For me personally (and I’ve heard other math people share this sentiment) the only way to understand a new area is to largely build it up in my own way, using the literature as a guide. Then depth is improved each time it connects to something else I’ve built up an understanding of. Otherwise depth decays overtime (but is easier to rebuild if I wrote my own notes).
I also agree with the idea that deeply understanding something is not merely a consequence of being able to derive it. Sometimes derivations (especially with too much algebra or via induction/contradiction) feel incomplete. Sometimes seeing two derivations of the same thing make it all fit together.
This general phenomenon is something I’d like to understand better as well.
For me personally (and I’ve heard other math people share this sentiment) the only way to understand a new area is to largely build it up in my own way, using the literature as a guide. Then depth is improved each time it connects to something else I’ve built up an understanding of. Otherwise depth decays overtime (but is easier to rebuild if I wrote my own notes).
I also agree with the idea that deeply understanding something is not merely a consequence of being able to derive it. Sometimes derivations (especially with too much algebra or via induction/contradiction) feel incomplete. Sometimes seeing two derivations of the same thing make it all fit together.
This general phenomenon is something I’d like to understand better as well.