I'm good at programming and I'm trying to get into math, which should be easy enough as programs are equivalent to proofs
see https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

I have begun looking at Haskell and Category Theory and trying to piece things together from that angle, hoping to fill in the holes by learning through analogy/isomorphism, but I feel I'm really missing some things.

In school they put me through basic math such as Calc1-3, DiffEq, Linear Alg, Statistics and Probability, and Discrete+Set Theory.
On my own I've studied formal systems enough to know about axioms, rules of inference, decision rules, theorems, isomorphisms.
Compilers has also given me some exposure to formal languages.

What should I be studying next?
Should I go back and do any basic math?
I still have no idea what groups and rings are.
Numbers allude me.