A Breakthrough in Graph Theory - Numberphile

[@ТимофейЧерников-щ2х]

Wow! Yaroslav Shitov is my teacher in university. Wasn't expecting to see him there

[@anandsuralkar2947]

Whoa

[@bevstarrunner9472]

So is he the math professor who collects stamps, does yoga or meditates?

[@aheldar]

Where do you study at?

[@onemanenclave]

That is an uncomfortable family name.

[@ТимофейЧерников-щ2х]

@@aheldar я учусь в М(ФТИ)

[@gcewing]

I think I've found a universal solution to all such party problems. You invite one graph theory specialist to the party. Since all the guests are part pf a graph colouring problem, they all have something in common with him.

[@danielsmerdel8214]

Top 3 comment I've read in this section

[@gregergreg]

Ah but then there's the philosophical question, if you invite a graph theory specialist to the party, will anyone else come?

[@purplecow3000]

@@gregergreg just dont tell the other guests that you are inviting a graph theory specialist

[@shobhitsinha1754]

Successful Event Managing 101

[@Desimere]

But then it will be a lecture (one to many). You want every pair of guests to have something in common so whoever one talks to, they could get along.

[@saulysw]

She is fantastic at explaining things

[@manuroitman]

+100

[@YouTubist666]

It was a long explanation. But I was able to follow the explanation. Nice work. 👍

[@flowerpt]

yep, great teacher.

[@DonnyPetit]

+4^10000

[@abcd-sf5ur]

Yeah pal

[@guinea_horn]

So the smallest counter-example is between 5 and 4^10000 vertices

[@paradoxica424]

so now we just need a sufficiently large computer to find the smallest counterexample

[@TemporalOnline]

@@paradoxica424 And everybody will moan forever because we brute forced it instead of insighting it.

[@Einyen]

Very accurate estimate compared to "between 13 and Graham's Number"

[@Martykun36]

@@TemporalOnline 4^10000 is quite large, to pure-brute force it you would need much more atoms than the universe has.

[@movax20h]

@@TemporalOnline It is not possibele to brute force. It is too big of a range. Not only number of vertices is enormous, but number of possible graphs for each specific number of vertices is huge and grows further as the number of vertices grow. It might not be feasible to check from 5 to 1000 vertices even in this century.

[@mueezadam8438]

I love these 20 minute videos because it allows the guest to really “sell” the topic. I never knew graphs could be used this way, absolutely fascinating demonstration by Dr. Klarreich!

[@Demki]

14:28 Graphs are always G or H because G stands for Graph and H stands for Hparg >:-)

[@robindawes3544]

I remember Steve Hedetniemi from many conferences in the 1980's - he always had the most interesting problems to work on. It's wonderful that he is still teaching.

[@kanewilliams1653]

She is very clear, more of her please!

[@StefanReich]

Was a bit for idiots this time though... the simplest things explained reaally slowly

[@blablabla1494]

@@StefanReich no u

[@turolretar]

@@StefanReich perfect for a big idiot like me

[@amradio1968]

I think it was Pandora radio? when it was still just a visual website of nodes(album covers) and edges (labeled with adjectives and genres) when I first thought graphs were actually useful. In this case songs were nodes with typological edge types. Following the edges revealed the decision making for the next song. That one simple case changed my understanding of what could be done with graphs in computing for connecting data by proxy to reveal hidden graph structures quickly. The fewest number of colors in this case would also ensure artists and songs, even by a cover band, would not be repeated and get stuck accidentally in a self referential loop in the graph. I later designed an art museum tour creation app based on graphs where people could name the edge type they wanted to traverse, such as color, material, genre, etc. Worked great. 👍 I went to art school, but math truly makes the world usable.

[@salerio61]

That was really interesting, the application of maths into other totally unrelated fields.

[@salerio61]

@X E I agree with you. However if you think of a network as being an n-dimensional object, then nodes would be the corners or vertices, and edges the the lines connecting the vertices. Like a (standard) die has 6 faces, 8 vertices, and 12 edges connecting the vertices.

[@zerid0]

This problem is so much simpler when your friend graph is an empty graph. I can color it with 0 colors and binge watch Netflix every weekend.

