ELI5: Explain Like I'm 5

homotopy type theory

Homotopy type theory is a new way of looking at mathematics. It's like a new way of putting together pieces of Lego. In homotopy type theory, you start with pieces that represent the basic building blocks of mathematics (like 0, 1, and so on). Then you combine those pieces in different ways to get different shapes. So what you end up with is a mathematical universe made out of different shapes. With homotopy type theory, you can explore these shapes and see how they all fit together to make up our mathematical universe.