"One thing I'd really like to know before I die is why the monster group exists" RIP John Conway

@matteovergani3474

4 жыл бұрын

This was the first thing that came to my mind as soon as I knew about his faith. RIP

@glmathgrant

4 жыл бұрын

@@matteovergani3474 What faith? Wikipedia says he was an atheist.

@L0wLevel01

4 жыл бұрын

@@glmathgrant he means fate I guess

@dougr.2398

4 жыл бұрын

Grant Fikes he believed in the usefulness of mathematical research. All people have to believe in something to give meaning to their lives. Whether ones mission in life is determined by a higher power is beyond debate. Either one chooses to believe that or not, and whether or not that makes any difference..... one might have to ask Augustin Cauchy, a firm Catholic, or Ramanujan who actually said his mathematics was a gift from a goddess

@lyrimetacurl0

3 жыл бұрын

Did he die?

Conway is an interesting guy. He comes across as an old and wise mathematician who has seen terrifying things that he can't quite explain to regular people

@TheMultiRaphael

2 жыл бұрын

what terrifying things? i like terrifying things in math

@unhingedegoist

2 жыл бұрын

@@TheMultiRaphael studying math is terrifying by definition (source: i have three people with PhD in mathematicics and like four engineers in my family and i might go for a minor in math myself, majoring in political science)

@kruksog

2 жыл бұрын

It is super frustrating to find something in math that blows your mind, or just feels super profound, and you want to explain it to someone... and then you start thinking about all the stuff you'd need to explain to even begin to talk about the profound thing, and then you consider the average attention span of your friends and . . . And you start to feel alone.

@spencer1980

2 жыл бұрын

Ketamine helps with the abyss

@timothyscheneman1689

2 жыл бұрын

Boy this is a fun reply chain

12:12 I love the transition from "okay, so it's very very complicated" to Conway just "It's like Christmas tree ornaments"

"It's very difficult to explain." "I like to think of them as Christmas tree ornaments."

@Port8ble

8 жыл бұрын

Then you realize he is referencing a 26 dimension tree ornament.

@nmarbletoe8210

7 жыл бұрын

and a 196,883 dimensional ornament :)

@fofolp1213

7 жыл бұрын

or a grahams number dimensional ornament :0

@AlchemistOfNirnroot

5 жыл бұрын

That's nothing compared to my boi infinite dimensions : D

@elviramadigan5296

5 жыл бұрын

most people like jewelery

Very cool and very well explained. "In mathematics you never understand anything, you just get used to things."

@l.3ok

3 жыл бұрын

@Electro_blob even in a low level, like addition and multiplication, if you think about it.

@Chubbywubbysandwich

3 жыл бұрын

- John von Neumann

@MABfan11

3 жыл бұрын

@@l.3ok if you think about it, multiplication is the first time you experience fast-growing numbers

@glyph241

3 жыл бұрын

Unfortunately Too Late To Help Me Pass Calculus 2 At GeorgiaTech 20 Years Ago... 🤣🥊❣️

3 жыл бұрын

@@glyph241 lol I just saw a georgia tech student's speaking presentation rn

from a 2-dimensional equilateral triangle to 196883-dimensional monster. Boy, that escalated quickly.

@kailomonkey

4 жыл бұрын

Yea they didn't exactly expand slowly enough to follow from start to conclusion!

@kailomonkey

4 жыл бұрын

I would like to at least have seen the first of the 26 if it were any simpler

@user-rv9vk8by5i

4 жыл бұрын

@@kailomonkey Welp you replied to a 5 year old comment so I'll go ahead and reply to a 7 month old reply. 13:33 A group of that size is still massive and wouldn't simplify the explanation at all.

@kailomonkey

4 жыл бұрын

@@user-rv9vk8by5i It's never too late to comment :)

@lyrimetacurl0

3 жыл бұрын

@@kailomonkey The M11 group is the smallest and only one anyone has attempted to do a visual representation of to my knowledge but still looks like a big freaky mess.

I once went to Princeton and was thinking about moving there... hoping for a friendly sign that I should be there... There was John standing on the corner scratching his head staring at pigeons... To this day it is one of my most vivid memories.

@PC_Simo

Жыл бұрын

I take it that convinced you to move there?

@omp199

3 ай бұрын

@@PC_Simo It convinced him to dedicate his life to staring at pigeons, in order to complete Conway's work in that field. Until he has completed this work, he will be unable to reply to your comment.

@PC_Simo

3 ай бұрын

@@omp199 Apparently so 😅.

