The Good Will Hunting Problem

This installment about mathematical problems is going to be on the problem from the movie, “The Good Will Hunting”. The focus will first be on the story behind the actual good will hunting, and secondly on the problem illustrated in the movie. The problem in the movie does not require an extensive amount of work to solve, but it seems to be a more popular problem that anyone could take a crack at. The hope is that this post will be more entertaining, and a little bit easier to read then some of the other posts made previously.

Will Hunting is more of an urban legend then an actual person. There are however several candidates, but there are two main candidates for the actual Will Hunting. One of them is thought to be George Dantzig. One day, while in university, George was late to class. He got there sat down and copied some problems down from the board, these were homework problems related to the lecture. George took them home, and he thought that the last two were rather hard problems, but he worked them out anyways. He turns in the assignment, and nothing happens for six weeks. Then early in the morning he gets a knock on his door, and it is his professor. The professor explains to him that he was only supposed to do the first few problems, the last two were unsolved problems dealing with statistics. George had solved these problems as a part of his homework. Later, when George was completing his PhD, he asked his professor what to write about, and he told him to put those two pieces of paper in a binder, and call it good. The second Candidate for Will hunting is a man by the name of William Sidis. William was a child genius. He was said to have been giving lectures at Harvard at the age of 11. He had a natural ability with math, but he had trouble with the law. He attended communist rallies and assaulted an officer. This lead him to be put in jail. He was released from jail under the condition that he saw a therapist. His therapist being with father. When he was finished seeing his father, he described it as a being a living hell, and swore to be done with academia. William Sidis never worked in a major academic position again. He found office jobs, and in particular he liked running adding machine, because they fascinated him. Though these are the candidates for the real will hunting the movie is not actually based on either, in fact the movie is based on a mathematician by the name of Ramanujan. Ramanujan deserves his own blog post, so in this post he will be covered briefly, but much like Will in the movie he was a math prodigy. Ramanujan was born in India, and his work was impressive considering where he came from. Ramanujan did not have a formal education. When he was in his twenties his potential was seen, and he attended Cambridge. Sadly he died soon after. Much of his work was done concerning partitions. Partitions are the ways you can break down numbers into multiples, and additions.

In the movie, “Good Will Hunting” an MIT professor presents a problem on the board. He claims that it took MIT professors two years to solve the problem. This is probably an exaggeration made for the film, because it is not that difficult to solve. The hardest part about the problem is to understand what the problem is asking. The question is to draw all the homeomorphically, irreducible, trees of size n=10. Breaking that down one piece at a time, trees refers to a network of lines and dots without cycles, meaning no closed polygons. Homeomarphically means you can stretch, and rotate a network tree but it still counts as the same trees. In doing so it puts a finite number on the number of solutions. Next, irreducible means that if there is a tree with a point that could be removed, and not change the tree, then the point should not be there. This is because it could be reduced, so the point was serving no purpose. The last part, n=10, means that the trees must have ten points, that need to be connected with lines using these parameters. There will be an example of one of the solutions in order to fully illustrate the problem at hand. There are ten trees that match the criteria explained, and there will be a link to the ten solutions.

All solutions http://25.media.tumblr.com/tumblr_lm8kawOpTO1qcj2hco1_400.png

Sources https://www.youtube.com/watch?v=iW_LkYiuTKE
              https://www.youtube.com/watch?v=SzjdcPbjaR4
              http://www.eoht.info/page/Good+Will+Hunting+(William+Sidis)