[@JamesFluker]

I love that the guy who came up with the conjecture was simply delighted to have an answer to the problem. It shows his love of math and learning isn't about ego, but about finding answers.

[@SiMeGamer]

It is about ego. HE wants to learn something. HE wants to do math and loves it. For himself. That's as egoistic as it can get and there is nothing wrong with that. Perhaps you meant second-handed appraisal (primarily being valued by others) rather than ego :]

[@SiMeGamer]

@Steven Moore the love itself no, but the pursuit of it, is.

[@Bengt.Lueers]

Gotta love how this comes out right before Christmas, when people gather with their families and commonly wonder why it is so hard to get along with each other.

[@itsmidtrib1569]

Bengt Lüers ohmy gosh 😂

[@Danscottmusic]

My family would be a complete graph here

[@shashishekhar----]

@@Danscottmusic lol

[@Gyzome]

Somehow the answer of "they're the wrong colour" is depressingly true in some families.

[@GusTheWolfgang]

I loved how clear and conscise she was expressing herself!

[@douro20]

Hedetniemi is 80 years old and still teaching.

[@wyattdesormeaux2616]

@Steven Moore It is cool and he is a wonderful person if you get to know him.

[@totlyepic]

C L E M S O N

[@nicorobin7666]

Wow

[@pepe6666]

man how stoked would you be getting an answer to your conjecture after 50 years

[@illogicmath]

This professor is so clear and explains so well. What a blessing it would have been to have her as teacher in my university math lectures.

[@MK-13337]

Usually counterexamples and the process of taking numbers "as big (or small) as you need" is really used in analysis. I remember discussing a possible proof and we were talking about approximating some real valued quantities with rational numbers. The thought process went something like "...we can approximate this number with error epsilon, lets just take epsilon divided by a million to be safe..."

[@NoNameAtAll2]

Why not epsilon squared?

[@MK-13337]

@@NoNameAtAll2 squares are hard man :D I remember rounding 4pi/17 to 10pi when proving a function was integrable. If you just have to show an inequality to be true usually you want easy numbers to work with ;)

[@VAFFANFEDE18]

I also remember the other day I was pretty sure that given a number n and some calculations stuff failed for n+1 but who casres? Slap there 10n and you are done

[@magicmulder]

Graham: „I could maybe prove that C < 10 billion but let‘s be careful and prove C < Graham‘s number instead.“

[@sammortlokk]

I really liked how Erica explained this, I felt like I really understood it despite not doing graph theory before!

[@bhanusri3732]

IKR

[@Wanon0]

Love the subtle jab at Matt Parker: 'Or you could go for my favourite audiobook so far, that's - **scrolls away from Humble Pi audiobook** - Endurance by Alfred Lansing...'

[@JimsMaher]

Brilliant introduction to graph theory

[@liamlouw4643]

Intro?!

[@ankitaaarya]

@@liamlouw4643 exactly, that was his point. He meant that there should be an intro

[@anandsuralkar2947]

Yes

[@MrNacknime]

@@ankitaaarya The first 10 minutes of this video are intro...

[@JimsMaher]

@@MrNacknime exactly

[@pyglik2296]

I like way mathematicians think. They ask a question and when they eventually get answer they ask another question. Like: I think it may be true. Is it true? Sometimes it is true... But not always. When EXACTLY is it true? What's the smallest counter example?

[@HaloInverse]

All science is like that - or at least, it _should_ be and _ought to_ be like that. Pure mathematics is more resistant to temptations to skew, falsify, or hide results to get more funding, since the "results" are generally harder to _directly_ profit from. If you're in it, you're in it for the truth, not for the money.

[@ペア-c5b]

gonna keep it as short and simple problems when u need to deal with these never ending things for a big part of your life i guess😉

[@rumfordc]

@@HaloInverse a proper scientific hypothesis should always be falsifiable, so if you hear a scientist asking "is it true?" that should be a big red flag that they don't understand the purpose of their own job. aside from that, you're right that they should ask a lot of questions.

[@alephnull4044]

Yes that is the way of the mathematician. Similarly, they like to generalise things ad infinitum.

[@mirogula]

That's standard procedure. When you try to get to the bottom of the things, you just ask this questions naturally.

