OpenAI has announced a significant breakthrough: an AI-generated solution to the Navier–Stokes Millennium Prize Problem, one of the seven most challenging open problems in mathematics. The solution includes a detailed writeup and a formal proof verified in the Lean theorem prover.
The Navier–Stokes equations describe the motion of fluid substances and are fundamental to physics and engineering. The Millennium Prize Problem asks whether solutions always exist in three dimensions without singularities, a question that has puzzled mathematicians for decades.
OpenAI's announcement marks a milestone in AI-driven mathematical discovery, demonstrating the potential of AI to tackle problems that have resisted human effort for years. The formal proof in Lean ensures the solution's correctness, adding a layer of rigor to the AI-generated result.
The full writeup and proof are being shared with the community, inviting scrutiny and further exploration. This development could open new avenues for AI in theoretical mathematics and beyond.