The problem in Good Will Hunting - Numberphile

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Just how hard was the second problem cracked by Will in Good Will Hunting? Matt Damon!
And who doesn't love Homeomorphically Irreducible Trees?
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Music by Alan Stewart - / alankey86
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[@toojkool4984]

He has an unsolved Rubic's cube. I don't trust him.

[@agent-sz2qj]

lol

[@victorselve8349]

he has discovered a truly marvellous way to solve the rubric but this comment section would be too narrow to contain it.

[@joepsnuiters4384]

And I don't trust you because you don't know how to spell Rubik's Cube.

[@calebbullis3262]

who said it was unsolved?

[@josephrasmussen7826]

TooJ Kool you spelt rubik's with a c. i don't trust you.

[@tomtom9509]

Maths in movies are always ridiculous. They love to have sigmas (sum) on blackboards and some integrals but most math in movies are either meaningless or terribly easy .

[@oanshirazi]

Watch "The Man Who Knew Infinity"

[@globalincident694]

+FacePlant 2 million views say you're wrong.

[@joselum.r.240]

So what are you doing here?

[@agent-sz2qj]

well said

[@minhquando100]

FacePlant I guess someone didn't pass high school algebra.

[@Depleted-Uranium]

3:15 he just pulled a ''this problem is trivial and left as an exercise to the reader''

[@okb6436]

I hate reading that lol

[@OrlandoRiveraLetelier]

The story he tells at the end of the video, about the student who solved an open problem thinking it was his homework, is a story of George Dantzig, a mathematician who later helped to develop a very important theory in applied mathematics.

[@sohangchopra6478]

Specifically, in economics

[@rhettorical]

That's a preview of the followup video to this which explains the story of that problem in full.

[@alexandersanchez9138]

His main contribution (“homework” problems not withstanding) was the simplex algorithm for solving linear programs.

[@doomsday7308]

Same people are really smart damn

[@drdre4397]

@Doomsday Very true, even better if that person happens to be in a field they have a tremendous passion for. You get an obsessed genius at that point.

[@olivor_h]

Those trees brought back horrific memories of organic chemistry...

[@baloog8]

Breathe slow im here for you

[@plaidmustache]

+Olivor Holman. Indeed. But isnt this a physics class he is in, why would they be solving ochem problems?

[@thefreebooter8816]

+Olivor Holman It's A-level maths

[@shanikhan00]

organic chemistry made a man out of me. and I'm not kidding

[@olivor_h]

shanikhan00 My chemistry teacher always used to say that organic chem separates the men from the boys :)

[@transdayofrevenge]

He didn't say that it took 2 years to draw them, but that it took 2 years to prove. I'm not a mathematician but I took that to mean that it took them 2 years to prove that those are the only possible trees with those parameters.

[@squeakybunny2776]

Someone in the comments who's not a mathematician but still understands the actual problem and doesn't act like "uh that's easy. Anyone with half a brain can do that" Saved my day...

[@dragons123ism]

@@squeakybunny2776 But did Will Hunting prove it when he wrote them up on the blackboard? It looks like he was just drawing them...

[@abhiroopreddy1948]

no but there can be more with those parameters I can show

[@armycin]

Still it wouldn't take that much time for an MIT Math professor for such a problem, at least for this specific one

[@jalajjain7218]

It also doesn't takes 2 years to prove this. With basic graph theory, one can easily find and prove an exhaustive list of degree sequences. And once you have the degree sequences there's aren't much trees(1 or 2 per sequence) that one can draw per degree sequence. Hence proof by exhaustion of all cases one can easily prove that only 10 and specifically these 10 are the graphs that satisfy the conditions.

[@malroth801]

My boy's wicked smaht.

[@Randy1337]

^^

[@jaypickett3552]

How do you like those apples ?

[@gohantanaka]

Barf.

[@daltonbedore8396]

the fact the cameraman is a seperate person and there's banter with them is so different than most youtubes today, charming!

[@NacToYT]

This video was made in 2013, dude

[@monkey7431_]

@@NacToYT That was their point

[@Vasu-qn6kj]

@@monkey7431_ bruh moment with a profile named bruh.. I think the stars have aligned. Bruh.

[@Vasu-qn6kj]

@@NacToYT bruh

[@scriptkiddie7485]

It's not your fault

[@asdasdasdasd714]

It's not your fault.

