OpenAI's recent Navier-Stokes proof breakthrough includes a machine-verifiable Lean 4 formal proof, dramatically reducing the time needed for formal verification from an estimated 132,800 person-hours to just 17 hours, with implications far beyond mathematics for security and critical systems.

Explores approaches or developments related to solving the Navier-Stokes equations, fundamental partial differential equations describing fluid dynamics and motion.

Anthropic's AI model has completed a formal proof of Fermat's Last Theorem in Lean, finishing the final theorem on Wiedijk's 100 formalization challenges list. The proof uses the Darmon-Diamond-Taylor exposition of the Wiles-Taylor-Wiles argument and spans over 13.4 million lines of code.

Directory containing HTML files related to Fermat's Last Theorem in the Anthropics repository.

Neural networks achieve strong performance in symbolic domains like language and logic despite representing information as continuous vectors rather than discrete symbols. This research shows that neural network representations can be closely approximated with explicit symbolic structures, suggesting that networks implicitly realize symbolic computation and providing a bridge between traditional symbolic and modern connectionist approaches to AI.

Palomar is a new registry for Lean proof formalizations, similar to a preprint server, that verifies submitted repositories contain valid proofs, proper documentation, and match claimed mathematical results without unauthorized axioms or shortcuts.