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An OpenAI Model Solved the Navier–Stokes Millennium Problem
OpenAI claims to have resolved the 90-year-old Navier–Stokes Millennium Prize problem using an internal AI model.
What: OpenAI reported that an internal system successfully produced both an analytical proof and a Lean-formalized solution demonstrating that smooth three-dimensional fluid dynamics can develop finite-time singularities.
Why it matters: This represents a major milestone in using automated reasoning systems to tackle longstanding, non-trivial mathematical problems that have previously eluded human mathematicians.
Decoder
- Navier–Stokes existence and smoothness problem: A famous unsolved Millennium Prize problem that asks whether smooth, globally defined solutions exist for the Navier–Stokes equations in three dimensions, which describe fluid motion.
- Lean: An interactive theorem prover and programming language used to formally verify mathematical proofs, ensuring they are logically sound without human error.
Original article
OpenAI announced that an internal AI system produced a proof resolving the roughly 90-year-old Navier–Stokes existence and smoothness problem, one of mathematics' seven Millennium Prize Problems. The model showed that smooth three-dimensional fluid dynamics can develop a finite-time singularity and produced both an analytical proof and a Lean formalization.
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