The Proof in the Code Explores How Lean Is Transforming Mathematics and AI

Summary

Kevin Hartnett’s nonfiction book, The Proof in the Code, tells the story of Lean, a computer program designed to provide complete formal verification that a logical chain is correct. Lean was developed in 2013 by Microsoft computer scientist Leo de Moura while he was seeking ways to reduce bugs and security weaknesses in software such as Word and Windows. Mathematicians later expanded the system to check complex proofs that would be difficult for people to assess reliably. The book describes how Google DeepMind and Meta AI have used Lean to train newer AI systems, with the goal of reducing hallucinations and improving accuracy. It also explains how DeepMind’s AlphaProof reached the level of a silver medalist at the 2024 International Mathematical Olympiad. Hartnett argues that formal verification may eventually help AI systems address problems outside mathematics, while presenting the subject in an accessible, narrative style. Publishers Weekly reviewed the 288-page book, published by Quanta at $30, in a June listing.