You're looking at Less Wrong's discussion board. This includes all posts, including those that haven't been promoted to the front page yet. For more information, see About Less Wrong.

Vladimir_M comments on Discuss: How to learn math? - Less Wrong Discussion

12 [deleted] 09 October 2010 06:07PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (28)

You are viewing a single comment's thread. Show more comments above.

Comment author: Vladimir_M 09 October 2010 08:13:00PM *  8 points [-]

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).

Comment author: stoat 09 October 2010 08:32:48PM 2 points [-]

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?

Comment author: Vladimir_M 10 October 2010 06:48:52AM 3 points [-]

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.