[@PeppercornBingBong]

it's not your fault

[@spensersembrat]

It's not your fault

[@kentatakao6863]

It's all my fault.

[@joshs5577]

It's not your fault

[@satyrkrieg]

Wouldn't the real difficult problem actually be to prove that there are only 10 trees and no more with that characteristics?

[@mattiasahlsen3650]

Right, how can people not understand this??

[@rastapatchmail2357]

No that's not very difficult either.

[@NoahBraun21]

@@rastapatchmail2357 2 years for an MIT math professor difficult? of course not. but for college freshman in their free time? sounds like a reasonably difficult problem to give out

[@rastapatchmail2357]

@@NoahBraun21 , lol. My eight year old could do that in about 10 or 15 minutes. anyone with enough intelligence to have some gumption would be able to finish that in less than half an hour. If you can't finish this in less time than it takes to show the video, you probably don't even belong in college.

[@NoahBraun21]

@@rastapatchmail2357 your 8 year old can write mathematical proofs? for sure

[@georgepapadakis2954]

"It might sound greek to you." *But i am greek*

[@tim72184]

...but did it sound Greek? Certainly "homeomorphic" did.

[@tim72184]

@Elena Covalciuc The prefix "homeo" is Latinized from Greek. The suffix "morph" is pretty indisputably Greek.

[@tim72184]

@Elena Covalciuc Пожалуйста.

[@magsteel9891]

Everything was directly or indirectly ripped off from the Greeks. At least that's what I tell my kids.

[@nat-moody]

Quoting Shakespeare, it's all greek to me

[@algio3041]

I know this video is old, but these mathematicians have such great excitement about math, I can't help but enjoy watching, it makes me want to learn more. The world needs more teachers like this.

[@ThomasJr]

the excitement is not for boring stuff, but for things that are logical problems, puzzles and some very deep results. Some stuff in math can be boring, but some can be really interesting

[@stargazer7644]

It doesn't matter if the video is old. There are people watching it for the very first time today. And, yes!

[@MappyTheSquire]

is it just me or does this dude give off an aura of being a total badass?

[@kdmc40]

TheNimbleTurtle No, he might sound like A.P if you're an alien and never heard the human voice before!

[@monstercolorfunco4391]

you venture to say he would own gotham city in the batman ventures?

[@saltyninja]

it's you. he does seem to enjoy life though, which is all that matters.

[@theywalkinguptoyouand4060]

ViralCarelessness not really

[@SimonGreenSighGee]

Yes, I imagine this is exactly what Bricktop from Snatch looked like when he was younger. And he is foooookin' badass!

[@hybby]

Matt Damon = Math Damon?

[@MegaSilverBlood]

Math Demon.

[@pascalstiemer]

+MegaSilverBlood Meth Demon

[@Steve.909]

MethoD Man

[@DonQuickZote]

Mat Daaaamon

[@piesho]

Damn 'Matto

[@tomkrys3331]

I swear he was kinda just a genius at everything in the movie, it wasn't just maths

[@Diegesis]

he definitely had perfect memory recall which probably aided in his ability to rattle off anything he had ever read. he makes up a bunch of brothers names and lists them off in the same order immediately.

[@boredcrab2]

Yeah he seems to be an expert on organic chemistry, early American history, and law. Among other things

[@peterk.6093]

I swear he had it all written in the scenario so that people would believe it. I saw that trick once already.

[@kennytee6882]

The lesser known and smarter Weasley brother

[@olbabybeard]

Squib

[@riparianlife97701]

Such a likable guy! This is why we have the internets. The vast majority of math teachers and tutors are criminally boring. The few who are interesting get to be on KZbin, probably decades after they've died, and we can see them from anywhere in the world.

[@XXgamemaster]

Math isn't intrinsically exciting from the perspective of the non-mathematician, so if you don't like math chances are you won't find it exciting.

[@unity303]

Docktor Jim dude I was absolutely charmed and instantly pressed subscribe, far more interesting than 9/10 of what I am suggested on KZbin, other than michio Kaku and NGT/Nye duo. but @ UCLA we needed more professors that were like this fellow, that spoke passionately and inspirationally. I only had about 3 profs I can remember that I never needed coffee for persay, and one of them was exactly like this guy.

