In math classes, generally we were given a bunch of very silly, trivial problems and made to solve the same exact thing fifty times (what's the root of (x^2)+3? Now what's the root of 3(x^2)+4? And on and on and on). Math is taught by 'memorize this stuff and stick it here and watch your signs'.

Historically, I've done well in these sorts of classes but sometimes I can't help but feel that there's a whole side of math that I'm missing. I know methodology and memorizing are important but it's taught to the exclusion of anything else. It's like being stuck in a gray room but there's a peephole in the wall that shows something more more exciting and creative than memorizing example problems. This simply can't be all there is to math. I talked to my adviser and his only advice was 'wait until you get to the proofs class, it gets a lot more 'fun' then'. The textbook isn't any help either, since it has the same tired problems and definitions.

My question, if I'm making any sense at all, is how can I get to this other side of math? I enjoy finding things out seeing patterns (that's why I'm majoring in physics) but I want to do the same in math. I know it's possible, but I just don't know how to get there. Any advice would be vastly appreciated and sorry for all the questions. Thank you.