As I try to learn differential geometry, one question I had was why differential forms are fundamental to integration. The word “differential” is an overloaded term, and its use in “differential forms” was confusing me. But thanks to this writeup from Terry Tao (https://www.math.ucla.edu/~tao/preprints/forms.pdf), I think I finally understand. I think the central idea is:
A one-dimensional signed definite integral is a map from a path to a real number.
See here for a detailed post:
https://freeenergy.blog/2022/DiffForms.html
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@Sunfishstanford the trick to understanding so much of math seems to be finding the right explanation!
@elfprince13 what’s great is that there are so many great online resources now, usually just a matter of persistence until you find the right one.