The problem in Good Will Hunting - Numberphile

y like all mathematicians he's tall blonde and handsome yeah yeah well I'm not talking well he's not tall or blond or is he yeah is he he's not tall I don't know I wasn't I wasn't counting I guess um the choice of maths was arbitrary they wanted to do a film about a troubled genius and uh the originally they were going to do physics genius um and then they were advised uh to pick a mathematical genius because it might seem it might work better with script it's a really good film and the maths is less important but shall we talk about what they' what they did in the in the film The maths yeah all right so we'll talk about that first near the beginning of the film um the MIT Professor sets his students a challenge who can solve this I put it on the Blackboard in the corridor and who can solve this problem it's taken it's taken us MIT professors two years to solve this problem you know can you it now is it as hard as he made out so what was the problem if I say it first of all I'm going to say the problem that he gave the students it might sound like Greek to you because some of it is Greek right so then I'll say the problem then I'll tell you how it works and it's a problem we can all do at home all right I promise so the problem is draw all homeomorphically irreducible trees of size Nal 10 what does that mean all right let's try this out these things are called trees uh so yeah so trees uh instead of that where they are networks of dots and lines so these are called graphs it's like a it's like the London Underground map so a network of dots and lines so this is called a tree uh what's not allowed what is banned is something like this okay this is baned this has a cycle in it and Cycles are banned now what was that other big word I said homeomorphic Kelly that's the worst one that's actually not so bad that means if I did this these two are the same picture can you see what I've done I've just moved the dots slightly so you can rotate them and reflect them or you could move them around slightly but those two pictures would count as the same thing and there was another clever word uh there was the word irreducible in there so that's another band thing here this time what is banded is something like this this is banned only two lines go into that dot which means pretty much nothing happens you go in and you go out again nothing happens right there's no change nothing interesting here so this is banned as well right those are the rules we want to do it for 10 dots this is the problem wheel hunting had 10 dots how many ways are there to do it I can tell you there are 10 ways to do it what I thought might be fun is if I did a couple of them and maybe leave some for people to try and work out what I've what I've left no yeah want to see all of them you want to see all of them boring right so the first one is [Music] so it's that so if you can do that in less than 2 years then you're better apparently you're better than it professors or if you prefer uh these are all the trees of size 10 or this is a spider with nine legs and that's a guy with a funky afro I don't think that's a particularly I think people can do this at home uh but the problem isn't the important thing um what I really would like to talk about is who was the real Goodwill Hunting story is well so World hunting solves this problem there is an urban legend that's that's similar of of a student who would who ran into his exam late and he copied down the problems from the board and he went and solved them and the last one seemed really hard but he kept working on it and he and he managed to solve it and he handed in his exam paper and then the professor Rings him that that night saying you're only meant to do the first few problems the last one was an unsolvable problem oh you've solved it