Learning math is hard. Those that have braved some of its depths, what did you discover that allowed you to go deeper?
This is a place to share insights, methods, and tips for learning mathematics effectively, as well as resources that contain this information.
My own experience is that it is fairly easy to identify points of confusion, and the hard part is finding a book or whatever, at the right level, to address that specific point. This is a tough problem to solve with self-teaching.
Interestingly, I never found this to be a problem with mathematics, although I did find it a problem many times I tried to teach myself physics. In my experience, textbook-level mathematics is almost always a perfect self-contained edifice of logic, whereas textbook-level physics often leaves unclear points that you can clarify only by asking an expert or finding another book that addresses that specific point. (I suppose things might be different if you're reading bleeding-edge math research papers.)
Out of the large number of mathematical texts I've read... (read more)