TITLE: Does advanced math "power" more rudimentary math?
QUESTION [46 upvotes]: I came across this quote by Eric Weinstein that "when things got supposedly more advanced, they actually got simpler because mathematicians started revealing what was powering all the things that you previously learn." I was wondering if anyone came to the same conclusion, and if so, care to give an example of such a revelation.

REPLY [2 votes]: A yet another suggestion: Group theory.
A lot of very basic maths (like, you can switch the summands) can be generalised to group theory. The actual root of it is an (successful) attempt to marry the integers $\mathbb{Z}$ and polynomials $R[x]$.