I remember when I started learning trigonometry. I learned that a side of a right triangle could be expressed with trigonometric functions and that was all I needed to know. It was amazing. As I progressed with trigonometry I realized that when I thought trig was amazing, I didn't know ANYTHING about trig (and I probably STILL don't).

When I started differentiating I thought: ''Amazing how Newton incorporated this idea into physics to explain all these phenomenons'' and now after a while I realize that I knew NOTHING compared to the vast knowledge that is calculus...

What I'm trying to get at is that mathematics make me feel stupid again and again. In return I get to feel smarter and it's a great feeling but is mathematics like this all throughout university? I'm a complete novice at maths but I intend to major in maths and I would like some input on how you come to 'understand' maths. Is it always such a mystery that surprises you infinitely?