A Breakthrough in Graph Theory - Numberphile
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- Опубліковано 14 чер 2024
- A counterexample to Hedetniemi's conjecture - featuring Erica Klarreich.
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More links & stuff in full description below ↓↓↓
Read Erica Klarreich's Quanta article on this subject: www.quantamagazine.org/mathem...
And visit her website: www.ericaklarreich.com/
Yaroslav Shitov's breakthrough paper: arxiv.org/abs/1905.02167
Thanks to Stephen Hedetniemi for providing us with photos and pages from his original dissertation.
Some more graph theory on Numberphile...
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An Unsolved Problem: • A Colorful Unsolved Pr...
Planar Graphs: • Planar Graphs - Number...
Perfect Graphs: • Perfect Graphs - Numbe...
Friends and Strangers: • Friends and Strangers ...
River Crossings: • River Crossings (and A...
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Wow! Yaroslav Shitov is my teacher in university. Wasn't expecting to see him there
Whoa
So is he the math professor who collects stamps, does yoga or meditates?
Where do you study at?
That is an uncomfortable family name.
@@aheldar я учусь в М(ФТИ)
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.
Top 3 comment I've read in this section
Ah but then there's the philosophical question, if you invite a graph theory specialist to the party, will anyone else come?
@@gregergreg just dont tell the other guests that you are inviting a graph theory specialist
Successful Event Managing 101
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.
People would be surprised how many things from everyday life directly reduce to a coloring problem.
Any NP complete Problem, actually
... which again, are all interchangeable / reducible into each other. So you *could* describe basically every decision process of your life as a knapsack problem. Or 3SAT, if you're more hardcore
Or I can relate may of my problems to Sudoku :p
Sudoku is NP-complete as well, so yes, you can probably restate everything as a Sudoku table. It might seem a bit cumbersome to first map your original problem into an initial number distribution in the table (there might be many sub-problems to solve here first), but hey, if that's your favorite way to figure stuff out...
I'm not sure if this counts as every-day, but I've come across it in compilers... the program that turns source code into something a computer can run. It's used for allocating CPU registers based on how certain instructions interact with each other. It tends to get rather complex though because there are situations where certain vertices are forced to be a certain colour (i.e. you have to use a particular register for some instructions, like x86's DIV instruction returns the quotient in RAX and the remainder in RDX).
So the smallest counter-example is between 5 and 4^10000 vertices
so now we just need a sufficiently large computer to find the smallest counterexample
@@paradoxica424 And everybody will moan forever because we brute forced it instead of insighting it.
Very accurate estimate compared to "between 13 and Graham's Number"
@@TemporalOnline 4^10000 is quite large, to pure-brute force it you would need much more atoms than the universe has.
@@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.
She is fantastic at explaining things
+100
It was a long explanation. But I was able to follow the explanation. Nice work. 👍
yep, great teacher.
+4^10000
Yeah pal
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.
She is very clear, more of her please!
Was a bit for idiots this time though... the simplest things explained reaally slowly
@@StefanReich no u
@@StefanReich perfect for a big idiot like me
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.
Bengt Lüers ohmy gosh 😂
My family would be a complete graph here
@@Danscottmusic lol
Somehow the answer of "they're the wrong colour" is depressingly true in some families.
14:28 Graphs are always G or H because G stands for Graph and H stands for Hparg >:-)
Hedetniemi is 80 years old and still teaching.
@Steven Moore It is cool and he is a wonderful person if you get to know him.
C L E M S O N
Wow
man how stoked would you be getting an answer to your conjecture after 50 years
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.
That was really interesting, the application of maths into other totally unrelated fields.
@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.
Brilliant introduction to graph theory
Intro?!
@@liamlouw4643 exactly, that was his point. He meant that there should be an intro
Yes
@@ankitaaarya The first 10 minutes of this video are intro...
@@MrNacknime exactly
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!
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..."
Why not epsilon squared?
