The problem I’ve always had with the higher levels of mathematics is that there’s no way to “start” for me (I’m not saying this is true of everyone).
With software engineering, which is what I’m good at, you can sit down and use software. You might not know how to write a text editor, but you can use one and get an intuitive idea of what it’s doing. Operating systems are hard, but you can use one and get a concept of “process” and “event” and “file” and so on without first having to learn operating systems theory.
These intuitive notions give you something to anchor your further study on.
I can’t get that with math past a certain point. I can’t sit down and “use” topology theory and get an intuitive idea of how it works. I can’t set out to “write my own text editor to learn how they work” in math. The branches of mathematics that I don’t use in my daily life (which, being a software engineer/researcher is limited to algebra, combinatorics/discrete math, and some mathematical logic) is just…impenetrable to me.
I wish that weren’t the case. I’m taking suggestions for how to fix that problem for me. :)
Edit working now…
Slashdotted? I get a “refused connection” message.