ME News reports that on September 9 (UTC+8), OpenAI announced it has solved the Navier-Stokes existence and smoothness problem, one of the Millennium Prize Problems, which had remained unsolved for approximately 90 years.
This proof was completed by a team of agents using OpenAI’s next-generation model, significantly more capable than GPT-6 Astra. OpenAI reports that approximately 10,000 agents worked in parallel over about 88 hours to derive the proof, followed by formal verification in the Lean theorem prover by GPT-6 Astra in 17 hours. The proof demonstrates that singularities can form in three-dimensional fluid flow within finite time: vortices contract inward, their cores stretch and accelerate until velocities become unbounded, while the system’s total energy remains finite. OpenAI has published the 165-page proof manuscript and the formalized Lean code, and has stated it does not intend to claim the $1 million prize. The Clay Mathematics Institute still lists this problem as unsolved, as its rules require the solution to be published in a qualified journal, remain publicly available for at least two years, and gain widespread acceptance within the mathematical community before being considered for the award.Source: X）
