Pi hiding in prime regularities

This is a really beautiful proof that connects complex numbers and primes to derive a formula for calculating pi. It should only require high-school algebra prereqs. [this video] If you want to truly follow the proof, there's one little bit on the chi function in there which is connected to something called the One Sentence Proof. This looks rather esoteric and takes a bit of pondering to wrap your head around, but again only really requires high-school level algebra. Doing proofs like this is what math is really about. This is how you come to really understand. And this video also happens to be entertaining in how well-put-together it is.

3Blue1Brown has been recommended on HN before ( [link] ) But it's so great I think it bears bringing up in case anyone reading this comment has missed it. This channel animates math proofs, shows you the intuition behind fields of math, and constructs subjects in such a way as to make you feel like you could have invented them yourself. You'll still need a good textbook or something to go with the videos, but they cement the understanding in your mind very well and even open the door to more formal proofs. My favorite video is [this video] . You'll have to take an additional step to get a complete proof (hint: read and work through the One Sentence Proof), but this is a beautiful piece of mathematics, shown in an understandable manner.