@@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 ;)
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
Graham: „I could maybe prove that C < 10 billion but let‘s be careful and prove C < Graham‘s number instead.“
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.
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...'
I really liked how Erica explained this, I felt like I really understood it despite not doing graph theory before!
IKR
I loved how clear and conscise she was expressing herself!
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.
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 :]
@Steven Moore the love itself no, but the pursuit of it, is.
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?
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.
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😉
@@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.
Yes that is the way of the mathematician. Similarly, they like to generalise things ad infinitum.
That's standard procedure. When you try to get to the bottom of the things, you just ask this questions naturally.
"Let's start by coloring the economist red."
Must be a Marxist.
Those damn commies
Or a Republicunt.
That makes as much sense as an anti vax doctor.
I perhaps should have said "Marxian" rather than "Marxist" in reference to the economist.
@@RolandHutchinson Marxist works too, contrary to much public understanding it's still taught in most universities, it's the foundation of sociology.
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.
Let me be a rich person.
Since I am rich, I no longer have to write proofs for a living.
END PROOF.
You have two options. Option number one is mathematician. Option number two is lefty.
The auto subtitles are saying "head-at-knee Amy's conjecture" and it's hilarious.
My brain was hearing it that way even without subtitles.
Amy finds this one just a little harder than Rodin's Thinker found whatever he was thinking about.
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.
Google needs to upgrade their calculator and autosubtitle alghoritms I guess :D
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.
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?? :)
To be fair, using colours in a sudoku puzzle might be quite useful for children, especially like 4 by 4s and 6 by 6.
Yes
How would a 6x6 sudoku work? Pretty sure sudoku sizes have to be square numbers.
@@unvergebeneid I've seen 6x6 sudokus divided up into six 2x3 rectangles.
@@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.
@@DomenBremecXCVI oooh, okay, if you allow rectangles you can use any number that's not a prime. Clever.
this woman is such a good explainer
Fake Account she has such a smoothing voice too
true, she's gifted
@@fugreek One trait of very smart people is the ability to explain convoluted concepts in a clear and concise manner
Whoelse but numberphile who will discuss really complicated maths mysteries in laymans terms. Thank you!
3 brown 1 blue
@@subschallenge-nh4xp -- It's a great channel, but it's not as accessible as most of Numberphile's content.
There's a flaw in the reasoning: Why watch Netflix when you can watch Numberphile?
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.
The recommended Numberphile videos about graph theory are a graph theory problem unto themselves.
Subtle Australian states graph
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").
And subtly pointing out that Brady's home state of South Australia is the superior state because it has the most borders.
Why so "sa", mate?
(｀・ω・´)
I too have considered mating offspring with either Australians or Britain’s
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.
I love these numberphile videos. They really inspire me and make me want to explore even deeper in maths
Oooh! I never realized until I saw the quanta magazine picture! I have read so many articles by Erica, she's great!
I would be really impressed if I saw someone solving a sudoku with that color technique
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.
kylteri Yeah actually I’d never thought about solving sudokus with coloring problem.
@@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.
@@blindleader42 maybe he's just saying he's ALWAYS impressed when seeing someone solve one? XD
@@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.
A really great intuitive explanation of tensor graphs! Thanks Erica!
I remember the „Every graph is 4-colorable“ book, one of the largest in the library at the Mathematical Institute where I studied.
That explanation though, great teacher! Wish my uni professors were that great at explaining graph theory...
Welp I have my final exam about graphs and data structures and algorithms in one hour
Good luck!
Hope it went well
How’d it go mate?
Thanks guys! Yup it went well, even though it was the hardest exam to date in this course.
Floyd-Warshall by hand with a 6x6 matrix
Numberphile's logo is π and currently they have 3.14 Million subscribers..........
Coincidence? I think not!
Is this our "pi million" sub special ?!
