√7 is missing – and it took 2000 years to find the real reason why

Double cube hides every square root from √1 to √6, but √7 is nowhere to be found. Why? The answer isn't in the geometry of this solid, but in the algebra. It all boils down to a number theory question that took over 2000 years and the work of many great mathematicians like Euler, Lagrange, Legendre and Gauss to answer. This is the origin story of additive number theory, starting from the Pythagoreans' polygonal numbers, through 18th century world-class brainstorm, to the final piece of Fermat's [redacted]. This topic is close to my heart since I'be been working on it for rougly 3 years now. So... enjoy! This video is a submission for #SoME5. [∞] Big thanks to: · my fiancee (!) for helping me on the design of the whole video and for the constant mental support that was VERY MUCH needed in the last days of SoME5 submissions. Love u ❤️ · Grant Sanderson from 3blue1brown channel, James Schloss and the whole SoME team for organizing the event · prof. Maciej Ulas, my future PhD supervisor, who introduced me to the topic · you for watching it and making me a happy person ❤️ [∞] References and sources · History of the Theory of Numbers, L. E. Dickson · Arithmetica, Diophantos · The Eureka theorem of Gauss, Stan Dolan · Legendre's three-square theorem, Wikipedia · Fermat polygonal number theorem, Wikipedia [∞] Music (all downloaded from the freemusicarchive) · Kevin MacLeod - Faster Does It · Mela - Horrible · Mela - Brainpower · Mela - The Strip · Chris Zabriskie – Readers! Do You Read · Kevin MacLeod – Backed Vibes Clean · Jesse Spillane – Gorgon · Kevin MacLeod – Impact Prelude · Á Minuit, le 31 Décembre – Monroeville Music Center · Quantum Jazz – Jingle Jazz [∞] Check out other places that you can go to and learn some math (or look at my face, take your pick) · INSTAGRAM - instagram.com/mathinity · X - https://x.com/Mathinity_ [∞] Chapters: 00:00 - Introduction 01:43 - 1. What's up with √7? 05:30 - 2. Ancient polygons 07:59 - 3. Diophantos for the help 13:07 - 4. Fermat and his damn margins 16:39 - 5. GOATs meetup 19:08 - 6. EYPHKA 24:13 - The end (?) [∞] Pictures come from Envato Elements, Wikipedia and following sources: ·   / pythagoras-pythagoras-the-greek-philosophe...   · https://www.britannica.com/biography/... ·    • Beauty in Simplicity