I meant basic memorization, not any advanced stuff. If you have to re-derive everything basic from scratch again and again, you will be less effective at advanced stuff.

This is not to say the basic stuff should just be memorized. Rather, it should first be understood and only then be memorized.

And definitions must be memorized, otherwise you're screwed. For instance, try proving something is a group if you forgot the definition of a group. Yes, the definitions have reason for being the way they are (which you will likely learn) but definitions just cannot be derived from your mind during an exam.

In OP's example with memorizing multiplication tables instead of doing them on-the-fly: This is a core skill required for so much later on. You don't want to waste time and energy thinking about how e.g. 7•8 = 7•2•4 = 14•4 = 14•2•2 = 28•2 = 56 because that's a quick way to lose focus. Especially if you – like me btw – have to invert a 7x7 matrix with two variables x,y put in a bunch of positions (and linear combinations of them) in an exam.

Edit: substitute unescaped *s with •