In this video, we explore the history of number systems that were invented in order to solve the Fermat’s Last Theorem, and we will see how concepts that were invented to tackle the problem such as rings and ideals gave rise to other number systems.
Links:
3Blue1Brown’s Video on Pythagorean Triples:
https://youtu.be/QJYmyhnaaek?si=qxhAY35hYYcSkHcu
Chapters:
00:00 Intro
03:08 Number Theory
08:08 Classifying Number Systems
10:05 Adjoining to a Ring
12:35 Number Systems Invented to Solve FLT
18:15 Kummer's Ideal Numbers
20:03 Dedekind's Ideals
23:13 Modular Arithmetic and Quotient Ring
25:16 2-Dimensional Numbers
31:45 Higher Dimensional Numbers
37:30 Outro
Music🎵:
Forest of the Elves – Jonathan Segev https://youtu.be/9XJQXz6RXos?si=D1lCT4St_MWv0KsZ
Midnight Tale - Kevin MacLeod https://youtu.be/VNctLX9oOJc?si=voCYkQy-dhLa5-N5
Arab Egypt Music – ALD https://www.youtube.com/watch?v=08IgwEu3UUs
Summoner's Rift (Late Game) - Riot Games https://youtu.be/FrSE_vpOk8s?si=rW_uxaSTLyjIFmo7
Confusion in my mind - BGM President https://youtu.be/wKpsOt1D5eU?si=8jCeaoghXRQAUOpM
Corrections:
36:09 Planar-quaternions, not dual-quaternions
36:17 M_2(R) is isomorphic to the split-quaternions