Univalent foundations are a way of organizing math that brings more clarity and rigor to proofs and theories. It does this by treating proofs more like pieces of software that can be run on a computer and checked for logical correctness. Instead of starting each proof with general assumptions, univalent foundations use precise definitions and accepted rules that provide a sound and strict framework for reasoning. This way, the steps of each proof can be verified, and mistakes can be easily identified and corrected.