math - memorization or understanding

Or, is math just for aspergers cases. I mean, when I did intro algebra it seemed like completing the square, long dividing polynomials, etc. were all just mindless memorization. I'm taking more math above this intro stuff, just to see if it gets any more interesting.

Speaking of math being interesting, does anyone have a branch of mathematics they find particularly interesting? I'm a math major in my first year and am looking for reading material.