I. Freaking. Love. This channel... Imagine the world, where Divinci or Newton could sit and have a conversation about their intellectual interests and the world could listen in. Numberphile came late but it found the party for sure

I wish I had this man's talent for drawing straight lines.

@XmarkedSpot

10 жыл бұрын

The trick is to imagine the line first, put the pen on the starting point and then follow the imagined line (fixating the endpoint) _without hesitation_; i.e. not stopping the pace or lifting the pen. It works for me, but then again im left-handed, so it might not be the same.

@supertrampolinethebatpony3841

5 жыл бұрын

Hi Present Perfect!

@Guust_Flater

4 жыл бұрын

Would not waste this to my 1 wish......

@GeneralKenobi69420

2 жыл бұрын

Furry

@TakeWalker

2 жыл бұрын

​@@GeneralKenobi69420 duh

"This is quite a difficult thing to explain..." - "I think of them as christmas tree ornaments." :D

Rest in Peace, John. Thank you for sharing your beautiful ideas with us. "We do care" :)

What Conway said was interesting here, "It's absolutely amazing. Incredible! ..It's the fact that the theorem is true - apparently, and we don't know why it's true." In science, scientists often have models or theories that they can't totally understand. But that's the fault of the theory not the scientists. But in math, the theorem IS the explanation, it is the perfect description. So for him to say that we don't understand even after we've gotten the theorem. That really is peculiar

@tpat90

3 жыл бұрын

No. The proof / theorem can conclude via proof by contradiction. Most of the time such a proof doesn't give you a why, just that it has to be true.

@doodelay

3 жыл бұрын

@@tpat90 Ah I hadn't considered that.

@alexandertownsend3291

2 жыл бұрын

Math and science have different epistemologies.

@zualapips1638

2 жыл бұрын

@@tpat90 I always found proofs by contradiction, to be particularly spooky. They tell you something about reality that can't be true, but that's it. It gives you almost nothing else, so you're still left not knowing why it can't be true or why it's true. You just know that it has to be.

@perfectoid8376

Жыл бұрын

@@zualapips1638 At the basic and fundamental level, saying something is not as it appears to be in a particular world is just as informative as saying the opposite. I don't know, but if you actually spend time breaking down the contradicting statement you've acquired from your proof down to its axiomatic state, then you know just as much were you to work backward from the opposite of your final destination as you traced from your contradicting statement.

RIP John. I hope people will follow in your footsteps of genius and continue your interesting work!

@yvesnyfelerph.d.8297

4 жыл бұрын

...what?

@Spiraljunky

4 жыл бұрын

@@yvesnyfelerph.d.8297 He died a couple weeks ago to COVID-19

Dr. Conway is a really interesting man

@unvergebeneid

10 жыл бұрын

Too bad that he made it quite clear that this interest is not mutual ;)

@Shnugs

4 жыл бұрын

Dan Hunt was* :(

@dougr.2398

4 жыл бұрын

As if 4-11-2020, past tense on that remark

@ManticoreRO

4 жыл бұрын

RIP Dr. Conway.

@GalexiDude

4 жыл бұрын

he was RIP Conway

I found amazing, how two different conversations were merged together, and it kinda completed each other.

@andrerenault

2 жыл бұрын

Numberphile hasn't done so many of these lately, but it's a fascinating style.

This is the greatest introduction to group theory I've ever heard! Well done!

@livintolearn7053

5 жыл бұрын

You know...there's a youtube channel called 3Blue1Brown. Go check it out, you'll see what I mean. But really, this IS an AMAZING introduction. All I'm saying is that calling it THE best introduction might not be correct.

@fahrenheit2101

2 жыл бұрын

@@livintolearn7053 He said it's the best he's heard. You can't exactly tell him he's wrong there, even if you think there's something better out there. Even if he had seen 3b1b's group theory vid, that wouldn't invalidate his opinion. So he is well within his right to say that. That being said, I do agree personally that 3b1b's explanation is absolutely brilliant.

as soon as I heard of his death, I thought of this video. I hope he managed to undserstand the monster group.

@sergeant5848

4 жыл бұрын

We will never know.... :-(

@Joghurt2499

4 жыл бұрын

I like to believe he just found a way to the 200.000th dimension to hang out with those monsters and he just went on to solve more problems with them :') RIP

@myriadsfeynman9096

4 жыл бұрын

@@Joghurt2499 What a magnificent thing you said!

