TITLE: What are examples of mathematicians who don't take many notes?
QUESTION [13 upvotes]: I see people like Terry Tao and others take extensive notes. But is this really necessary? When I do this I feel like I am rewriting a textbook.

REPLY [34 votes]: About notes and rewriting: if the topic is important and non-trivial, it is all too easy to delude oneself, optimistically, into believing that one grasps all the points... if one is at all passive. To avoid this (as well as to have a perhaps more convenient personal archive), I think there is no substitute for an intensely (self-) critical rewrite.
Yes, this is "expensive" in time and effort, so should NOT be allocated to trivial matters, to "exercises", or to things one doesn't care much about.
Personally, if I've not rewritten something, I don't feel I understand it, except perhaps distantly, passively, as with gossip or hearsay. By the end, the ideal is to perceive the thing that cost effort as being, in fact, as trivial as possible, once one has adjusted one's viewpoint. It is important to remind oneself that this is not an indicator of wasted time or of foolishness, but of success in rewriting/rethinking. Then the significance of things that don't quite become trivial is vastly clearer.