There are already some great answers to this question. Math begins with intuition. We don't memorize facts in order to build intuition -- we explore, discover,

There are already some great answers to this question. Math begins with intuition. We don't memorize facts in order to build intuition -- we explore, discover, and synthesize. Formalism is an impediment to the early stages of this process. The most blatant example is set theory. Nearly everyone has a basic grasp of naive set theory and hardly any layperson has a basic grasp of formal set theory. Just as an aside, many of the most interesting things in mathematics are extremely counterintuitive. It also turns out that our intuition is broken and leads us to say crazy things. Again, set theory has clear examples. Back to the point, the things you memorize help to organize your untamed mathematical data. I seriously doubt that you'd have any good results from memorizing something about which you do not have intuition.