I was about to agree, but then I realized it's not immediate that Set Theory has practical applications either. However, Set Theory is essential to build mathe

I was about to agree, but then I realized it's not immediate that Set Theory has practical applications either. However, Set Theory is essential to build mathematics. Taking points from: https://mathoverflow.net/questions/10334/what-practical-applications-does-set-theory-have https://mathoverflow.net/questions/10334/what-practical-appl... Analysis, Number theory, most of modern mathematics rely on set theory, even computer science in the definition of Turing machines and dealing with infinities there are implicit axioms of set theory. Likewise, perhaps category theory may not yield immediate applications, but it can be useful as a language (like a programming language, natural or mathematical) to express mathematical ideas, and to build mathematical systems and foundations. I'm not sure how closely it relates to Category theory, but Homotopy Type Theory has yielded the fantastic Univalent foundations, a seemingly more modern and simple foundation for mathematics. This line of work also yielded a solid basis for Proof assistants. I don't know enough about functional programming to comment...