Have you tried just creating problems that applying the mathematics you're trying to learn would solve?

"Learning math" to understand "cryptography" seems to me as a narrow goal. I have an impression that observing it that way you can get disinterested as soon as "the math" is doing its "mathy" things of developing itself just for the sake of it. Because that's math in essence. You want to be on the level of "applied" math but you have to be ready to "dirty" your hands with math "just so" too. Once you are proficient enough to feel comfortable of approaching math as something that doesn't have one purpose and not even some universal consistency (e.g. not in all cases is the notation the same) it will be easier for you: then you use math as a tool, but you aren't afraid of that tool. But a lot of math exists for itself.

My suggestion, it worked for me: buy a lot of paper, like, thousands of sheets. Take some books with the problems (and also with the solutions) then work through, maybe more than once. Don't say you haven't tried until you actually used all these sheets to write your own derivations of the solutions. If you once see the solution, you have to try the second time without looking. I could not learn by not really doing it, a lot, and I don't think anybody can. You can't just "read" it as you read history books, you have to "work" it.

A lot of people simply can't imagine themselves sitting and filling the papers with formulas (also in the comments here), but don't have problems spending months doing video games, for example. It's this "belief" that's limiting.

On another side, you need to have some kind of context too, but you have to find the interactions of the context and the actual work you do yourself. I like the "historical" context, because the big steps in math were traditionally not accidental. Archimedes invented the kind of "infinite" methods to calculate volume of some solids, and the methods remained forgotten, people remembering just results, Newton also invented a new math just to solve the problems he considered etc. For you, you have to adjust your steps to the knowledge you already have: if you know little, you can't avoid spending time learning the basic stuff. You have to work through, step by step.

Maybe also watch the documentary about Fermat's Last Theorem as an example of how it looks like doing math.

I've considered this, I was planning on reimplementing `bc' or something on those lines. Perhaps some kind of crypto suite or physics sandbox would work for me? What sort of programs did you write, I'd love to hear more!

What I'm looking for is theoretical knowledge, and that's something else I struggle with. Can I still get that with more hands on experience?

For instance, something I find fascinating are One Time Pads. They're perfectly secure, given len(k) >= len(m); so the key must be the same length as the message.

As far as I understand, it's because each possible key may produce any possible message which I think is expressed:

    Pr(x) = 1/|U|

Where U is the universe of all possible messages: {0, 1}^n where n = len(k)

I probably wrote some mistakes there. I was able to pick this concept up, I think as it just made sense to me; maybe I was able to visualize it or I could just think it through and realize the conclusion made sense.