[@unity303]

Docktor Jim beat u to it doc!

[@riparianlife97701]

unity3o3 Does he remind you of Bricktop? Picture him saying "You're not worth much to me alive, are you Turkish?"

[@unity303]

Docktor Jim my takeway forever was, it was foive minutes, ten minutes eggo

[@NoriMori1992]

"Like all mathematicians, he's tall, blonde, and handsome. Yeah? …YEAH?" Oh James. XD Besides, you're a ginger! XD

[@legathar8558]

he's CLEARLY blonde!!!!!!!!!!!!!

[@MrsGreenStrauss]

In French we call that kind of ginger-y blond, blondish ginger, "blond vénitien".

[@shack8110]

Why is this a math problem and what is the difficulty?

[@NoriMori1992]

King Lesome Nope.

[@HN-kr1nf]

@@MrsGreenStrauss "blond vénitien"?

[@lin2k4]

His enthusiasm is infectious! I wish I had more teachers like that.

[@Lep_19]

Always fun to look back on these and get a feel for the relationship between these two. Both so invested in and excited to partake in the process of making these that they would make extra videos on a whim ("alright, we'll talk about that first"; see also the square the circle videos). There's a certain comfy feel that's been captured in the resulting videos.

[@Chyrosran22]

This just looks like molecules to me xD . Ethane, acetaldehyde, isobutane...

[@cheasea]

looks like graphs to me

[@JohnEthan777]

danielgr86 might have meant ethene

[@emperorpingusmathchannel5365]

Ethan9750 but aren't any double bonds

[@carlospelcastre6545]

Where's the carbonyl group?

[@Kurtlane]

Some do look like molecules. But the last one... What molecule has a central atom surrounded by 9 others?

[@ahmadshokry5945]

My deep respect to you Dr James Grime. I am a doctor, but you bring back my old passion for math with your awesome videos. Thanks

[@c.c.7687]

I laugh at how completely unbelievable this movie would've been if Affleck had taken the lead role.

[@Randy1337]

[@daphnedaisy9108]

I believe anything with Affleck so I can see it in my mind now. Ahhh nice. P.S. Watch out, people who can believe in things are able to create them. (at least I know I can) hmmmm

[@thejesusaurus6573]

He was surprisingly belivable as not a goon from boston in the accountant and, dare I say, not the worst batman.

[@tommerker8063]

@@thejesusaurus6573 to be fair though, not being the worst batman is not that hard.

[@Dylanm94]

Wait. We used to make fun of Ben Affleck as an actor. What has changed?

[@butt5810]

never been a "math" guy, but your videos are really showing me how someone could be passionate for this stuff. thank you for sharing

[@Leonie1483]

The pigeon wallpaper is arguably the best part of this video :D

[@mikemma6695]

There are, on average, 183 sesame seeds on every Big Mac bun from McDonald's. I counted.

[@ralstonwithanr]

Mike Stuart how many seeds over how many burgers?

[@zoeychevalier5132]

I just love how useless this information is xD

[@Alexagrigorieff]

But how many holes are in the Blackburn, Lankashire? And how many takes to fill the Albert Hall?

[@XxJIVONxX]

how much that would be in grams?

[@littlefishbigmountain]

Alexagrigorieff This remains unsolved since originally posed in 1967

[@Lightn0x]

I feel like in order for the solution to be complete, we shouls also prove that there are no other trees than the ones drawn. And that's not so trivial.

[@asabry4126]

"It might sound like greek to you because some of it is greek" I'm stealing that

[@BDM276]

It looks like drawing isomers of molecules.

[@davecrupel2817]

it may be relevant to that.

[@messidona2011]

+chomage This ties to it. Arrangement of molecules based upon covalent and ionic forces might be dictated upon these mathematical trees.

[@readysetgo4607]

+Sebastian Hidalgo are there any mathematical lesson (accessible on internet) that can explain me this so i can understand better my biochemistry lessons?

[@chiralSPO]

+chomage Yeah, as a chemist I found this problem trivial, once the rules were explained. This is effectively the same type of problem as generating isomers, but the rules are a little different (in chemistry cycles are definitely allowed, the number of bonds is restricted, and each vertex can be assigned as a chemical element.

[@anticdisposition5908]

Arthur Cayley studied the representation of saturated hydrocarbons by rooted trees. Look it up.

