It’s a bit unsettling to me how much of mathematics is grounded in the description of something like physical space. A lot of large areas of math (topology, geometry, various kinds of analysis) start out with one particular property of physical space (or of an intuitive idea of what physical space is), separate that property from all the others, and then generalize it. The generalizations can get pretty far from the starting point, but even then it’s a strange way of classifying different abstractions: “which property of space did you abstract from?”
I guess one could ask “what else would we do?”, but there’s algebra and number theory. So it’s like, we have the math that “starts with space” and then the other math, and each of those groups comprises closer to 50% of the math people think about than 90% or 10% (I have no idea how you would measure such a thing, or even define it, but I hope you see what I am getting at). Which seems strange to me.
(Then again analysis is very useful in number theory, which I have always found spooky, but I’m too ignorant to know whether I should find it spooky.)
Really, I don’t know enough about the super-abstract parts of math subfields to talk about this sensibly, so I welcome input from the less ignorant + you should take this with a grain of salt.

