Short answers, pulled from the story.
Lean is a proof assistant and functional programming language based on the calculus of constructions with inductive types. It verifies mathematical arguments step by step, accepting only reasoning that can be formally checked from first principles. It is free, open-source, and hosted on GitHub.
Lean was developed primarily by Leonardo de Moura, a Brazilian computer scientist, first at Microsoft Research and later at Amazon Web Services. The 2025 ACM SIGPLAN Programming Languages Software Award recognized four contributors: Gabriel Ebner, Soonho Kong, Leo de Moura, and Sebastian Ullrich.
As of May 2025, mathlib contained over 210,000 formalized theorems and more than 100,000 definitions. The library began in 2017 as a community project with the goal of formalizing as much of pure mathematics as possible, up to research level. In 2026, it was awarded the Demailly prize for open science.
AlphaProof, created by Google DeepMind in 2024, proved mathematical statements at the level of a silver medalist at the International Mathematical Olympiad. It was the first AI system to achieve medal-worthy performance on math olympiad problems, working in Lean.
Terence Tao released a Lean companion to his real analysis textbook Analysis I, formalizing selected sections of the text. In 2023, he also used Lean to formalize a proof of the Polynomial Freiman-Ruzsa conjecture, a result he and collaborators published in the same year.
In 2025, Joseph Tooby-Smith used Lean to discover an error in a 2006 paper on the stability of the Two-Higgs-doublet model potential. The paper had been in circulation for close to two decades before formal verification identified the mistake.