[@varigdc10]

With the advent of the Internet and all current technologies the first time I was introduced to the term " Google " a bell rang inside my head. I knew I heard this strange word somewhere a long time ago. I went to sleep that day thinking about it. The next day, bam!, I remembered. In 1964 I was a sophomore in High School ( Lane Tech, Chicago, Illinois ) my Calculus teacher asked if any of us knew what a "googleplex" was, nobody even heard the word. He went on to say it is a number, integer, with an infinite number of zeroes after it. The whole thing made sense in no time, today's Internet Google is exactly this, infinite number of information as I first heard from my teacher in 1964, wonder what he would think if he was alive today. Math is wonderful, and I hated it all during school, but had to do it towards BS EE.

[@guy3717]

A googolplex isnt infinite. Its 10 to the power of a googol, a googol being 10 to the power of 100. Its just a really big number.

[@myaccount4400]

When maths finally solve all the issues physics will create new one...

[@Colin-kh6kp]

You’re a genius, it took MIT professors 2 years to do what you did in the course of this video.

[@win_cole]

It took him two years to prove it, not to resolve it and he doesn't even say at what age so who knows

[@HantaaPL]

I seems like anyone who was taught about basic organic chemistry could solve this.

[@orssidia]

+Hantaa k

[@VesseshHebbar]

+Hantaa Exactly. Kinda like the different isomers of a hydrocarbon.

[@MJ-oh1td]

+Hantaa It seems like anyone could solve this.*

[@sauravkushwaha9252]

The rules are quite different. Do it for yourself after you really understand what's not accepted while making the structure.

[@MJ-oh1td]

+Saurav Kushwaha If this is difficult for you, maybe it's you that doesn't really understand...

[@henriok]

When I went to university and got an assignment like this, it either assumed or expressed that you should both show the solutions and prove why there isn't any other solution. So, even if it takes less than 2 years to find 10 solutions, it might take a bit longer to prove that there isn't any more solutions. In this case, that might be easy as well, but I don't think you stressed this point that finding solutions that satisfies the problem doesn't really solve the complete problem.

[@BiaZarr]

I don't know, I mean it might have been a bigger problem back then, or I might be underestimating it, but I'm pretty sure that I could write an algorith that creates every possible tree with n=10 dots, thus proving that there aren't more solutions to it by creating every possible combination. Might not be the most elegant way to do that, but it's a way to do that.

[@zyrohnmng]

How many different trees can you create like that? How can you differentiate between two homeomorphic trees? How well does this method work as you increase n?

[@Serfdomftw]

You can do it on an excel spread sheet in 5 minutes, since the definition of the graph is on how many nodes that any point has, so you just branch out. You take a 1-10 table and cut of any value above 9 and then split down the middle as it replicates itself. Each number represents the total number of nodes used. Order is irrelevant as they cannot be homeomorphic nor can you have cycles, therefore it can only be independent of another node (branches).

[@Afredericknyc]

this is my thought exactly. I don't believe I had any solutions in my applied mathematics degree that didn't show there weren't any other possible solutions. The proof of nothing else is what makes the problem difficult.

[@SageGibbons]

Could you explain this more or show how this would be done? I want to try it.

[@nicklibrizzi9656]

That's actually a pretty simple explanation of tree's for math. Love it. Thank you! I don't know and wouldn't know what it's for but great example!

[@jarretberenson1214]

I don’t get why everyone is saying that this problem is so easy. I got a 760 out of 800 on the SAT in math (top percentile). I have also passed the AP calculus AB test with a score of 4 (not great, but still better than the majority of students that take the test). I have also gotten an A in my college calculus course, but I could not draw those diagrams. I don’t really understand the problem to be honest. I am willing to bet that most people could not actually draw all of the trees so easily.

[@HowardBunjo]

Why is this the too comment if it was posted 5yrs ago and has no replies🤔

[@jackburns7963]

This wasn't the problem that took MIT professors 2 years to solve in the movie. This was the problem: 1) Find the adjacency matrix A of the graph G 2) Find the matrix giving the number of 3 step walks in G 3) Find the generating function for walks from point i to j 4) Find the generating function for walks from points 1 to 3 Don't know if anybody can do it at home or not.... I know i can't. As for the tree problem the movie never mentions if it was difficult or not.