[@siddhantkumar6340]

I love these numberphile videos. They really inspire me and make me want to explore even deeper in maths

[@Roarshark12]

It brought such a smile to my face at the end when Erica mentioned having gotten Hedetniemi's his reaction to finally getting an answer to his conjecture. Any chance we can get you guys back on camera, with him, talking about this together?? :)

[@hectorh.micheos.1717]

16 minutes of setup but i really felt that I understood the issue. So nice. She is a really good teacher, even if she may not be. Really good.

[@cwaddle]

Whoelse but numberphile who will discuss really complicated maths mysteries in laymans terms. Thank you!

[@subschallenge-nh4xp]

3 brown 1 blue

[@mvmlego1212]

@@subschallenge-nh4xp -- It's a great channel, but it's not as accessible as most of Numberphile's content.

[@DomenBremecXCVI]

To be fair, using colours in a sudoku puzzle might be quite useful for children, especially like 4 by 4s and 6 by 6.

[@anandsuralkar2947]

Yes

[@unvergebeneid]

How would a 6x6 sudoku work? Pretty sure sudoku sizes have to be square numbers.

[@shoo_be_doo]

@@unvergebeneid I've seen 6x6 sudokus divided up into six 2x3 rectangles.

[@DomenBremecXCVI]

@@unvergebeneid I know it's a thing, there used to be one in my local daily paper... It's split into 6 2 by 3 rectangles.

[@unvergebeneid]

@@DomenBremecXCVI oooh, okay, if you allow rectangles you can use any number that's not a prime. Clever.

[@FakeAccount]

this woman is such a good explainer

[@drmontorsi7498]

Fake Account she has such a smoothing voice too

[@okarakoo]

true, she's gifted

[@imoffendedthatyoureoffende7461]

@@fugreek One trait of very smart people is the ability to explain convoluted concepts in a clear and concise manner

[@inyobill]

That's genius, taking a complex subject and presenting it in a manner accessible to non-experts.

[@mikapeltokorpi7671]

My mother was not into sudouks, because it was "about numbers". I said to her, that do not think those as numbers, but as symbols. She is still doing sudokus - about a ten years later.

[@Gregoryzaniz]

i am so charmed by all the examples of jobs the professor gives are things related to the university!!

[@adityakhanna113]

Oooh! I never realized until I saw the quanta magazine picture! I have read so many articles by Erica, she's great!

[@IceDave33]

A really great intuitive explanation of tensor graphs! Thanks Erica!

[@magicmulder]

I remember the „Every graph is 4-colorable“ book, one of the largest in the library at the Mathematical Institute where I studied.

[@fotonical]

This actually made sense, wish had teacher like this explain everything.

[@brianlane723]

The recommended Numberphile videos about graph theory are a graph theory problem unto themselves.

[@AGeniusDexter]

Great explanation. Didn't even have to open a book to see the conjecture. Love the simple language devoid of jargon. Brilliant explanation and analogies 😇

[@Lunareon]

What a great introduction to graph theory, and so easy to understand. I can instantly see various situations where it could be applied: seating orders, forming teams, arranging work shifts, traffic control, urban planning... Also, anything that has circles connected by lines looks like a finite-state machine to me. xD

[@rustedcrab]

I would be really impressed if I saw someone solving a sudoku with that color technique

[@aijoo00]

Isn't it the same as solving a sudoku the traditional way with numbers? Numbers and colors represent the same thing, they're just a different type of visualization.

[@sushanlamgade]

kylteri Yeah actually I’d never thought about solving sudokus with coloring problem.

[@blindleader42]

@@aijoo00 Yeah, pretty much the same. I've constructed (converted actually) sudoku using, letters, dingbats (remember them?) and other arbitrary symbols. It never occurred to me to use colors. The biggest problem with not using numerals is, if it's a really difficult example, It's much harder to pencil in candidates.

[@omikronweapon]

@@blindleader42 maybe he's just saying he's ALWAYS impressed when seeing someone solve one? XD

[@l00d3r]

@@aijoo00 Objectively, yes. But the human mind is subjective, and some people will find it easier one way or another. In my case, I know I would have a harder time solving a color sudoku, as I can visualize numbers better than colors.

[@puskajussi37]

Thats exactly why Im into mathematics. If I want to become a rich person with friends and a mansion, I just declare myself as one.