The Blue Fox Productions I screenshotted it
7 months later I saw your comment and checked current subscriber count... 3.41 million. Coincidence? Yeah probably
Youre channel is one reason I probably attempt to become a math teacher next year😂
I wish you all the best, but I'm glad your goal isn't to become an English teacher.
Did you?
@@oz_jones thanks for reminding me of this comment, I didnt knew it existet. And yes, I‘m currently writing my bachelor thesis 😂
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 😇
In Polish there is no ambiguity wirh graph and graph. Graph in graph theory is called graf, graph of function is called wykres.
In portuguese the graph for graph theory is "grafo" and the other is "gráfico"
@@JoaoVictor-gy3bk Same as in Spanish.
@@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)
Stop flexing your superior languages on us unilingual people! ;-;
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)...
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.
She is a professor I would like because she writes so beautiful while most professors’ writing are hard to read as hell.
And explains things well.
Wow, you connected the dots very well on this one!
Dammit
I absolutely didn’t know about graphes being a mathematical object this way, and this is super interesting
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
Erica Klarreich seems to be a wonderful teacher!
Amazing, practical explanations & easy to follow. More of her please!
This actually made sense, wish had teacher like this explain everything.
I like the follow up paper disproving it asymptomatically.
I really appreciate you making this video with an astonishing explanation. Thank you very much!
Please, talk about new partial proof by Terence Tao and Collatz Conjecture.
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
This is a really great video. Interesting concept, explained in depth, but in an understandable and engaging way. Erica was fantastic.
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.
graph
same here in polish
Same in french. English just seems to be running out of words
@@natmath2576 Oh, it's just the worst.
And what's the one that is a count?
Maybe its G & H because G is for graph and H is the next letter!
Yep, that's exactly it. Unlike physicists, mathematicians are lazy bastards in terms of coming with nomenclatures.
It's because G is for Gobs, and H is for Hobbies.
Like the function f
@@RibusPQR Is this like how people argue how to pronounce gif?
@@zmaj12321 HEY, it's prounounced gif
One of my favorite numberphile videos ever!
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.
Congrats on 3.14 million subscribers!
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
such clarity! Please continue making more videos, Erica.
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!
Erica is a great presenter! Excellent video.
According to Python, 4^10000 = 398027684033796659235430720619120245370477278049242593871342686565238635974930057042676009749975595510836461137504912702831400376935319143621753470415827025981215282426893498224826615977707595539466961019588699726772279731941315198182787264034852821200164566127930390710398182979935327718016873784821349516406114982916691867361875370024545872140793827277482562824192439237801588697814168520338650090909697535966525032757049430286459482977357373598020450589927318365663076719136934132593126761906696003770385305284570331119691001526584347722012386381881779425549210851696458253943578557699072154639655630793883941961378971846841113804188730258903839103669626086974468150655710480841592465655211805257863007811676888839555017536731758113448656752514158601444051645154665514388431619042396106716755762338728183461369854648923972904427556158821823778729193111453445844216979095435045778144571378954652122396061615147642540250745857228893999875491625014946013839340891326060933901036249999238637827577774666644809734033861619420363936465178730919233673114244563915058438996625834112132967998495576249320462871747777012165543887156255858358784852335060574881876552025685704823768078710818951860741379429242110855644973977420413810373514584504006896392675854997866870818564207239083874324953871276375716101506575153205747363963740749867514682619756775534507006871485887812402927738227576635284174246988540785975240020481266853076127172228024330561550120182008777598230542033702463408316671120886169260934006805799864598636311179787776738608992346063063099659648279663878174074787179237169752957046404584525301384153358344055908219695854852185210739761460551596658211013159915409566145426809737550417578228465835830890294497535463112081537672664056891624345779311524560019984315456142126282898486728345004767873499752683471409587