[@ariadnarodriguez6254]

Exactly. Those were the questions.

[@melontusk7358]

is that Linear algebra?

[@azizalimov6417]

@@melontusk7358 Stochastic processes I'm pretty sure

[@asherujudo7383]

It didn't take MIT professors that time. It was when they were still students and not professors.

[@jackburns7963]

​@@asherujudo7383 In the movie, the professor said: "that took us more than two years to prove" that's it. Didn't mention when those two years took place or what the circumstances were. They may as well have solved it in kindergarten or in a previous life in ancient Mesopotamia. And that hypnotist psychologist, the one the professor took Will to, helped them to retrieve it. It doesn't really make any difference to the point I was making. The "that took MIT professors two years to solve" is a quote from THIS video. I used it only as a frame of reference.

[@davidandrews1730]

From an American point of view, the take home message in the movie is that there are in our country brilliant people who never get a shot. I knew one. Unfortunately, he fell under a bus and was killed on his way to his job on the nightshift. The odds are--I will never meet another person as gifted.

[@EGarrett01]

David Andrews Hi!

[@davidandrews1730]

I got the point of the movie, but I was moving on to reality...something you might have a fleeting knowledge of.

[@disgruntled181]

hulk0hulk From an American point of view..... No

[@jamesstuart3346]

I know nothing about math, but a therapist who treats a patient without looking at his medical records would lose his licence

[@dspsblyuth]

Are we sure Will had medical records?

[@Anand-vx2xx]

@@dspsblyuth he did since he knew about the abuse and will's injuries right?

[@dspsblyuth]

@@Anand-vx2xx so he did look at his medical records?

[@Anand-vx2xx]

@@dspsblyuth i assume so, either the psych pulled out some documents or they were inserted on screen because i definitely remember seeing them + either way there doesnt seem to be any other way he could have found out about the abuse

[@dspsblyuth]

@@Anand-vx2xx you don’t necessarily need medical records to treat a new patient either. Some people just don’t have them for various reasons such as children in the foster care system or from poor families that never took them to a doctor. I’ve seen doctors who didn’t have my records because I just didn’t remember the names of the doctors

[@janewelsh8578]

Mwah! I love that you shared this with me. Really love it. You're a radiant, mighty star of a man. Thanks for sharing you with me 🙏💛

[@NOTWorthless]

The "urban legend" is not a legend. This is roughly what happened to George Dantzig, who is famous for his contributions to linear programming among other things. Snopes has a page on it.

[@marcochimio]

I believe that there were TWO problems on the board. He took weeks to months to solve them both, and I believe he included an apology for submitting one of them late.

[@monstercoinz9460]

It's always easy once you know the answer. It took hundreds of years just to design a working lightbulb. We all know how they work now.

[@tricksock]

I don't.

[@irokosalei5133]

This example is so bad. There is a difference between a simple logical system and a piece of technology that requires Maxwell's theory of Electromagnetism and other engineering abilities. You probably don't know how a lightbulb works.

[@cryptomaniac3327]

the professor claimed that he "proved" the solution with theory - that's a whole magnitude of complexity beyond just the solution

[@tristanwh9466]

Not really, this can be proved exhaustively fairly easily with abiut as much effort as it woukd take to find the answers

[@fermatslasttheorem6298]

@@tristanwh9466 If you tried to do it yourself without ever knowing the answers, you would probably end up drawing "new" trees without realizing that you have already drawn them in a different shape. Also brute force drawing isn't really an acceptable method of proof. You could say you have only drawn 10 trees and can't any more variations after 10 - but you still didn't prove the limit is 10 - you only shown you could only do 10.

[@qqqaaa9994]

Whoever you are sir, thank you for this video.

[@jackmiddleton2080]

Like most mathematics and scholastical problems, the hardest part is understanding the pseudo intellectual peacock question phrasing handed out by the bureaucratic hierarchy of the same variety.

[@njihnjihnjih]

+Jack Middleton speaking of pseudo-intellectual peacocks...

[@jackmiddleton2080]

njihnjihnjih You got me. But they're worse than me because they're paid for it. And they're entrusted with the minds of the youth.

