I'm going to do the unthinkable: start memorizing mathematical results instead of deriving them.

Okay, unthinkable is hyperbole. But I've noticed a tendency within myself to regard rote memorization of things to be unbecoming of a student of mathematics and physics. An example: I was recently going through a set of practice problems for a university entrance exam, and calculators were forbidden. One of the questions required a lot of trig, and half the time I spent solving the problem was just me trying to remember or re-derive simple things like the arcsin of 0.5 and so on. I knew how to do it, but since I only have a limited amount of working memory, actually doing it was very inefficient because it led to a lot of backtracking and fumbling. In the same sense, I know how to derive all of my multiplication tables, but doing it every time I need to multiply two numbers together is obviously wrong. I don't know how widespread this is, but at least in my school, memorization was something that was left to the lower-status, less able people who couldn't grasp why certain results were true. I had gone along with this idea without thinking about it critically.

So these are the things I'm going to add to my anki decks, with the obligatory rule that I'm only allowed to memorize results if I could theoretically re-derive them (or if the know-how needed to derive them is far beyond my current ability). These will include common trig results, derivatives and integrals of all basic functions, most physical formulae relating heat, motion, pressure and so on. I predict that the reduction in mental effort required on basic operations will rapidly compound to allow for much greater fluency with harder problems, though I can't think of a way to measure this. Also, recommendations for other things to memorize are welcome.

Also, relevant