[@vidblogger12]

Let me be a rich person. Since I am rich, I no longer have to write proofs for a living. END PROOF.

[@chesshooligan1282]

You have two options. Option number one is mathematician. Option number two is lefty.

[@jedrekantkiewicz]

That explanation though, great teacher! Wish my uni professors were that great at explaining graph theory...

[@thebluefoxproductions8398]

Numberphile's logo is π and currently they have 3.14 Million subscribers.......... Coincidence? I think not!

[@vj_henke]

Is this our "pi million" sub special ?!

[@mitchgilbert6894]

The Blue Fox Productions I screenshotted it

[@Whitsoxrule1]

7 months later I saw your comment and checked current subscriber count... 3.41 million. Coincidence? Yeah probably

[@lemonteurdesanuseur9686]

I absolutely didn’t know about graphes being a mathematical object this way, and this is super interesting

[@RafaelSCalsaverini]

The auto subtitles are saying "head-at-knee Amy's conjecture" and it's hilarious.

[@danieljensen2626]

My brain was hearing it that way even without subtitles.

[@iabervon]

Amy finds this one just a little harder than Rodin's Thinker found whatever he was thinking about.

[@rofl22rofl22]

And so a few hundred people across the globe just tried hitting their head with their knee, chuckling like morons. Well, at least I did.

[@sumilidero]

Google needs to upgrade their calculator and autosubtitle alghoritms I guess :D

[@jacobtech7]

In my Graph Theory class, we had to prove this statement for the special case chi(G)=3 on the final... i can thankfully say that i got it, but unfortunately almost no one (understandably) did

[@RalphDratman]

Erica Klarreich seems to be a wonderful teacher!

[@Kasparovwannabe]

This is a really great video. Interesting concept, explained in depth, but in an understandable and engaging way. Erica was fantastic.

[@Adam-cn5ib]

Amazing, practical explanations & easy to follow. More of her please!

[@burnere633]

I found the first few minutes of the video to be wonderful exposition. I scrolled down to see who this new(?) guest on Numberphile was. I wasn't surprised. I have been fan of Erica Klarreich's writing on Quanta for some years now.

[@ProfOmarMath]

I like the follow up paper disproving it asymptomatically.

[@Noelciaaa]

i thought i was procrastinating by watching math vids when i'm supposed to be making my project as senior thesis in graphic design but i actually learned something i can apply wow

[@mc101]

Please, talk about new partial proof by Terence Tao and Collatz Conjecture.

[@tommyrjensen]

Very nice lecture indeed. Two small remarks: The graph of a function, as known from school, does fall under the same umbrella as a graph in Graph Theory. Only it is drawn in a different way. And "tensor product" is not the only name for the product in question, nor even the most common name. Just "product" or "Cartesian product" seem more used.

[@alexkoshuta6219]

I really appreciate you making this video with an astonishing explanation. Thank you very much!

[@scotthendricks5665]

Subtle Australian states graph

[@joshuaychung]

It was probably a bit easier to draw than the map of the USA with 50 states (although 2 of them don't touch the other so you'd only have to worry about the "contiguous 48 states").

[@Jivvi]

And subtly pointing out that Brady's home state of South Australia is the superior state because it has the most borders.

[@HasekuraIsuna]

Why so "sa", mate? (｀・ω・´)

[@atkgrl]

I too have considered mating offspring with either Australians or Britain’s

[@neilgerace355]

It's incorrect, as Victoria and Tasmania do have a land border: it runs across Boundary Islet. This fact was discovered only after the border was fixed.

[@bonbonpony]

21:35 So now the next question is: what is the SMALLEST graph that breaks that conjecture? :J See you in the next couple of decades ;)

[@IslandCave]

Maybe its G & H because G is for graph and H is the next letter!

[@Wecoc1]

Yep, that's exactly it. Unlike physicists, mathematicians are lazy bastards in terms of coming with nomenclatures.

[@RibusPQR]

It's because G is for Gobs, and H is for Hobbies.

[@VAFFANFEDE18]

Like the function f

[@zmaj12321]

@@RibusPQR Is this like how people argue how to pronounce gif?

[@RibusPQR]

@@zmaj12321 HEY, it's prounounced gif

[@m.rohwer6989]

Youre channel is one reason I probably attempt to become a math teacher next year😂

[@Not.Your.Business]

I wish you all the best, but I'm glad your goal isn't to become an English teacher.