[@Fluxquark]

What you call pseudo intellectual phrasing is just mathematical terminology which is actually very concise, efficient and necessary. You don't want to have to say "it does not matter if you move the dots and lines around or mirror or rotate the graph or alter the length of the lines" every time. This problem is a bad example, usually understanding the concept is a 1000 times more difficult than remembering the terminology.

[@jackmiddleton2080]

Fluxquark Okay, I understand. I just disagree. I don't doubt that it is more concise but I don't think it is necessary nor do I think it efficient.

[@Fluxquark]

+Jack Middleton Oh, I'm sorry, I thought me doing mathematics for more than 5 years now meant I could form an accurate opinion about this but I forgot your uninformed opionion carries more weight. I was clearly in the wrong, my mind was clouded by facts and years of experience and you are totally right; all mathematicians have been in the wrong for hundreds of years with their mathematical language. If only they were a bit more intelligent, they might be able to grasp that which seems so simple and clear to your superior intellect.

[@Schneeeulenwetter]

the beginning reminded me so much of chemistry

[@NinjaAdorable]

Damn ... I am crushing HARD on James in these older videos ...

[@Raikaska]

Matt Damon turned out to be a real Math Demon

[@christophersewell6611]

When Dr. Grime describes the first type of banned transformation, he is actually showing something called graph isomorphism. Two graphs are isomorphic if there exists a mapping from the vertices of one graph to another which preserves the edges between them. Now before you really understand a homeomorphism, I believe it is first necessary to understand the concept of an elementary subdivision. Note how Dr. Grime goes from the first graph to the second banned graph by deleting the middle edge and replacing it with a vertex and two edges to reconnect the graph. This process is called an elementary subdivision. Finally, we say two graphs are homeomorphic if they can both be obtained by elementary subdivisions of some other graph. For a more complete introduction to graphs and trees check out "Discrete and Combinatorial Mathematics" by Grimaldi. In all honesty, you could begin reading this book with a basic understanding of high school mathematics.

[@Quantris]

Indeed...his explanation of "homeomorphism" IMHO wrongly conflates the concept of a graph with its embedding. The type of isomorphism he's talking about wouldn't even be worth mentioning as a condition in such a problem (on unlabeled graphs)...because obviously without it the answer is infinity if just moving vertices around on the paper would be considered a different graph. In the context of this problem, the term "homeomorphically irreducible" should be explained as a whole.

[@VEX_INC]

Omg i remember doing something like this with isomeric organic compounds in primary school. At the time i was so baffled now its just fun finding all the possibility's.

[@saltyninja]

If we'd had a math unit on drawing pretty little trees I might have enjoyed it more.

[@240ups]

I heard it was originally suppose to be a sassy troubled wedding planner, and it was called Goodwill Bunting!

[@KerrySoileau]

Your video ended before you gave the name of the person who was supposed to be the real Will Hunting. I remember in grad school I heard a legend about the mathematician John Milnor, who came in late, copied down what he assumed were homework problems and solved them all. It turned out that they were all unsolved problems in knot theory.

[@Oaklev]

+Kerry Soileau There's also George Dantzig and the simplex algorithm.

[@nezZario]

+Kerry Soileau I can't find any citation that Milnor does this, but the wikipedia article for the Simplex Algorithm cites that George Dantzig did this, as +Oaklev stated.

[@NoriMori1992]

+Kerry Soileau That was George Dantzig, and it was for two unproved statistical theorems. Also, the end of the video links to a continuation that talks about that exact thing.

[@sjbrooksy45]

Finish the f-ing story! What happened?

[@abysmal5422]

en.wikipedia.org/wiki/George_Dantzig

[@Wetsuitboy]

That explains a lot. I think my math tests at school were full of unsolvable problems xD

[@bumpinugly4985]

Matt Damon is an amazing actor. To think that that man passed himself off as a genius, incredible performance.

[@benshaw750]

Z Ed he wrote the script

[@honknoodle]

2 years for this problem? I found them all in less than 20 minutes.

[@arthurbond]

Actually there are 14

[@sbunny8]

It took me about 10 minutes to find all 10 and show there can't be more than 10. This is challenging but no way would it stump a math professor for 2 years let alone a whole math department at MIT. it's easier than a Rubik's cube

[@zyrohnmng]

How did you prove there can be no 11th graph?

[@zyrohnmng]

How did you prove there can be no 11th graph?

