陶哲轩：感谢Lean，我又重写了20年前经典教材！

Core Viewpoint - Terence Tao has announced the creation of a Lean companion project for his undergraduate textbook "Analysis I," aiming to provide an alternative learning method through formalized mathematics using the Lean proof assistant [1][2]. Group 1: Project Overview - The Lean project will convert definitions, theorems, and exercises from "Analysis I" into Lean format, allowing students to engage with the material interactively [2][4]. - The project is intended to transition towards the standard Lean library Mathlib, which is one of the largest and most active formal mathematics projects globally [1][2]. Group 2: Educational Goals - "Analysis I" focuses on foundational topics such as the construction of natural numbers, integers, rational numbers, and real numbers, providing sufficient set theory and logic knowledge for rigorous proofs [2]. - The Lean project aims to enhance the learning experience by allowing students to complete exercises directly in Lean code, although official answers will not be provided [2][4]. Group 3: Structure and Content - The textbook consists of 11 chapters, with some chapters already formalized in Lean [3]. - The project maintains a deliberate strategy of partial independence from Mathlib, initially constructing certain mathematical structures independently before transitioning to Mathlib's definitions [5]. Group 4: Community Engagement - The Lean version of the textbook is now available for users, including mathematics students and researchers interested in formal verification, to engage with the material and provide feedback [7]. - Users have expressed excitement about the project, noting its potential to bridge the gap between traditional mathematics education and programming-based rigor [9].