Group theory, abstraction, and the 196,883-dimensional monster

An introduction to group theory (Minor error corrections below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/monster-thanks Timestamps: 0:00 - The size of the monster 0:50 - What is a group? 7:06 - What is an abstract group? 13:27 - Classifying groups 18:31 - About the monster Errors: *Typo on the "hard problem" at 14:11, it should be a/(b+c) + b/(a+c) + c/(a+b) = 4 *Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do comprise tens of thousands of pages, but no one paper was quite that crazy. Thanks to Richard Borcherds for his helpful comments while putting this video together. He has a wonderful hidden gem of a channel: https://youtu.be/a9k_QmZbwX8 You may also enjoy this brief article giving an overview of this monster: http://www.ams.org/notices/200209/what-is.pdf If you want to learn more about group theory, check out the expository papers here: https://kconrad.math.uconn.edu/blurbs/ Videos with John Conway talking about the Monster: https://youtu.be/jsSeoGpiWsw https://youtu.be/lbN8EMcOH5o More on Noether's Theorem: https://youtu.be/CxlHLqJ9I0A https://youtu.be/04ERSb06dOg The symmetry ambigram was designed by Punya Mishra: https://punyamishra.com/2013/05/31/symmetry-new-ambigram/ The Monster image comes from the Noun Project, via Nicky Knicky This video is part of the #MegaFavNumbers project: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo To join the gang, upload your own video on your own favorite number over 1,000,000 with the hashtag #MegaFavNumbers, and the word MegaFavNumbers in the title by September 2nd, 2020, and it'll be added to the playlist above. Thanks to these viewers for their contributions to translations German: dlatikaynen Hebrew: Omer Tuchfeld Italian: mulstat