[@RobertMorgan]

How did you prove there CAN? Boom, sit down

[@vitorvilasanchez]

"and that's a guy with a funky afro" best quote EVER!

[@jc5146]

I'm out of my depth regarding the mathematics, but the pigeon wallpaper I can appreciate.

[@raybeeze5522]

pigeon wallpaper.... i like this guy even more🐦🦆🐧🐦🦆🐧🐦🦆🦞🦉🦉🦉

[@darealzorka5323]

The "Urban Legend" about a student who shows up late and copies an unsolvable problem is not an urban legend. It is George Dantzig who was the student at UC Berkeley. Though now the story might be altered depending on where you hear it, it really happened.

[@ginoginoh]

Actually in the movie there were two problems. A first one, which Will solved, and then after the professor asked in class who did that, but noone stepped forward, he decided to put another one on the blackboard (which is the one you have showed here).

[@dgillies5420]

I remember in grad school one day the professor gave out an "open problem" (unsolved) in computational geometry. The professor the following year would win the Waterman Award - NSF top researcher - all fields of science. A graduate student I knew solved the problem by the time the class ended.

[@cooperjk55]

Thank you, I am so doing this with my AP physics class!

[@holycow343]

this reminds me of organic chemistry

[@holycow343]

wow thank you for stating the obvious. you want your nobel prize now? All I said that this video reminds me of organic chemistry, I didn't say this is organic chemistry.

[@holycow343]

***** alright but just so you know I like to fight naked

[@RhydianCrescent]

+holycow343 Fukn best reply to rage EVER

[@kcorb882988]

+holycow343 The term chiral came to mind for me.

[@readysetgo4607]

+holycow343 yes, me too!

[@FingeringThings]

Bro my connect the dots colour book has *30* dots. I will see you guys at my harvard lecture

[@madamepigeon]

Awwww your pigeon wall behind you is soooo cute!!❤

[@Unexpectedthings007]

And u r cute tooooooo💙

[@madamepigeon]

@@Unexpectedthings007 Hahaha😅

[@vikkysingh4857]

So simple. Every Indian draw such kind of tree 1000 times in class 11 to 12th.but your efforts is priceless Thank you

[@KamilOttoman]

Love this dude,looks like a young version of Bricktop from Snatch

[@kerrywsmyth]

When my dad was in college for engineering back in the 1960's and 70's he got lots of unsolvable problems on tests. The difference was that it was simply just a mistake by the professor.

[@Zett76]

It isn't even a mathematical problem. It's perfectly solvable by trial and error.

[@alcoll1038]

Well, it's still Graph Theory

[@soilbroker]

There is a simple pattern to solve this. Make the first tree in a symmetric manner (like the one in upper right corner) and then carefully move around the dots. The key is to see the dots as the important factor not the lines.

[@leetingfung]

It took me only like 5 minutes to find out all 10 trees and I don't know the answer, that makes me think that drawing is not the hardest part. The real question is how do you know there are only 10.

[@manualLaborer]

is that a tattoo on your hand? maybe a tear? indicating you've killed someone with your lethal mad math skillz?

[@n.l.4025]

manualLaborer The color of the mark on his hand looks purplish to me, which was probably made by that same marker that he drew the “trees” with. I know it’s more fun for you to poke fun at someone else, but it’s not real. Too bad.

[@jgun4125]

@Jeffro Lans Do the math.

[@nagualdesign]

My uncle Joe wrote "JOE" on his hand with an original magic marker in the late '50s / early '60s and it's still there to this day, faded but still legible.

[@Doar_edy]

This guy makes your day better

[@DragonBornGirl50]

I really like this guy on numberphile i feel he gives nerds a laid back image

[@cshark899]

Those pigeons in the background! Reminds me of "A beautiful mind". An algorithm that can draw the pattern on how pigeons move! _/\_

[@mario6279]

They look like network topologies

[@readysetgo4607]

+mario rojas i think everybody sees a correlation with the field they study.

[@JohnyScissors]

Exactly, it's an underlying of logic in science

[@crookedpaths6612]

All the same, if you saw a janitor doing maths equations like that, you'd think that this guy is under utilising his abilities.

[@donsurlylyte]

the boss move is to leave it scrambled, because you can solve it anytime you wish

[@JohnHorak]

reminds me of drawing isomers in orgo

[@RCAvhstape]

So how much money did it cost nd how many people died saving Matt Damon in that movie?