RIP John Conway

Pete's very cool Monster Group painting is full of little gems and the original is available at: bit.ly/brownpapers

"First of all, it has the, do nothing element" *cue triangle doing nothing*

@peterhunt1968

4 жыл бұрын

Jackson Kehoe the do nothing is called the identity. It’s like multiplying by 1. The identity acting on its self gives the identity.

Mr. Conway is on a different level. You can tell he's not even all there, like his mind isn't even to be bothered by such trivial conversation, just brilliant

@fleecemaster

7 жыл бұрын

His mind is slowly making its way into the 196,883rd dimension

@Henrix1998

6 жыл бұрын

Now when you said it, Conway reminds me of one scientist in Star Trek The Next Generation who had seen other dimensions. They even look very similar

@sergiogaribayluna1423

5 жыл бұрын

Watch out you are cutting air with such edge

"The one thing I'd really like to know about is why the Monster Group exists." "I'd like to understand what the Hell is going on."

I go into this video thinking, "maybe I can solve this one day'. Finish the video and I`m like 'skrew dis I`m not dealing with 200,000 dimensions'.

@leonenaj

9 жыл бұрын

Bricks Of Awesome You know you're screwed when you're rounding off the number of dimensions.

@judithkostromitin8011

7 жыл бұрын

True, I'm barely coping with three here...

@NathanTAK

6 жыл бұрын

I see your through your thin façade to your Odobenable interior, you secret walrus!

@DeathBringer769

6 жыл бұрын

If it was easy someone would have done it already, lol ;)

@bokchoiman

4 жыл бұрын

You got this man, I believe in you!

Rest in peace John Conway :(

Just want to say I love the longer, more detailed videos you guys have been doing lately. The Riemann Hypothesis, -1/12, and now this. For a layman with an interest in mathematics, these videos are deep enough to draw you in and get thinking about the concepts involved, but not so technical or esoteric as to completely scare away the non-professional. Great stuff!

RIP John Conway. I don't understand what you did for Mathematics but I love that you are so comfortable with your limitations.

John passed away but his work will continue to inspire many 💙

Rest in peace my guy a truly interesting and inspiring mathematician

Man, group theory is the coolest field of mathematics. I wish there were more uses for it in my everyday life; it was by far my favorite course in uni. So far, I've only really seen it used in database theory, but I'd love to see it elsewhere

@cameronspalding9792

2 жыл бұрын

It’s fundamental in physics

"Group Theory Legend". Very apt.

We will miss you, John

rest in peace :(

Gems, gems are truly outrageous; they are truly, truly outrageous.

Rest in peace John Conway.

@scoreunder

2 жыл бұрын

A modern genius 🌹

I'm enjoying this a lot!

@numberphile

10 жыл бұрын

very good!

Now I get what 3blue1brown was talking about in his last video

Now we're never going to find out what's going on with the Monster Group. RIP John Conway.

@Shnugs

4 жыл бұрын

KakarotSC RIP indeed, only 299 some other mathematicians mentioned in this video still working on what he was working on.

@yvesnyfelerph.d.8297

4 жыл бұрын

...nobody cares. Absolutely nobody.

@KakarotSC

4 жыл бұрын

@@yvesnyfelerph.d.8297 Sounds like someone did their PhD against their will lol. Maybe some people care.

@loneranger4282

3 жыл бұрын

Nah, that's not true. In fact, when the Atlas was published, Conway stopped with his work in Group theory while many others continued their work on it.

Welcome if looked this up after watching Grants video about his mega favourite number

@Peeves22

3 жыл бұрын

Thanks for the welcome, happy to be here :)

@fisharecute5642

3 жыл бұрын

Real chads come here from Conway’s death wish

John reminds me of the famous Nietzsche quote: "Whoever fights with monsters should beware that he does not become one. If you gaze long enough into the abyss, the abyss will gaze back into you."

I hope, that in the end, he sat down with the creator and he finally explained it to him. Rest in symmetrical peace, mister.

John Conway is the man!

Yet another intriguing video! Please make more videos with Dr. Conway, these are great!

@oskarmamrzynski

10 жыл бұрын

He finds these videos boring. :P

@numberphile

10 жыл бұрын

Oskar Mamrzynski I don't think he even watches the videos… he just finds my questions boring! :) But he was still kind enough to answer them all.

@wierdalien1

7 жыл бұрын

Numberphile thats all you can ask from a interviewee isnt?

@erik-ic3tp

4 жыл бұрын

@@numberphile, Will there be future videos with Conway in it? :)

@bokchoiman

4 жыл бұрын

@@numberphile This dude is that smart huh...

