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:
   • All possible pythagorean triples, vis...  

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 2Dimensional Numbers
31:45 Higher Dimensional Numbers
37:30 Outro

Music:
Forest of the Elves – Jonathan Segev    • Forest of the Elves | Celtic Music | ...  
Midnight Tale Kevin MacLeod    • Midnight Tale  
Arab Egypt Music – ALD    • Arab Egypt MUSIC   Free no copyright...  
Summoner's Rift (Late Game) Riot Games    • Summoner's Rift  Late Game (From Lea...  
Confusion in my mind BGM President    • [브금대통령] (방황/혼란/Emotional) Confusion i...  

Corrections:
36:09 Planarquaternions, not dualquaternions
36:17 M_2(R) is isomorphic to the splitquaternions