[Tainnor]

I think this is only half true. Of course, if you want to be good at maths, you will have to remember things because you can't always look up or re-derive every smallest detail (and because you have to become good at pattern-matching at some point). But the memory tends to work best if it's activated by deliberate practice. For example, instead of memorising a proof line-by-line it's much better to try to remember the key points and then practicing filling in the gaps. If necessary, repeat this process several times. When I was studying for ODEs, I tried to re-derive many of the standard techniques by trying to remember which trick to apply instead of trying to memorise the formula.

[KMag]

^ This. For my Mechanical Engineering undergraduate courses, almost all of the formulas (models, actually) could be re-derived from linear approximations on infinitesimal elements. Memorize and internalize how the model is derived, practice re-deriving the model, and you can re-derive the formula during the exam, and do a bit of hand-wavy intuitive double-check of your answers. If you've only memorized the formula, you're going to have a very tough time coming up with an estimate against which to check your formula's answer.

On a side note, I really wish we had more emphasis on the conditions under which the linear approximations broke down. I remember sitting at the front of the MIT 2.002 class, and there was a demonstration of metal fatigue using a hydraulic press at the back of the classroom. Professor Sanjay Sarma stepped up to the front row in order to better see the demonstration at the back, and so I asked him about my intuitions about which way the model diverged from reality under vibration frequencies high enough that the quasistatic assumptions built into the model broke down. He looked to both sides of us and told the students on either side of me not to listen because they might get confused, and then we had a little discussion about conditions beyond which the model applied and which way the model's error went under those conditions. It was simultaneously one of the best and most disappointing moments in my education. It was an exciting discussion, but I was sad that the world beyond the linear approximations was considered to be likely too deep a rabbit hole for most of the class. Sanjay (as he preferred to be addressed) was an excellent educator, and I'm sure his judgement was based on past experience... each semester has a given complexity budget, and the field of Mechanical Engineering is so broad (statics, dynamics, thermodynamics, fluid dynamics, mechanisms, control theory/sensors/OpAmps, manufacturing techniques, design for mass manufacturing, numerical process control, destructive/non-destructive testing, etc., etc.) that undergraduates need to spread a limited complexity budget across so many subjects that they can each only be covered relatively shallowly.