Why Was This Visual Proof Missed for 400 Years? - Fermat's Two Square Theorem

Explore a groundbreaking visual proof of Fermat's two square theorem in this 34-minute video. Delve into the history of this 400-year-old mathematical problem and discover why an odd prime can be written as the sum of two integer squares if and only if it is of the form 4k+1. Learn about Zagier's famous one-sentence proof and its visual interpretation using the innovative "windmill trick." Examine the uniqueness of representing 4k+1 primes as the sum of two squares of positive integers. Follow along with detailed explanations, historical context, and mathematical insights as the video unravels this complex theorem through simple, visual methods.

Intro.
Chapter 1: Discovering a theorem.
Chapter 2: 400 years worth of proofs.
Chapter 3: Zagier's one-sentence proof.
Chapter 4: The windmill trick.
Chapter 5: Windmill maths interlude.
Chapter 6: Uniqueness !!.
Credits.
. Later on I also present a proof that there is only one way to write 4k+1 primes as the sum of two squares of positive integers. .