Foundations 1: Introduction to Mathematics

In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about set theory, and introduce notions from category theory, logic and type theory, until we are in a position to understand dependent type theory, and in particular, homotopy type theory, which promises to replace set theory as the foundation of modern mathematics. We also take an interest in computer science, and how to write computer programming languages to formalize mathematics. In this first video, we introduce the material, and discuss the important basic ideas of sets and functions from a rough, intuitive perspective. Some people have said they want to support my efforts to make educational videos and software, and so I have made a Patreon page Any support would really help me produce more videos and software. Another way you can support me is by becoming a member of my