As a math PhD student I concur. I got through most of my undergrad memorizing nothing. It was easy back then. The definitions were simple and intuitive. what's a group? I hold an intuitive picture in my head which can be translated into words if I want. What's the Taylor series of cosine? If you want to do serious work in applied math you'd better have that on the back of your hand. You can derive it every time of course. You'll just take WAY longer. What is are the homology groups of a group with integer coefficients? Ha. Good luck doing anything with it if you haven't memorized it. Not memorizing might work in undergrad. I've reluctantly come to the conclusion that it doesn't work anymore. In fact not memorizing anything is biting me in the ass. It seriously hampers my workflow to have to look up the definition of Calc iii stuff. If you don't have some things mmeorized you won't even understand lectures. They don't take the time to let you get used to a definition in grad school. They give it to you and just RUN with it. They expect that out of you. They don't remind you. They expect that they can just give you the definition and start using it to prove theorems right away. Most of the time they don't give you the intuition for it either. No examples. You need to get used to the language of math and do it fast.