One of the most frustrating parts about learning math is that it is a body of knowledge driven constantly to generalization. This usually pays off, because once mathematicians connect just a few dots then often whole new problem spaces just collapse into yesterday's math, taken down by powerful, general theories, like convex optimization, applied with just the right slant.<p>The problem is that often those applications are so wide and varied that nobody bothers to talk very much about them. You're just supposed to understand the underlying purpose and need on your own. For someone with the background, that's ok, because the background is the context that lets you internalize the math. Without the background, applications are necessary.<p>Of course, this is well known for basic math. That's why you learn how to add apples and subtract oranges instead of number theory and fields. At some point, though, if you want to understand "real" mathematics, you need to somehow build that critical mass and context shift to where you can get by on the general level.<p><i>My advice is to take the math you do know and go read the proofs that make it operate.</i> Use the applications you already are comfortable with and understand the reasons why they work. Instead of diving both into generalized math and a complex new subject at once, just use your strengths.<p>My anecdote is that I liked math but never really had a grasp on it until I got thrown through the ringer on infinite series, linear algebra, abstract vector spaces all at once. I learned to read and understand proofs (sometimes), I learned how to prioritize when reading complex math (i.e. internalizing definitions is often half or more of the battle), I learned how to synthesize my own general mathematical arguments.<p>I wouldn't call myself anything close to a mathematician, but by jumping into the language and structure of generalized math, I have a lot of the tools to get somewhere with whatever field I want. Wikipedia still often confuses me, but if I want to learn it I know how to take what I learn and use it as the building blocks to a deeper understanding.