OpenAI has announced that it derived a solution to the Navier-Stokes equations, one of the Millennium Prize Problems in mathematics, using its internal AI systems. The Navier-Stokes equations describe the motion of fluids; for approximately 90 years, the question of whether the motion of a smooth three-dimensional fluid develops a singularity—a phenomenon where velocity becomes infinite—within a finite time had remained unsolved.

According to OpenAI's announcement, the solution was achieved using a system that combined internal models with capabilities exceeding those of GPT-6 Astra and approximately 10,000 collaborative agents. It was reported that the agents reached the solution in about 88 hours by utilizing tools such as code execution and internet information retrieval. The derived solution demonstrates that fluid vortices contract toward the center and form a singularity while keeping energy finite. OpenAI stated that it does not intend to claim the prize money for this result.

Meanwhile, the announcement of this achievement has sparked debate. Tristan Buckmaster and other mathematicians at New York University expressed concern that OpenAI may have obtained the solution by accessing Codex session contents used in their own research processes. While OpenAI denied the fact that it accessed specific user data to solve the problem, it stated that it cannot deny the possibility that anonymized data obtained from product usage contributed to the model's improvement.

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