[mbrock]

I think this is a fundamental problem of learning and teaching, especially via text.

It's also that most people who teach just don't have Feynman levels of understanding. Mostly we are all kind of groping in the dark, and we all participate in some kind of cargo cult.

I also think there's a deep problem with how people want to learn math, and other abstract concepts. Look at how frustrated many students get by notions like imaginary numbers, groups, and monads. These things provoke some serious anxiety and confusion because students want to understand what they "really are" in some clear and straightforward way, when really all they are is hard-won abstract definitions that have proven interesting or somehow useful.

In a way it's disappointing that math books need to have "exercises." Why can't they just explain in a comprehensible way? I guess it's because the topics of study are abstract relations that only sometimes have some analogy in the "real world" (of course, some mathematicians believe that the structures of mathematics are in some sense the most real of all)...