367450593302392307908004590644754012537113320493601682133709318222647489080531644015321391157387178232154126828007760313716872242209614200967522180475716199973689467714010404673961454146466045855232217196687665143147612199151921277432309700460321430381533385245877431330533479476152339364503436322919665631042328740463612565842560411947020174006507893396276103834436233140915025391014386119201176462659556388343058600326710618903683746516577021214276933289179021059956925949717956040857979165914170970056212869933593589268626151996676594370800885093048230687152803213254735594741799076039453057272319884322341883241036382617598401889439130301876975498681736174215711287053447013711596004574803562701388246822510391522419061320663740921321754344166744899588160649291823535983386025904942040724581017615968429577015808090360968544059204594200069304612417366398776831532265596224715750301792207725607932534543693758772262010387360435567635232718343420679693057360004073679493008945813961012439574397373178636054628207647520675194420244271036343729318858430871461978866964772362057290577326080664463129657590249859748544101333842092713653096656066266827446079145590196644643417403723220085696202719321533233027169599734928971588850348415000070034027025298183104148343980297663148971586607903771717880683175436445585810610546882073571556162324659351310326560804448974229349743425637164834242799991427145050899469511954834774847172360693568437689147399455672090773686782511054291185172381917008889957645311339950993044779783607140593766508017935992581357858306525303783231752425242008347844867988333025417249944092118578113687403158162707075154006053416374075765162668533127078605316562826337193606242535290683224423660462222408680300498714149607265550441220738075941633988435051594487256802874182264814425923111193188280632013127802897889605338783089532740877202304122498193625454768343775535498872821099981620497070810489137457106892573248498734243717184800822956334469415666818858073218653977954309023182851723246522042792401461382001601920501284439325214084210736400630884929942272982943613708123011355260915545831043160243523599372006226150289664982113944898886610710824955096724626895416484521819026132177640598691658035986285376355033719094568083122219345722063613609779158338084375331431276527548482566210071347744541292871876134764249704859840950276227627328897424208932988115108907187647698491814375639614313178092528678007370045871748218421786396197284213209022623762734630836006864192414605237248983289006905268988475197599781524158913583701325199090352274252608342971303907669363045656232183978755853064004010895030834921988601355201181158877254807798058635127708445592064519563115094749276606697559529332807221414021024905241788974917755034700510432039890197393691722911126889174394312127254793141624975830429097997705531781908242083922068769027355129212617244130640289994777413026624013157329948333586377955103195844817163822484232700763859290253400376515701986753596890075818544485475785780031843579065754095099970940504640212850809997051128976563880886392410766321449987529690463262182894272302749154535447233331028841215215533602398281107050696017507827602761547816324743297938177204183765821117818869959795031848201322436053103778993541384779857262311465895754085538371969040922420936915076653500310175006188572019017358300979056992161958286882575984331858170857303361269891312794369244896540323192451678830668180455059289743580640736076233561935888109525845803125912388965524166819855977061399043499229843517930169118036812460794615667808961600389778306540324849286501515292799391304510997298128228258006156017389878086272789993321416349205921635696963703558971391123174877353757536774013315034956942784403824181551741629180658414081905650333672638983416786388095026169496605199749691595798835947189777822765198767949699778106683862989103096006505865271003566346191382406011673958404009194852110016915222433459641787170917872140367871023596464051647947388580570774462304347896201676197195521428782313608583714399238092208362933211302942806480175589402387976531080436906856834377344137698180789562645974374155400497754843905032231188252125802180353577510519869570675234892321663406309376
calculated instantly. It's 6021 digits long.
So "a one with 6000 zeroes" was only off by a factor of about 400,000,000,000,000,000,000.
But express that error as a percentage of 4^10000 and it's less than a percent
You mean 4**10000?
You don't need python or similar to write out that number, though - just write it in hexadecimal for instance..
@@brianlane723 ha ha
What a great educator you are, Erica! Great video!
i am so charmed by all the examples of jobs the professor gives are things related to the university!!
Almost 3.14 milion subs.
