>>13793186He's right. Every mathematician should strive to use category theory and set theory as little as possible. You only need the bare minimum for algebraic geometry, especially for the work Serre was doing.
Obviously its needed in some areas and is useful in formulating new areas, Connes and his NCG have benefited greatly from the categorical language.
I am a probabilitist, but you bet I only know the minimal measure theory i need, occasionally I will need to learn something new but im not about to go and read a whole series of papers on measure theory.
