OpenAI Artificial Intelligence System Solves Navier-Stokes Problem
An artificial intelligence system within OpenAI has achieved a milestone by analytically solving the Navier-Stokes existence and smoothness problem, one of the Millennium Prize Problems.
OpenAI announced that a developed internal artificial intelligence system has produced a mathematical solution proving that the Navier-Stokes equations can develop a singularity up to a finite time.
Background of the Navier-Stokes Problem
The Navier-Stokes equations use Newton's second law of motion to describe the movement of fluids, treating fluids as a continuous medium. These equations in fluid mechanics are widely applied in aircraft design and weather forecasting.
The question of whether the equations can develop a singularity in finite time, even if they start with initially smooth motion, has been seeking answers for about 90 years.
AI-Powered Solution Process
OpenAI stated that they began training a new internal model that demonstrated unprecedented performance in benchmarks, including mathematics. The system, composed of coordinated agents, evaluated problems using tools such as code execution and internet cache reading.
The group that produced the Navier-Stokes solution consisted of approximately 10,000 concurrent agents, and the agents performed their tasks under secure monitoring and isolation measures.
Details of the Analytical Proof
The agents produced an analytical proof and Lean formalization indicating that a fluid initially at rest and smooth can develop a singularity in finite time. It was demonstrated that while the fluid's energy remains finite throughout the dynamics, its velocity can increase without bound.
Concurrent Studies and Statements
Following the completion of the studies, it was learned that researchers from Anthropic and NYU were conducting a similar study. OpenAI reported that they prioritized this team's work on the forced Euler problem and celebrated their success.
Future Perspective and Responsibilities
OpenAI stated that their primary purpose in sharing this result was to report the significant progress in AI models and that they do not intend to claim the Millennium Prize. Going forward, the focus remains on developing safe and responsible artificial intelligence systems.