AI Assists Mathematician in Formalizing Complex Vlasov Equation.

Researchers have successfully formalized the well-posedness of the nonlinear Vlasov equation using the Lean 4 proof assistant, a complex mathematical achievement. This formalization was accomplished through an innovative approach where a mathematician directed an AI system, framing the entire process as a "formalization game." In this game, the human's role was strategic: defining scopes, steering decompositions, and identifying gaps in the existing library, while the AI agent executed the proof-writing tasks. The objective was to transform a LaTeX document into a fully compiling, axiom-clean Lean development, ensuring the target theorems rested solely on Lean's foundational axioms. The project not only certified the Vlasov equation's proof but also yielded a significant, self-contained layer of general mathematics, particularly properties of the Wasserstein-1 metric and the Kantorovich-Rubinstein duality theorem, which can be absorbed into the broader Mathlib. This demonstrates the potential of AI-assisted formalization to accelerate mathematical research and build robust, verifiable knowledge bases.