[@oz_jones]

Did you?

[@m.rohwer6989]

@@oz_jones thanks for reminding me of this comment, I didnt knew it existet. And yes, I‘m currently writing my bachelor thesis 😂

[@STKeTcH]

he showed ... in just the right way ... then you have a counterexample. Great explanation!!!!

[@RolandHutchinson]

"Let's start by coloring the economist red." Must be a Marxist.

[@krakow10]

Those damn commies

[@theultimatereductionist7592]

Or a Republicunt.

[@wurttmapper2200]

That makes as much sense as an anti vax doctor.

[@RolandHutchinson]

I perhaps should have said "Marxian" rather than "Marxist" in reference to the economist.

[@cravinghibiscus7901]

@@RolandHutchinson Marxist works too, contrary to much public understanding it's still taught in most universities, it's the foundation of sociology.

[@ryanlind5239]

Man this was an awesome explanation. I put off watching this all day cause I was like "okay, Graph Theory, I'm gonna need to focus for this one." I think that's the first time there's been a numberphile video using the word "tensor" that I actually followed. Thank you!

[@Deadly_Laser]

Wow, you connected the dots very well on this one!

[@mauz791]

Dammit

[@gunhasirac]

She is a professor I would like because she writes so beautiful while most professors’ writing are hard to read as hell.

[@kwcy92]

And explains things well.

[@MrPictor]

There's a flaw in the reasoning: Why watch Netflix when you can watch Numberphile?

[@duffman18]

I'd absolutely watch a more in depth maths show made by the Numberphile crew to be a Netflix show. Go really in depth with the maths instead of just the surface level stuff, but still produced by the Numberphile guys who are used to explaining things in a more lay way.

[@Robbedem]

In dutch, there are different words for graph and graph. ;) grafiek is the one with axi, while graaf is the one that represents a network.

[@leo17921]

graph

[@kvdrr]

same here in polish

[@natmath2576]

Same in french. English just seems to be running out of words

[@huverdoose]

@@natmath2576 Oh, it's just the worst.

[@pierreabbat6157]

And what's the one that is a count?

[@kleko]

Gotta comment on the most important part here: Stamp collecting is a form of meditation and collectors are a blast at parties. I like this video.

[@esejsnake1503]

Exactly

[@ApertureCombine]

One of my favorite numberphile videos ever!

[@wojtekburzynski654]

In Polish there is no ambiguity wirh graph and graph. Graph in graph theory is called graf, graph of function is called wykres.

[@JoaoVictor-gy3bk]

In portuguese the graph for graph theory is "grafo" and the other is "gráfico"

[@marcoswappner8331]

@@JoaoVictor-gy3bk Same as in Spanish.

[@amoledzeppelin]

@@marcoswappner8331 same in Ukrainian (graph in graph theory is "граф" and graph of function is "графік"), but "граф" also means "count" (a person, as in count Dracula or count Dooku)

[@frimi8593]

Stop flexing your superior languages on us unilingual people! ;-;

[@ganaraminukshuk0]

Graph (in English): the X-Y Cartesian coordinate thing for a function, or a collection of nodes/vertices and edges that connect said nodes. Graphic (in English): depending on context, a digital image or an adjective used to describe art or gory detail. Apparently there's an additional context for these words and that's linguistics, but this isn't Linguaphile (sadly)...

[@alan2here]

Someone actually explained what tensor multiplication is and how to do it! Thank you. Direct, Rooted (more interesting on vertex transitive), Truncation (feels multiplication like), and Tensor.

[@SoleaGalilei]

Erica is a great presenter! Excellent video.

[@mydemon]

Shes a great communicator. Top notch.

[@josefranco480]

I wonder if this is similar to how our brain's neurons makes connections, and then efficiency would be how well it can avoid necessary separations

[@Bill-yd3jg]

Was just in Code Jam 2020, and one of the problems was about Latin Squares, and I stumbled upon a lecture paper also by Yaroslav Shitov! What a small world.

[@AGuitarFreekOfficial]

Congrats on 3.14 million subscribers!

