Homotopy Type Theory (HoTT)

Homotopy Type Theory (HoTT) is an approach to understanding mathematics that combines ideas from logic, topology, and algebra. It treats mathematical objects as shapes or spaces, where different ways of transforming one shape into another (called homotopies) are fundamental. In HoTT, types can be seen as spaces, and equality between elements is considered as a continuous transformation. This perspective allows mathematicians to reason about structures and their relationships more flexibly, unifying various areas of math and providing new ways to verify proofs and explore concepts using geometric intuition.