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I feel like there are some interesting ideas in pure math topics like Real Analysis, Abstract Algebra, etc. Although I'm terrible at actually writing proofs and such.
Formalizing e.g. limit is quite interesting! Limit is related to tendency; sequence x_n converging to x means for large enough n, x_n is sufficiently close to x. That is, you can choose N such that | x_n - x | < eps for n >= N. In some sense, you are concretely defining what rough terms mean!
To look into these, you can read through books disregarding proofs. While proofs do hold ideas, they can be headache-inducing.