[@kenc2257]

How intriguing! Never have heard about this type of "graph" before, but it is so interesting, and so well presented/explained by Ms Klarreich.

[@Omar-of4tz]

But how many colors do exist in the observable universe (Vsauce theme)..

[@eliadbu]

Studying CS I learnt quite a bit about graphs and it relates to many problems and applications.

[@programaths]

22:27 We can safely assume that one's friend is made of at lest one particle of the observable universe. Therefore, nobody has as much friends. Now, if we speak about imaginary friends, we have to understand how much information the mind can hold. I don't thinks it's that many, but that would be a conjecture.

[@raykent3211]

If you're seeking evidence to support your hypothesis, I can confirm that each of my two friends has more than one elementary particle. Mathematics gets loony.

[@HL-iw1du]

Christian Baune There is no such thing as the mind.

[@Cloiss_]

I had 2^26 imaginary friends when I was younger... (I’m not even joking)

[@haris525]

I have gotten into graph theory recently. I like it a lot and It makes neural networks easier to understand. It is pretty complicated if you try to look at the analysis portion of it.

[@alveolate]

"i don't know if there's anyone out there with that many friends..." right after saying the number is orders of magnitude larger than the total number of particles in the universe :O

[@galgrunfeld9954]

Brady, thanks to you I had the joy of listening Edward Frenkel's audiobook version of his book Love and Math: The Heart of Hidden Reality, and I've wanted for a while for mathematics to be a bigger part of my life, so thank you for promoting (beyond creating, of course) great popular mathematics content.

[@invaderpopz]

What a great presenter! She made the math really clear and well-motivated and interesting and fun! :)

[@ProfessorDShaw]

I gave this as an example to my students as an unsolved problem and it was proven while the class was still meeting!

[@samwhite7717]

The best conceivable Christmas present. Thank you.

[@AndrewBlucher]

The digits used in sudoku are just symbols. You can use colors, fruits, whatever. It is great to see science in action.

[@Belissimo-T]