6.28 is where it's at. xD
Lol
next stop 42 mil
Naveen Dookia get that tau outta here
IT IS
I think one fact is important to note: the reason why this conjecture seems _obviously_ false with the presented example is that for most friend groups, we only have a subgraph of the full product. Obviously there are subgraphs, i.e. graphs where certain nodes are deleted, that can be colored with fewer colors. That's not what the conjecture is about, though.
Penny Lane what?
@@HL-iw1du You'd help me answer your question if you elaborated a bit ;)
@@unvergebeneid I'm guessing you mean that people don't have a friend for every combination of job and hobby in real life, so their intuition tells them that the problem is easier than it actually is . The conjecture does seem obviously false at first glance because, as Erica points out, you're throwing away information that can only help you if you just default to the starting solutions. I quickly realized how difficult it was to actually create a counterexample, however, since you apparently have to make both G and H require at least 5 colors, which means that even the simplest examples you want to try take quite a while to write down (I gave up already, haha).
@@trogdorstrngbd yes. For the problem in the video you will of course have plenty of real life friend groups that will allow everyone to come on the same weekend, i.e. the graph only needing one color. But as you said, that's not what this conjecture is about, so this example will mislead many people which is also reflected in the comments for this video.
@@IlIlllIllIlIIIll Not sure I understand your question. What graphs don't share any edges?
That's genius, taking a complex subject and presenting it in a manner accessible to non-experts.
How intriguing! Never have heard about this type of "graph" before, but it is so interesting, and so well presented/explained by Ms Klarreich.
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.
Exactly
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 ;)
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.
Thanks for getting this video out so quickly!
Is the breakthrough that they finally managed to spell his name correctly?
Shiny Swalot That’s still an unsolved problem.
She actually pronounces it really well. :D
It's a pretty typical finnish heritage last name though. Nothing difficult to spell.
oldinion This is an aspect of social interaction called a “joke”, which is easy to spell, but difficult for some to understand.
Hedetniemi can be spelled right by just copying and pasting but it's obviously tricky to pronounce. Those dang diphthongs!
"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
This was very interesting and also well explained. You opened up a new universe to me. Thank you ❤️
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
Wanted to stab myself in the eye during college advanced math. Now watching math for entertainment. The hell?
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.
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.
@@letsmakeit110 Exactly. Like forced charity. Utter oxymoron.
@@zoomskiller Unless you live for physics.
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.
But damn this is interesting i always wanted to know about this map thing
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.
Ok. So this is kind of breakthrough I've been long waiting for? Starting from tomorrow, I'm gonna use it in my daily work for now on.
But how many colors do exist in the observable universe
(Vsauce theme)..
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.
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.
Christian Baune There is no such thing as the mind.
I had 2^26 imaginary friends when I was younger... (I’m not even joking)
Brilliantly explained. I thoroughly enjoyed this video 🙂
Thank you Erika. Easily understood and well explained.
These dots on the a paper with text fascinates me
Epic
What a great presenter! She made the math really clear and well-motivated and interesting and fun! :)
Great explanation and so easy to follow. Thank You
Superb introduction to graph theory! Thank you!
Last time I was this early, UA-cam used to pause at 301 views
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!
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 :))
@@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" 😅
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).
Great video! Thank you, Erica and Brady!
I loved the video. Very captivating. Thanks for that.
*Look at this graph* 🎶
*everytime I do I Laugh*
Everytime I do I color it nice
and people joke about math having no practical applications. PFFT! This is exactly the kind of thing that people planning seating arrangements at weddings need lol.
And now I want to learn more about graph theory [after I teach myself calculus... after I graduate college, cuz I'm pressed for time and energy]
@@epsi well, with or without optimized seating arrangements, humans will find SOMETHING to fight about :P haha
I listened to Humble Pi on Audible. I had quite a nice time with it while driving to work and back home for a few days
he showed ... in just the right way ... then you have a counterexample. Great explanation!!!!