Mathematical Conversations

A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. For instance, together with Kevin Buzzard and Johan Commelin, I recently formalized enough topology and algebra to define Scholze's perfectoid spaces to a computer. In this talk I'll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be useful (in our usual sense of "useful"). This will not be a talk about foundations of mathematics, and I will stick to elementary examples.