For many people, it's a fine thing to learn mathematics by doing proofs. But that's not the only way. At the college level you sometimes find a division betwee

For many people, it's a fine thing to learn mathematics by doing proofs. But that's not the only way. At the college level you sometimes find a division between "Pure Mathematics" courses and "Applied Mathematics" courses. Doing proofs is the name of the game in pure math classes. In applied math, while proofs are used as needed, the emphasis is on gaining intuition about how math works when it relates to the physical world. I found that approach more satisfying and rewarding. Proofs are neither the only way nor necessarily the best way for everyone to "grasp the underlying principles." There can be great beauty in proofs - I'm not knocking them - but their are other routes to advancing your mathematics knowledge that still avoid the trap of rote memorization.