The problem in Good Will Hunting - Numberphile 

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

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 .

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

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

It's not your fault

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

Matt Damon = Math Damon?

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.

My boy's wicked smaht.

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

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

The lesser known and smarter Weasley brother

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 RU-vid, probably decades after they've died, and we can see them from anywhere in the world.

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

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.

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

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

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

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

It looks like drawing isomers of molecules.

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.

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

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

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

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.

Finish the f-ing story! What happened?

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

this reminds me of organic chemistry

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.

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.

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.

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

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.

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

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

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

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.

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.

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.

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

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.

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

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

How do you prove there are exactly ten solutions?

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.

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.

They look like network topologies

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.

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.

This is not hard hahaha... The hard part is proving the maximum number of trees, which is what the "mit professors" do in the movie. What you did barely even has a mathematical aspect to it... It's just a series of random trial and error drawings

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

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.

What the heck is that machine directly behind you on the table (around 2:06)? Is that an Enigma Machine, for Christ's sake, lol?

the beginning reminded me so much of chemistry

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?

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

reminds me of drawing isomers in orgo

the problem coudnt have simply been draw 10 things that's just tail and error

This comment section has the lowest number of f-bombs that I've ever seen... I know now I'm among greatness.

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

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

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

Yes this is easy, and its funny how hard for you guys to realize this is not the correct problem that took MIT lecturers 2 years to solve. This is the later one.

Do you like apples?

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!

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

Lol you look just like my son

Unbelievable that a math nerd has so many subscribers. Actually... IT IS AWESOME! I SUBBED :D

I guess the difficulty is on prove that there are 10 forms for n=10 ¿?

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

I'd solved for size 15 . GUESS THE NUMBER OF STRUCTUTES :)

Reminds me of stereoisomers from organic chemistry.

i feel like this branch of mathematics (if youll pardon the pun) comes up a lot in organic chemistry, would i be right in that assumption- and what is it called?

What might take 2 years is if you came up with a theory that predicted the number of trees you could make for any number of dots.

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.

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

Just got a short question to anyone who can answer or help :) Are circles only banned in this type of "triangle shape", or is it also banned when it contains 4 or more dots (square or pentagon or whatever). Because in this case, the second one that he shows would be banned, wouldn't it? Because if you turn the middle branches to the respective side, you will get two such circles, right? Whoever reads this, have a nice day:)

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.

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

2 years? 10 mins ... childsplay. Don't think a couple of them are valid - I rejected the "cross" forms as extensions: ---- * ---. Silly me!

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

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

Pretty sure you left out the rest of the problem in the movie. Doing this is easy yes and we can all do it at home in less than 2 years. The hard part, which you forgot, was that he had to prove it as well. WHY are there only 10 ways? How do you know 11 isn’t possible? That’s the hard part, to show that in some kind of elegant equation

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

Yeah but was it numberwang?

I disliked the film. Matt Damon had the personality and acting skills of a cardboard box. Didn't warm to the character at all. Robin Williams briefly threatened to make it almost interesting, but I wouldn't watch it again.

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

Those MIT professors are now janitors

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

In Greece we say "It sounds like Chineese to me" :P

Cute. But the American student came late to a regular day's class (not an exam) and thought it was a homework problem. His name was George Dantzig and the professor was Jerzy Neyman. The paper was accepted in 'The Annals of Mathematical Statistics'.

The man who knows infinity is better that this childs play, the guy tells many theorms attributed to his life, than this guy in this movie doing basic math and express like he contributed something to mathematics, this movie trolled the heck out of mit professors to mathematicians. Movie is goofy, idk any mathematicians exists like this goofy guy.

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

The song while he was drawing tha graphs reminded me so much o Avatar: The Last Airbender

I honestly thought this was going to be a statistics video about your chances of finding actually valuable items in Goodwills xD

Ok, now prove that you've found all the possibilities using probability theory, and without assuming that there are only 10 options. Then write a script in Python that can solve the problem by itself.

"some of the words are greek." then says latin words....

Impressive. Now solve the mystery of crop circles and I will be very impressed. Who makes em? How and why? It ain't ALL Doug and Dave.

Everyone: I love connect the dots! Numberphile:

I found all of them by my own