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

2020-08-19

[public] 1.64M views, 115K likes, 737 dislikes audio only

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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:

/youtube/video/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: mulstato

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These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.

Download the music on Bandcamp:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

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If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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