The last line John Conway said in the video is, he really want to know why monster group exists. He died in 2020 due to COVID induced pneumonia. Rest In Peace, professor.

HOW DID YOU GUYS GET JOHN FREAKING CONWAY AND NOT SHOUT IT FROM THE HEAVENS?!

You should make more videos on Group Theory or Abstract Algebra in general......you can't just excite us about something and never address it again

@user-kh5tv9rb6y

4 жыл бұрын

Group Theory is a bit too deep for the average Numberphile viewer.

@goutamboppana961

2 жыл бұрын

@@user-kh5tv9rb6y true

It won't be for a while until Numberphile will have another perfect cube number of videos... Cherish this moment.

Hey Brady, great job as usual. I really enjoy the videos you've done interviewing amazing mathematicians such as Mr. Conway. Is there a possibility that we could see more of these types of videos?

RIP John.

This one caught my by surprise. Poor guy was remembered almost entirely for The Game of Life. I hope his other contributions to maths lives on too.

@tpat90

3 жыл бұрын

His introduction title was "Group Theory Legend". He is one of the monsters of group theory.

I started watching this thinking I could use this information for my paintings. I am now a little terrified of the next part of my life.

@eulefranz944

3 жыл бұрын

How did it work out?

Came back to this video afterany years, RIP John Conway. The monster group seems frustrating to the non-initiated that I am because based on how it's explained, it doesn't make (intuitive) sense that it would stop abruptly. I got the same feeling about Heegner numbers and 163. There's the list, and there's nothing else, and it's not a matter of searching harder.

Absolute Legend. Massive inspiration for generations to come.

Really great video, and well explained.

Very clear explanation, seems like a great teacher.

So... simple group is some kind of "prime" in terms of group theory?

@admink8662

3 жыл бұрын

Yes

@henrikljungstrand2036

3 жыл бұрын

It means a group having no non-trivial quotient group (identifying certain elements into equivalence classes, respecting group multiplication), or equivalently having no non-trivial *normal* subgroup. Groups G naturally split into short exact sequences 0→N→G→Q→0 with Q a quotient group and N a normal subgroup, unless G is simple, then either one of N or Q must be G, and the other one 0 (trivial group). N is the kernel of the map to Q, and Q is the cokernel of the map from N. All normal subgroups are invariant under conjugation with any element from the larger group, while other subgroups are not. For groups, all quotients are normal but not all subs. It is different for Hopf Algebras (which have non-trivial co-multiplication and co-identity instead of merely plain copying and forgetting, but are otherwise similar to groups), and still different for monoids, where not all quotients look like quotients from a set-theoretic framework (/Z+ being a quotient of |N+ e.g.), but things become clearer from the category theoretic pov, using monomorphisms and epimorphisms, plus their normal variants. When factoring groups into quotient groups and normal subgroups, simple groups are the prime objects. They may not be when factoring into two disjoint and spanning subgroups (factoring the order of the group) say through Zappa-Szep product.

this is probably my favourite from numberphile and i've seen many

@madisonkallisti9228

6 жыл бұрын

john conway is so incredible

This is a great motivation for why groups are important.

Amazing stuff, thanks for sharing!

I really like the use of Conway's sink for composition.

Conway has serious Gandalf energy

Are we sure there are only 26 sporadic groups or is it still possible someone will find another one, the Godzilla group even bigger than the Monster?

@pifdemestre7066

8 жыл бұрын

There is a proof (of 10000+ pages) that the simple groups are exactly the non sporadic group plus this list of 26 groups, so there should be no more. This proof is in thousands of different math papers written by hundred of mathematicians. Such a long proof might have a mistake (very likely), and such mistake might "hide" a sporadic group (a little unlikely, but not impossible)

@lyrimetacurl0

5 жыл бұрын

Pretty sure there's a proof that there are no others.

@Ziplock9000

4 жыл бұрын

ML is the way forward

@treefittycents

3 жыл бұрын

@@Ziplock9000 Literally never true for problems like this.

@Ziplock9000

3 жыл бұрын

@@treefittycents LITERALLY it already has. Google for some breakthroughs in ML relating to this

Bradys editing skills are extrordinary

Nice to hear Conway speak.

Wow, the non-monster sporadic groups aren't exactly small either, are they? I was hoping that there was some toy example of a sporadic group that can be visualized but given that the smallest sporadic group already needs 10 dimensions to fully show its symmetries ... not gonna happen :/

May you rest in peace, sir!

