium Prize formulation. The solution involves a vortex that spirals inward and elongates, maintaining finite energy throughout its dynamics. OpenAI aims to empower scientists and inform the world about the pace of AI progress with this achievement.
Source: OpenAI
