Math for philosophy
(of physics and science)

This somewhat disorganized collection of notes will hopefully eventually get organized into a guide for aspiring philosophers of science.

Differential geometry

It has seemed to many people that there is something special about the theoretical representation provided by differential geometry. Some more sophisticated types would say that what’s special about differential geometry is captured by something even more general, viz. fiber bundle theory. That’s an interesting thing to reflect upon, and it connects with the philosophical questions about gauge theories — which is a huge topic. Nonetheless, here are some scattered thoughts about differential geometry.

Category theory

Category theory is so general that it is almost more like a language than like a theory. In other words, one can talk, or think about, almost anything in category-theoretic language. That also means that the best ways to learn category theory are by immersion, and by moving in circles where people already speak this language.

Despite these qualifications, one can still learn a lot about category theory by studying books. Here are some that I have benefitted from.

Category theory and computer science

Categorical logic

Fancy probability theory

Functional analysis and operator algebras