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I've never regarded memorization highly. Whenever we had to learn the times tables or the squares at school, I would just work them out in my head instead of memorizing them. Of course, I still ended up learning the squares and the times tables by heart, but not because I actively memorized them, but because I just used them so much that I couldn't help but remember them eventually. I'm of the opinion that this leads to a good rule of thumb: never memorize anything - if you use the thing often enough, you can't help but memorize it anyway. Of course, you could argue that how often you use something isn't necessarily equivalent to how much utility you might get out of memorizing said thing, and I don't disagree with that. All that being said, I do agree with the article's premise that an expansive knowledge base aids reasoning, which does seem to be in conflict with my principle. I definitely do possess a basic knowledge of geography, and it does definitely aid my reasoning, but I don't ever remember actively memorizing that - not at school, nor elsewhere. |
After having studied maths and physics at university and worked as a programmer in a mathematical field for 20 years (and studied much more maths in my spare time), I now see my poor recall as the limiting factor in my abilities in maths. The main reason I don't think I could ever have been a professional mathematician is that I would have reached (and have reached in my own learning as an amateur) a ceiling.
I have maths books that are beloved to me, that I have read multiple times (actively, working with pen and paper as one should) and which I will enjoy again in future. But the concepts in those books do not remain in my mind. I don't reach a point where the structure of basic linear algebra, say, is baked in.
I am good at the problem solving, but maths is an edifice, one people have been building onto for millenia. I explore that edifice, and keep returning to my favourite bits of it, but the portion of that structure that is resident in my mind is, and I think always will be, small. It's a window, and as more comes into it, more slides out. Everybody must have such a window, but I know others have much larger windows than me. And that's fine - I'm a programmer, not a mathematician. But I think it's something I would have benefitted from understanding earlier in my life. Perhaps I would have set about "learning to learn" differently. Rote memorisation and active curation of memories already formed could have benefitted me greatly.