When I took real analysis, I didn't get an intuitive sense of limits and all that delta/epsilon stuff. It was too abstract. Strangely enough, when I read David Foster Wallace's "Everything and More" on the history of infinity it all made more sense, because he described all the paradoxes and dead ends that mathematicians had run into before Cauchy and others brought rigor to the problem. Wallace was a postmodern novelist. I don't know why he described infinity so clearly; I didn't enjoy his other work.
The maths appendices in Infinite Jest are about half the book. There's a section written by Hal's friend (?), proving something like the intermediate value theorem where he says something like: we'll use epsilon delta because it's mad fun to say.
Interesting... This ε-δ stuff is needed when you talk about functions, but when you start instead with the limits of numeric sequences, which are easy to grasp, the function limits come easy as well, because of the analogy between the ways these are defined.
It’s not so much that I didn’t understand the principles behind continuity. It’s just that the way my teachers presented the material lacked historical context.
After a BSc in pure math I discovered that I enjoyed applied math and CS much more, which told me that I need concrete examples to understand a theory: if you tell me about abstractions like groups and rings, which took years to establish, I lose interest. Tell me that groups express properties of matrix multiplications, or permutations, or modular arithmetic, and I’ll get it right away.
It’s the way my mind works, but I’m sure I’m not alone, and mathematical pedagogy would benefit from historical context.
