When I learned the group e^iθ under complex multiplication is isomorphic to the group of SO(2) matrices under matrix multiplication , it changed everything. I knew love for the first time, my wife came back, I quit fentanyl and started reading romantic fiction. U(1) - SO(2) isomorphism fixed my credit score and my relationship with my father.
I once got corrected for using the term “embarrassingly parallel” and told I should use “natively parallel”
Who was I committing a micro aggression against. Embarrassed people? The map-reducible?
Administratively, the trickle-down strategy did later bite me in the ass.
I recently had to do an intro topology course because I had skipped past it to do more advanced topology courses, but it was still a degree requirement🙃
You should look back on your embarrassing past selves with an urge to wrap them up in the most comforting hug imaginable, not with condescending resentment
The best thing I did in undergrad was taking some courses way above my level.
I took a PhD-level course in harmonic analysis in my 2nd year. It was so hard that I think my brain structure got permanently altered.
A friend of mine calls this concept trickle-down mathematics.