number theory: The Queen of Mathematics, in that it takes a lot from other fields and provides little in return, and people are weirdly sentimental about it.
combinatorics: Somehow simultaneously the kind of people who get really excited about Martin Gardner puzzles and very serious no-nonsense types who don’t care about understanding why something is true as long as they can prove that it’s true.
algebraic geometry: Here’s an interesting metaphor, and here’s several thousand pages of work fleshing it out.
differential geometry: There’s a lot of really cool stuff built on top of a lot of boring technical details, but they frequently fill entire textbooks or courses full of just the boring stuff, and they seem to think students will find this interesting in itself rather than as a necessary prerequisite to something better. So there’s definitely something wrong with them.
category theory: They don’t really seem to understand that the point of generalizing a result is so that you can apply it to other situations.
differential equations: physicists
real analysis: What if we took the most boring parts of a proof and just spent all our time studying those?
point-set topology: See real analysis, but less relevant to the real world.
complex analysis: Sorcery. I thought it seemed like sorcery because I didn’t know much about it, but then I learned more, and now the stuff I learned just seems like sorcery that I know how to do.
algebraic topology: Some of them are part of a conspiracy with category theorists to take over mathematics. I’m pretty sure that most algebraic topologists aren’t involved in that, but I don’t really know what else they’re up to.
functional analysis: Like real analysis but with category theorists’ generalization fetish.
group theory: Probably masochists? It’s hard to imagine how else someone could be motivated to read a thousand-page paper, let alone write one.
operator algebras: Seems cool but I can’t understand a word of it, so I can’t be sure they’re not just bullshitting the whole thing.
commutative/homological algebra: Diagram chases are of the devil, and these people are his worshipers.
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