Avigad J., Massot P. Mathematics in Lean 2025

Textbook in PDF format

The goal of this book is to teach you to formalize mathematics using the Lean 4 interactive proof assistant. It assumes that you know some mathematics, but it does not require much. Although we will cover examples ranging from number theory to measure theory and analysis, we will focus on elementary aspects of those fields, in the hopes that if they are not familiar to you, you can pick thhem up as you go. We also don’t presuppose any background in formalization. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a regimented language, like a programming language, that Lean can understand. In return, Lean provides feedback and information, interprets expressions and guarantees that they are well-formed, and ultimately certifies the correctness of our proofs.
Lean is an open-source programming language and proof assistant that enables correct, maintainable, and formally verified code