Rote memorization might help you with exams and book problems, but it won't help you develop long-term mathematical problem-solving skills. If you can't explain it from first principles, you don't truly understand it.
I'm saying that you still need memory to justify whatever domain your knowledge is in, and that memory seems to be the bedrock of further knowledge (understanding, creativity, problem solving etc.).
Am I missing something here? Do you not need some element of memory to explain things from first principles, and to have an understanding of something?
edit: I've just realized from reading wtallis' comment that I might be confusing two different forms of knowledge: memory and reasoning, insofar as reasoning can produce further truths. Is that what you are getting at?
PS: It's a common thing for most calculus classes to redirive old formulas. Not because they stoped working, but rather because you really should understand why it's 4/3 pi * r^3.
As an example, I had a maths professor who derived the formula for solving a quadratic equation in class (in 30 seconds or so) because he did not remember it.