[@sauravkushwaha9252]

😂😂😂 unfortunately he wasn't stuck in some situation this time...

[@gunslinger2566]

About $20 in chalk and I think we all died a little bit after Robin's monologue in the park.

[@quantummath]

This channel deserves an equivalent of an Academy Award.

[@Cubinator73]

You make this problem easier than it actually is by simply stating "there are 10 possibilities". Try proving that!

[@SmileyMPV]

Fun fact: Only for n=3 there exist no irreducible trees.

[@jadencm4862]

SmileyMPV makes sense

[@georgetownsend1479]

SmileyMPV n = 0? 8)

[@SmileyMPV]

George Townsend The empty tree is definately irreducible, so there exists an irreducible tree for n=0.

[@kentatakao6863]

I think you mean that there are no homeomorphic trees for n=3.

[@kiraacorsac]

+Callous Kunth There is literally only one tree with three vertices. It's the opposite - it's homomorphic to every other 3-vertex tree.

[@ronin6158]

i always knew I was a secret math genius who just mops floors.

[@daphnedaisy9108]

lol...well who wouldn't if it gives them free time and peace of mind so they can solve harder problems like saving the world....hmmmm

[@jc4jax]

You earned 10 points for House Gryffindor for solving the bonus problem

[@billypool8453]

What was amazing about this problem was that he used the correct math to solve the problem. He didn't have to guess possible solutions by trail and error.

[@artophile7777]

Aye Billy

[@oriagruber]

I'd like to ask a more interesting question - how can we know that there aren't more? Who said that there are only 10 homeomorphic irreducible trees with 10 nodes? maybe there are more and you missed them?

[@riskitonme]

I was thinking the same thing, I think the problem becomes a bit more difficult when you have to prove that there are only ten and no more.

[@zyrohnmng]

That's part of the problem and why it could take a while to solve.

[@SebastMorillo84]

Best scene: One, don't do that. Two-- you dropped a hundred and fifty grand on an education you coulda' picked up for a dollar fifty in late charges at the Public Library.

[@ractheworld]

Thank you Mr cameraman for preventing the maths professor from being naughty and leaving the rest as an exercise for the viewer.

[@HalSchirmer]

Still a great video - The morale of the story- never let somebody who thinks like an organic-chemist compete in maths department games.

[@RayFloresdeNL]

Nice. But the problem is not quite "finished". How can you be so sure there is no other trees? Just because you can't find it, it doesn't mean the 11'th tree doesn't exist.

[@icecubatron]

@@stefdevilliers3840 n=3 has zero solutions. n=10 having 10 solutions is just a coincidence.

[@govegan6682]

@@stefdevilliers3840 that is simply wrong, n=11 has 14 soultions for example

[@bix16000]

You mustn't prove your 10 trees are the only ones of that kind ?

[@AmberAmber]

5 yrs after your initial upload but *Wow* I still totally love this channel!💗 Signed, Elektric (a math-worshipper with an unfortunate case of dyscalculia 😍👍🏼).

[@jersydevil111]

The maker of this video directly recorded a tube TV for the scenes in the movie for this video. I can tell because when I was 13 that's how I edited my videos as well : )

[@HowBored]

How do you prove there are exactly ten solutions?

[@inchicago]

exactly. that's what actually makes it difficult

[@stylesnhl7004]

+seacaptain72 wrong

[@starfall0]

you don't have to know the answer to know that someone is wrong (in math, at least). But pointing the error would be neat.

[@ChucksSEADnDEAD]

If you do the same problem with n=11, there will be 14 solutions. n is just the number of vertices, and 10 vertices happens to have 10 solutions.

[@Qladstone]

And if you do the same problem with n in {1, 2, 3} you have no solutions.

[@danhorus]

Paused at 3:20, found all of them :D 9/1: 9 8/2: 4-4 5-3 6-2 7/3: 2-3-2 2-(1-2)-2 3-1-3 3-2-2 4-1-2 6/4: 2-1-1-2

[@romanchomenko2912]

Hi Dr James this is similar to the crossing the seven bridges in the city of Konigsberg and was solved by Euler it is used in electronics but a fun pub game I introduced to some friends.

[@jimmybuffet4970]

I can assure you that George Dantzig was not an urban legend.