It has to do with more than memory, right? At least if you want to come up with new things, whether directly in mathematics itself, or to use it creatively in some other field. The idea is that intelligence is partly indicated by how you can visualize things that cannot be seen, and often when someone cannot figure out a derivation of get at a result, it's more likely because they are not seeing the big picture.

I don't mean to say that people in general cannot be taught to see mathematics, it's just that they need good teachers and textbooks.

Edit: of course, all this comes only after having grasped the basic terminology at your fingertips.