A lot of smart people have a rule not to memorize anything that they can derive on the spot. That’s a good rule, up to a point. But past that point it becomes a liability.
Most students err on the side of memorizing too much. For example, it’s common for students to memorize three versions of Ohms law:
- V = IR
- I = V/R
- R = V/I.
Not only is this wasteful, tripling the number of facts to remember, it’s also error prone. When you memorize things without understanding them, you have no way to detect mistakes. Someone memorizing the list above might think “Is I = V/R or R/V?” but someone who knows what the terms mean will know that more resistance means less current, so the latter cannot be right.
I got through my first probability class in college without memorizing anything. I worked every problem from first principles, and that was OK. But later on I realized that even though I could derive things from scratch every time I needed them, doing so was slowing me down and keeping me from seeing larger patterns.
The probability example stands out in my mind because it was a conscious decision. I must have implicitly decided to remember things in other classes, but it wasn’t such a deliberate choice.
I’d say “Don’t memorize, derive” is a good rule of thumb. But once you start to say to yourself “Here we go again. I know I can derive this. I’ve done it a dozen times.” then maybe it’s time to memorize the result. To put it another way, don’t memorize to avoid understanding. Memorize after thoroughly understanding.
Related post: Just-in-case versus just-in-time