Number Systems Invented to Solve the Hardest Problem - History of Rings | Ring Theory E0

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