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: https://youtu.be/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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