2017-05-19

[public] 1.61M views, 53.9K likes, 462 dislikes audio only

3Blue1Brown

A story of pi, primes, complex numbers, and how number theory braids them together.

Mathologer on why 4k + 1primes break down as sums of squares: /youtube/video/DjI1NICfjOk

Help fund future projects: https://www.patreon.com/3blue1brown

An equally valuable form of support is to share the videos.

Special thanks to these supporters: http://3b1b.co/leibniz-thanks

Home page: https://www.3blue1brown.com/

For those of you curious about the finer details, here's a writeup from the viewer Daniel Flores justifying the final approximation: https://www.overleaf.com/read/wdzkfjbkwzyf

The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as "Fermat's theorem on sums of two squares": https://goo.gl/EdhaN2

Music by Vince Rubinetti:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Timestamps

0:00 - Introduction

1:39 - Counting lattice points

5:47 - Gaussian integers

10:30 - The lattice point recipe

17:50 - Counting on one ring

20:14 - Exploiting prime regularity

25:19 - Combining the rings

28:36 - Branches of number theory

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

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