Yeah, real analysis sucks. But you have to go through it to get to delightful stuff— I particularly love harmonic and functional analysis. Real analysis is just a bunch of pathological cases and technical persnicketiness that you need to have to keep you from steering over a cliff when you get to the more advanced stuff. I’ve encountered some other subjects that have the same feeling to them. For example, measure-theoretic probability is a dry technical subject that you need to get through before you get the fun of stochastic differential equations. Same with commutative algebra and algebraic geometry, or point-set topology and differential geometry.
Constructivism, in my experience, makes real analysis more mind blowing, but also harder to reason about. My brain uses non-constructive methods subconsciously, so it’s hard for me to notice when I’ve transgressed the rules of constructivism.
Yeah, real analysis sucks. But you have to go through it to get to delightful stuff— I particularly love harmonic and functional analysis. Real analysis is just a bunch of pathological cases and technical persnicketiness that you need to have to keep you from steering over a cliff when you get to the more advanced stuff. I’ve encountered some other subjects that have the same feeling to them. For example, measure-theoretic probability is a dry technical subject that you need to get through before you get the fun of stochastic differential equations. Same with commutative algebra and algebraic geometry, or point-set topology and differential geometry.
Constructivism, in my experience, makes real analysis more mind blowing, but also harder to reason about. My brain uses non-constructive methods subconsciously, so it’s hard for me to notice when I’ve transgressed the rules of constructivism.