3Blue1Brown

8,510,000 subscribers

⏱ 👁 3,708,356 views

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

Video Overview & Insights

An introduction to group theory (Minor error corrections below)

“

"What could be more universal than symmetry?" Asymmetry.

— @dabajabaza111

Help fund future projects: https://www.patreon.com/3blue1brown

An equally valuable form of support is to simply share some of the videos.

“

Bla bla bla. I hate group theory. Or the course structure is made such that it seems boring

— @specialrelativity8222

Special thanks to these supporters: https://3b1b.co/monster-thanks

Timestamps:

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In Quintic functions why can't we just use ln(x^Y) to have each x in the same base of lnx?

— @ogradus

0:00 - The size of the monster

0:50 - What is a group?

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3837532 is the only coprime number with both factors being Weiferich primes. It could thus be used to communicate a 1093x3511 grid image to an alien race in the same manner as in the Arecibo Message.

— @ExtantChivalry

7:06 - What is an abstract group?

13:27 - Classifying groups

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Probably 100000000000

— @NikolaiSmith-n5n

18:31 - About the monster

Errors:

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I've been working with D_{\infty h} for my master thesis and it was glorious

— @SalmonPenny

*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.

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MAX SAFE INTEGER WHY BECAUSE IF YOU INCREASET HAT BY 1 IT SONT BE PRESICE VALUE IS 2^53 - `

— @SaravananRamamoorthy-o4f

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:

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Happy Family😂

— @ShivamTripathi-q8d

http://www.ams.org/notices/200209/what-is.pdf

If you want to learn more about group theory, check out the expository papers here:

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7:38 red 6 standing by

— @robertstevensii4018

https://kconrad.math.uconn.edu/blurbs/

Videos with John Conway talking about the Monster:

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Great video. It helps understand QFT

— @beauchum

https://youtu.be/jsSeoGpiWsw

https://youtu.be/lbN8EMcOH5o

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This is my favorite math video for years.

— @joschkazimdars

More User Perspectives

someone remind me to come back here in like 3 years when im studying this shit in my cs+maths BSc, thanks

@lemonamon

my favorite number over 1 million is 1048576

@aidandarmawan2750

"read from right to left" why? we do almost all operations left to right. sometimes math is just stupid like how sin^-1(x) is not (sin(x))^-1 it should only be called arcsin.

@J05IAH

1:44 EINHEIT

@a2sprobrother140

wrong false and a lie.... but you walk with.... have a nice dinner

@alijamali-u3z

dawg the background music is heavenly. reminds me of both Mass Effect and Skyrim at the same time

@Robotomy101

You should revisit this and make a 10-hour video (or a 20-part series). I didn't understand anything about this video but after 5 years now I've heard about C2 C3 A5 M11 and the Monster and has better appreciation. But I'm still struggling to understand why the quintic is insoluble because A5 cannot be broken down to cyclic groups. And how it is known that all the simple groups have been known?

@takbolehsebut

Oh😮😮😮

@pastli

I'm taking a different approach to group theory. I'm associating it with relatable social aspects as analogies because the example of traditional math really doesn't make sense even when it's partnered with beautiful visualizations like this. You too objective with it the math is already the math so it's not illegal to associate an analogy that is non-mathematical isn't that the whole point of the symmetric invariance?

@poetlemar.369

can we map out the possibilities of 3 objects to move in 4 d space. or do we need 5 D space to see the 3d possibilites as we see now :D

@nippon_banzai_oe

stopped at 1:52 to comment --> "The do nothing (state)" the 0, In my eyes the are the point that defines our limits and there are many other do nothing states that differ the range of possibilites :D

@nippon_banzai_oe

Bruh I just wanted to know what the meme was about

@Valin9275

@MarcusAurelius-d6t5j

I've done all my calculus classes, watched from start to end, and I still have no idea WHAT "the monster" actually is. A group with a lot of numbers? A group of numbers that start after a very large number, that is is closed under multiplication over a certain matrix multiplication? What is it?
There's so much theory in between it just all gets lost in the sauce. He just talked a whole lot about random things, and then at the end mentioned the Monster, and I've no idea when he even started describing it.

@TrojenMonkey

I'm starting to understand why so many famous mathematicians and physicists ended up believing in God.

@dellortteg6875

my favorate number over million would be 6060711605323

@Azmoth64

Mappings, transformations, functions, symmetry actions .... pretty much all the same notion.

@dwinsemius

Omega 1^omega^omega^omega^omega^omega^omega^omega^omega^omega^omega… omega 1 times then power set it then you get my favorite number over one million.

You are probably thinking “HOW LONG IS THIS GONNA TAKE!” The answer is you almost there😊

Also it comes after infinity

@RYANCHEN-s9o

Outstanding presentation of the basic meaning of group theory with some visualization that helps to understand. I'd like you could do the same for rings and fields. And for another hard subject that would fit so much this style of explanation: tensors.

@marcoe6704

i know all about monster thoery. Just ask the women.

@ddd8639

7:14

@Osean_Man

This might be the best video from 3blue1brown

@MathematischeAnalyse

6:42 THOSE ARE THE UNCERTAINTY PRINCIPLES WAAAT

@AdamGuinen

7:22 no, that's stupid

@vecvan