According to Python, 4^10000 = 398027684033796659235430720619120245370477278049242593871342686565238635974930057042676009749975595510836461137504912702831400376935319143621753470415827025981215282426893498224826615977707595539466961019588699726772279731941315198182787264034852821200164566127930390710398182979935327718016873784821349516406114982916691867361875370024545872140793827277482562824192439237801588697814168520338650090909697535966525032757049430286459482977357373598020450589927318365663076719136934132593126761906696003770385305284570331119691001526584347722012386381881779425549210851696458253943578557699072154639655630793883941961378971846841113804188730258903839103669626086974468150655710480841592465655211805257863007811676888839555017536731758113448656752514158601444051645154665514388431619042396106716755762338728183461369854648923972904427556158821823778729193111453445844216979095435045778144571378954652122396061615147642540250745857228893999875491625014946013839340891326060933901036249999238637827577774666644809734033861619420363936465178730919233673114244563915058438996625834112132967998495576249320462871747777012165543887156255858358784852335060574881876552025685704823768078710818951860741379429242110855644973977420413810373514584504006896392675854997866870818564207239083874324953871276375716101506575153205747363963740749867514682619756775534507006871485887812402927738227576635284174246988540785975240020481266853076127172228024330561550120182008777598230542033702463408316671120886169260934006805799864598636311179787776738608992346063063099659648279663878174074787179237169752957046404584525301384153358344055908219695854852185210739761460551596658211013159915409566145426809737550417578228465835830890294497535463112081537672664056891624345779311524560019984315456142126282898486728345004767873499752683471409587367450593302392307908004590644754012537113320493601682133709318222647489080531644015321391157387178232154126828007760313716872242209614200967522180475716199973689467714010404673961454146466045855232217196687665143147612199151921277432309700460321430381533385245877431330533479476152339364503436322919665631042328740463612565842560411947020174006507893396276103834436233140915025391014386119201176462659556388343058600326710618903683746516577021214276933289179021059956925949717956040857979165914170970056212869933593589268626151996676594370800885093048230687152803213254735594741799076039453057272319884322341883241036382617598401889439130301876975498681736174215711287053447013711596004574803562701388246822510391522419061320663740921321754344166744899588160649291823535983386025904942040724581017615968429577015808090360968544059204594200069304612417366398776831532265596224715750301792207725607932534543693758772262010387360435567635232718343420679693057360004073679493008945813961012439574397373178636054628207647520675194420244271036343729318858430871461978866964772362057290577326080664463129657590249859748544101333842092713653096656066266827446079145590196644643417403723220085696202719321533233027169599734928971588850348415000070034027025298183104148343980297663148971586607903771717880683175436445585810610546882073571556162324659351310326560804448974229349743425637164834242799991427145050899469511954834774847172360693568437689147399455672090773686782511054291185172381917008889957645311339950993044779783607140593766508017935992581357858306525303783231752425242008347844867988333025417249944092118578113687403158162707075154006053416374075765162668533127078605316562826337193606242535290683224423660462222408680300498714149607265550441220738075941633988435051594487256802874182264814425923111193188280632013127802897889605338783089532740877202304122498193625454768343775535498872821099981620497070810489137457106892573248498734243717184800822956334469415666818858073218653977954309023182851723246522042792401461382001601920501284439325214084210736400630884929942272982943613708123011355260915545831043160243523599372006226150289664982113944898886610710824955096724626895416484521819026132177640598691658035986285376355033719094568083122219345722063613609779158338084375331431276527548482566210071347744541292871876134764249704859840950276227627328897424208932988115108907187647698491814375639614313178092528678007370045871748218421786396197284213209022623762734630836006864192414605237248983289006905268988475197599781524158913583701325199090352274252608342971303907669363045656232183978755853064004010895030834921988601355201181158877254807798058635127708445592064519563115094749276606697559529332807221414021024905241788974917755034700510432039890197393691722911126889174394312127254793141624975830429097997705531781908242083922068769027355129212617244130640289994777413026624013157329948333586377955103195844817163822484232700763859290253400376515701986753596890075818544485475785780031843579065754095099970940504640212850809997051128976563880886392410766321449987529690463262182894272302749154535447233331028841215215533602398281107050696017507827602761547816324743297938177204183765821117818869959795031848201322436053103778993541384779857262311465895754085538371969040922420936915076653500310175006188572019017358300979056992161958286882575984331858170857303361269891312794369244896540323192451678830668180455059289743580640736076233561935888109525845803125912388965524166819855977061399043499229843517930169118036812460794615667808961600389778306540324849286501515292799391304510997298128228258006156017389878086272789993321416349205921635696963703558971391123174877353757536774013315034956942784403824181551741629180658414081905650333672638983416786388095026169496605199749691595798835947189777822765198767949699778106683862989103096006505865271003566346191382406011673958404009194852110016915222433459641787170917872140367871023596464051647947388580570774462304347896201676197195521428782313608583714399238092208362933211302942806480175589402387976531080436906856834377344137698180789562645974374155400497754843905032231188252125802180353577510519869570675234892321663406309376 calculated instantly. It's 6021 digits long.

[@Jivvi]

So "a one with 6000 zeroes" was only off by a factor of about 400,000,000,000,000,000,000.

[@whong09]

But express that error as a percentage of 4^10000 and it's less than a percent

[@brianlane723]

You mean 4**10000?

[@pH7oslo]

You don't need python or similar to write out that number, though - just write it in hexadecimal for instance..

[@SLAMgamer11]

@@brianlane723 ha ha

[@Yuki_Matsumoto_7]

One of the few things I really like about math terms in Spanish is that we do can easily distinguish between the two concepts: gráficos o gráficas (for XY plots) and grafos (dots and lines)

[@sakshamsingh4378]

These dots on the a paper with text fascinates me

[@mauz791]

Epic

[@BainesMkII]

@18:00 You don't even need to look at the combination of the two graphs to find compatible people who were separated. The Job graph by itself had already forced the compatible Teacher and Professor to be different colors, which at least raises the concern when combining two more complex graphs (requiring many more colors) filled with such indirect separations. (I say many more colors because you need room to simplify.)

[@ShinySwalot]

Is the breakthrough that they finally managed to spell his name correctly?

[@macleadg]

Shiny Swalot That’s still an unsolved problem.

[@X_Baron]

She actually pronounces it really well. :D

[@oldinion]

It's a pretty typical finnish heritage last name though. Nothing difficult to spell.

[@macleadg]

oldinion This is an aspect of social interaction called a “joke”, which is easy to spell, but difficult for some to understand.

