Abstract
We present a new foundation for mathematics based on the correspondence between homotopy theory and type theory. This framework, known as homotopy type theory, extends Martin-Löf type theory by interpreting Type as spaces and terms as points. The central addition is the Univalence Axiom, which identifies equivalent types. We further introduce higher inductive types to represent cell complexes, such as spheres and quotients, directly within the formal system. This synthesis provides a computational environment for formalizing constructive mathematics and homotopy theory simultaneously.