This question is about efficiency of studying habits in math.
Clearly, rote learning everything without trying to develop an understanding of concepts in a math education is a bad idea, and this doesn't need an explanation.
On the other hand, rejecting rote learning completely is obviously highly inefficient, since there are things that cannot be understood, but merely memorized (e.g. the fact that $\partial$ is the symbol for partial derivatives).
My question is about what the optimal role is for rote memorization in math. What are best practices that are generally accepted regarding rote memorization for optimal learning speed in math?
Should you rote memorize definitions before trying to understand more intricate aspects of their meaning? Or should you study examples and theorems so that you will eventually remember the definition "naturally" by understanding the deeper meaning?
Should you memorize key theorems as facts without understanding why they're true, and try to get an overview of the theory first before studying the deeper nature why they're true? Or should you ruthlessly try to understand the proof of every important theorem, and not give up until you've understood it so well that you no longer need to rote-memorize it because you can just "see it"?