Kevin Hartnett, Author of 'The Proof in the Code': How the Formalisation Gap Explains AI Math Verification Challenges
Machine Learning Street Talk releases a documentary centered on Kevin Hartnett's new book, 'The Proof in the Code'. The film explores the evolution of the Lean theorem prover from a Microsoft Research side project to a core tool for mathematicians, and delves into the 'formalisation gap' raised by AI systems like AlphaProof: when a machine produces a proof nobody can read, what has actually been checked?
In a documentary released by Machine Learning Street Talk on October 26, 2026, host Tim Scarfe converses with Kevin Hartnett, author of The Proof in the Code, exploring the intersection of formal verification and artificial intelligence in mathematics. Hartnett, a senior writer at Quanta Magazine, focuses his new book on the history and current state of computer-assisted proofs.
The film traces the development of the Lean theorem prover, from its origins as a side project at Microsoft Research to its status as a foundational tool mathematicians now use to check their own field. Through perspectives from participants including Leonardo de Moura (Lean's creator), Jeremy Avigad, Kevin Buzzard, and Paul Lessard, the program showcases the construction of Mathlib, Peter Scholze's Liquid Tensor experiment, and Terence Tao's Equational Theories project.
The second half turns to AI's impact on mathematics, specifically AlphaProof and autoformalisation techniques. The program introduces a core concept: the 'formalisation gap,' defined as the distance between the mathematics people mean and the statement a checker certifies. This framework aims to explain the true meaning of verification when machines generate proofs that no human can read.
For readers interested in the boundaries of AI reasoning capabilities and evaluation credibility, this resource provides narrative context for understanding current technical limitations. While a full transcript is not provided, the official description clarifies the thematic arc, making it suitable as an introductory material for grasping the challenges of AI mathematical verification.