This is good advice, to which I’d add: once you’re done studying some particular area, be sure to have a clear and systematic “bird’s eye view” of the basic definitions, lemmas, and theorems, how they depend on each other, and what the salient point of each one is. Because if you don’t use this knowledge for a few years, it’s surprising how thoroughly you can forget almost everything—and in case you ever need it again, you’ll be in a much better position if your knowledge decays into a still-coherent outline of this “bird’s eye view” than a heap of disorganized fragments.
I find it scary how thoroughly I’ve forgotten some large chunks of math that at some point I knew so well that I would have be able to reconstruct them, with proofs and everything, given just paper and pencil. Those I still remember very well after 10-15 years are either those that I drilled so intensely that it developed into an irreversible skill like bike riding, or those where I organized my knowledge into a very systematic outline (even if I never had a truly in-depth understanding of all the logic involved).
Oh, yes, definitely. But the amount of effort necessary to relearn them is much smaller if you remember something resembling a coherent outline than if your knowledge decays into incoherent fragments.
This is good advice, to which I’d add: once you’re done studying some particular area, be sure to have a clear and systematic “bird’s eye view” of the basic definitions, lemmas, and theorems, how they depend on each other, and what the salient point of each one is. Because if you don’t use this knowledge for a few years, it’s surprising how thoroughly you can forget almost everything—and in case you ever need it again, you’ll be in a much better position if your knowledge decays into a still-coherent outline of this “bird’s eye view” than a heap of disorganized fragments.
I find it scary how thoroughly I’ve forgotten some large chunks of math that at some point I knew so well that I would have be able to reconstruct them, with proofs and everything, given just paper and pencil. Those I still remember very well after 10-15 years are either those that I drilled so intensely that it developed into an irreversible skill like bike riding, or those where I organized my knowledge into a very systematic outline (even if I never had a truly in-depth understanding of all the logic involved).
I also find that scary/frustrating. But don’t you find you can relearn those forgotten chunks much more rapidly than the first time, if you need to?
Oh, yes, definitely. But the amount of effort necessary to relearn them is much smaller if you remember something resembling a coherent outline than if your knowledge decays into incoherent fragments.