The Univalent Foundations Program

The Univalent Foundations Program is an approach to mathematics that uses concepts from type theory and computer science to build a new, flexible foundation for all mathematical knowledge. It aims to provide a more consistent and constructive way to define and work with mathematical objects, emphasizing how different structures relate and are equivalent. This framework allows mathematicians and computer scientists to formalize proofs and verify correctness using computer proof assistants, promoting rigor and collaboration. Ultimately, it seeks to unify varying mathematical ideas into a cohesive, understandable system grounded in modern logic and computation.