The Monster Structure is the true shape of Azathoth.

@LucasRodmo

7 жыл бұрын

Jonathan Morgan This name is familiar, what it is?

@jreaganmorganchannel

7 жыл бұрын

***** Lovecraft

@LucasRodmo

7 жыл бұрын

Jonathan Morgan Oh yeah thanks

@alveolate

5 жыл бұрын

honestly, this number seems like it should appear in more technobabble fiction.

@erik-ic3tp

4 жыл бұрын

@@alveolate, so what's the problem then? :)

The question to the answer is: How many roads must a man walk down.

Cool, now I know what I can to decorate my next high-dimensional Christmas party with! You're all invited by the way. It's just outside Paris: you just follow the Allée des Bouleaux until you get to the Parc de Bagatelle, then you turn left, follow that street for roughly 100m and then you go straight $@#(* until you see the large tesseract. Turn $@#(* again and at the hyperroundabout just look around and you can already see my high-dimensional fractal mansion. It's easy to find, really, since you know, in higher dimension most street corners are orthogonal.

@Transblucency

2 жыл бұрын

I followed your instructions and am now in Flatland. I may be a few years late.

Is that the same thing I once heard referred to as the "Tarski Monster"? Is it the 196,883-D object? Fred

@kjl3080

3 жыл бұрын

Yea,

More Conway please! What a dude!

I didn't understood a thing about "Montser Group"… I hope it is simply because I was concentrated at eating a grapefruit while listening to this video… I think I'll re-listen to this video another day… When I'll be more concentrated.

@lyrimetacurl0

5 жыл бұрын

To that grapefruit, you are a Monster!

Very nicely explained.

@fofolp1213

7 жыл бұрын

not

I like to think that when Conway died he went somewhere he could see his 196883 dimensional Christmas tree. I hope he gets to hold it in his hand and play around with it, watch as it’s symmetric properties become clear.

love this channel

Amazing.

RIP John Conway 🙏🕊❤

More Group Theory!!! Thanks for the video, Brady.

2:34 "so how many triangles have you drawn in your life?" "all of them"

"The number of dimensions we're talking about here is 196,883, so it is a very difficult thing to picture on your mind" Yes it is.

Hopefully I'm going to Bristol for Uni next year :)

I love how "Group Theory Legend" is John Conway's formal job title. LOL!

Very helpful 🙏, thank you

A farewell to u, we love u and we thank u

...and my head hurts trying to imagine a mere four dimensional object...

@Cschesch

10 жыл бұрын

Use colours... :)

@fofolp1213

7 жыл бұрын

and lines

@cormacwatson1038

4 жыл бұрын

try smoking weed, then imagining. You'll thank me later

@zimNvgcatsfan

4 жыл бұрын

I can try to picture Infinities such as the size of our universe. Then I start contemplating the absolute nature of some infinities. For example, that there are distinct infinities such as what "does not exist" that are "outside" other infinities (like what "does exist," or our known universe). When I think about that kind of contradiction too long, I feel myself start to claw out the insides of my brain.

@tfae

4 жыл бұрын

At some point you stop trying to visualize it, and just trust the equations.

Conway looks so wistful all the time

I like Tim and they way he explains things.

At 3:52, you've written the product with a first, then R120. Note that the composition of functions or in this case, multiplication of transformations does not commute. The version written on the paper is the correct version unless you define this not as composition, but left-to-right application of the transformations.

I will never understand abstract algebra, but thanks for showing up, John!

I love the artist's rendering of the monster group! Bottle of moonshine next to the drummer, cheeky!

An nice example of Plato's Forms ....and an example of Kant's synthetic a priori knowledge all rolled into one monster! ...

Thank you, thank you, thank you!

Conway looked like a Mathematician that has seen it all. RIP sir.

This periodic table of groups is nice. :)

The potential for the Monster Group is formed out of a process of spherical symmetry forming and breaking.

Aww, no more videos in this chain? I hoped for this to keep going and then eventually end up at the beginning in a very logical, symmetric way. Nice mini-series though :)

@vvvss-cx1vd

2 жыл бұрын

Hard to make a video concluding something which doesn’t have a conclusion sadly

Would have been worthwhile to talk about how the mathematician found the monster and the orher monster.

'It's not incredible if I don't understand it'.... So true and honest.

RIP

I have a book on my shelf about the monster group that I've never read all the way through. I think I'll do that this summer.

Brady, can you do a video on E8, and its relation to the theory of everything?