Machine-Checked Proofs and the Rise of Formal Methods in Mathematics

The domains of mathematics and software engineering are witnessing a rapid escalation in complexity. As generative artificial intelligence emerges as a potential force in mathematical exploration, a pressing imperative arises: ensuring the correctness of machine-generated proofs and software constructs.

The Lean proof assistant addresses these challenges. Conceptualized as a nexus for mathematics and software, Lean functions as an integrated development environment in which mathematical proofs undergo interactive construction and verification. Concurrently, software undergoes mechanical verification. A salient feature of Lean is its inherent extensibility, permitting users to imbue it with bespoke extensions, crafted within Lean's own framework. This extensible design paradigm fosters an ethos of decentralized innovation, wherein practitioners are not merely users but active contributors.

In his presentation in our Theoretically Speaking public lecture series, Leonardo de Moura (AWS) described Lean's contributions to the mathematical domain, its extensive mathematical library encapsulating over a million lines of formalized mathematics, its pivotal role in cutting-edge mathematical endeavors such as the Liquid Tensor Experiment, its impact on mathematical education, and its role in AI for mathematics.