Sometimes people ask me what math they should study in order to get into agent foundations. My first answer is that I have found the introductory class in every subfield to be helpful, but I have found the later classes to be much less helpful. My second answer is to learn enough math to understand all fixed point theorems.
These two answers are actually very similar. Fixed point theorems span all across mathematics, and are central to (my way of) thinking about agent foundations.
I’ve now also highlighted Scott’s tip from “Fixed Point Exercises”: