The Lean Proof Assistant - Introduction and Challenges - IPAM at UCLA

Explore the Lean proof assistant in this comprehensive lecture by Leonardo de Moura from Microsoft Research at IPAM's Machine Assisted Proofs Workshop. Delve into the introduction and challenges of Lean, the preferred proof assistant for the mathematics community. Discover its efficiency as a programming language and learn how users can extend its functionality. Gain insights into the Lean mathematical library (Mathlib), boasting over one million lines of code and contributions from more than 200 individuals. Examine topics such as meta programming, simple examples, trustworthiness, and the magical library. Investigate the ecosystem, Olympic channel, and impacts of formal mathematics. Address challenges including overhead factors, scalability, and accessibility. Explore the role of AI in mathematics, hypertree proof search, and the interactive process of proof development. Understand the engineering aspects, community excitement, and the main message behind this powerful tool shaping the future of mathematical proofs.

Introduction
How to install
Meta programming
Simple example
Should we trust
Magical Library
Perfectoid Spaces
Ecosystem
Olympic channel
Mathematical Library
Cancer Experiment
Impacts of formal mathematics
Extensions
Performance
Syntax
Domainspecific languages
Framework
Case analysis
Challenges
Overhead factor
Scalability
Accessibility
Trace messages
Visualizations
AI in mathematics
Hypertree proof search
Marketplace
Interactive process
Engineering
Tower of Babel
Community excitement
Manufacturing originalization
The main message