[@t71024]

Hedetniemi can be spelled right by just copying and pasting but it's obviously tricky to pronounce. Those dang diphthongs!

[@pierangeloerrico3776]

Numberphile now has 3.14 million subscribers. That's Beautiful.

[@ChrisLuigiTails]

Welp I have my final exam about graphs and data structures and algorithms in one hour

[@ZedaZ80]

Good luck!

[@Septimus_ii]

Hope it went well

[@carolebeni30]

How’d it go mate?

[@ChrisLuigiTails]

Thanks guys! Yup it went well, even though it was the hardest exam to date in this course.

[@JerseySlayer]

Floyd-Warshall by hand with a 6x6 matrix

[@loukas10760]

0:40 Just to point out that the confussion for the word graph comes from the shortening of 2 different greek words... Γραφική αναπαρασταση meaning graphical representation is the one used for x, y axis and Γράφος is the one used for the network representation. Englishs words and phrases, as a habbit, have always been shortened for the ease of use but details are lost in the process

[@wopol538]

She explains graphs better than any of my university teachers

[@aquilazyy1125]

I’ve always find it hard to explain the concept of tensor product intuitively to others. The party planning example is very nice.

[@ZandarKoad]

Wanted to stab myself in the eye during college advanced math. Now watching math for entertainment. The hell?

[@zoomskiller]

Discrete math (which includes things like graph theory) is very different from something like calculus. Discrete is like logic puzzles, and challenging but fascinating. Integral calculus/ differential equations is more procedural like algebra, and easier but boring.

[@letsmakeit110]

Doing things autonomously instead of being forced makes them more fulfilling. I remember reading books in school and hating them, and then rereading those same books after graduation in my free time. Industrial Society and its Future explains the phenomenon well.

[@ZandarKoad]

@@letsmakeit110 Exactly. Like forced charity. Utter oxymoron.

[@michaelcheverie7579]

@@zoomskiller Unless you live for physics.

[@cedricgabionza]

Doing math under time pressure and deadlines added unnecessary burden to an otherwise fascinating subject, also the grading system encourages results over learning so there you go.

[@martinepstein9826]

The two kinds of graphs are really the same thing in a certain sense. If G is a set then the two kinds of graphs are two different ways of representing a set of ordered pairs of elements of G. For instance, let G = {1, 2, 3}. To represent the ordered pair (1,2) on a graph with axes you can plot the point with coordinates (1,2). To represent (1,2) in a directed graph you draw an arrow from node 1 to node 2.

[@42f87d89]

She's so good at communicating, I almost forgot she called sudoku pseudo-coup

[@nelsblair2667]

Stamp collection can be a lot like meditation 🧘‍♂️. Coin collection can be a lot like yoga 🧘‍♀️. You nailed it on the math professor 👨‍🏫 and the camp counselor 👩‍🏫.

[@oz_jones]

Also, I would argue that the math prof and the teacher can have overlap in their professions, but I get the argument being made that the position isn't a teaching one.

[@KauanRMKlein]

This video is like a Christmas gift, an opportunity to ask: *where can I find easy literature (or online courses that don't suck) about graph theory?* I always try to stay ahead by learning a subject _before_ I get classes into it, and I feel like graph theory will be a huge problem next semester in Discrete Mathematics II, because my intellect is very limited when it comes to understanding spatial problems especially when they are described in those awfully arcane mathematical notations. Thank you, any and all help is appreciated!

[@BryanLeeShiYang]

Me too, it's such a blessing. I've always wanted to prepare for olympiads but graph theory always keeps me confused. Now that this is out, it's going to help me :))

[@KauanRMKlein]

@@BryanLeeShiYang Yeah. I don't want to buy a book that won't teach me anything (I don't have that kind of money). I need a book on Discrete Mathematics made for people with "spatial thinking disability" 😅

[@leodarkk]

Check in order in my opinion : Main results on distances, Dijkstra mainly. Main results on trees, BFS algorithm and such. Main results on planar graphs (Euler formula). Main results on graph coloring. Mains results on flows (Edmonds-Karp). Main results on graph minors (That is more intricated).

[@ruittenb]

Brilliantly explained. I thoroughly enjoyed this video 🙂