Good Will Hunting is a movie about a young genius, played by Matt Damon. In the movie, Damon’s character figures out the solution to a problem that has alluded mathematicians for many years. The problem is find all the homeomorphically irreducible trees such that n=10.

Now this problem really that difficult? Turns out, not really. The most challenging part to most people is figuring out what the problem wants. Well we know what trees are: connected graphs using all vertices but not creating circuits. So it this case, the number of vertices would be 10 as n=10. Now then, what are homeomorphically irreducible trees? Simply put, they’re trees that are actually different(2 tress are the same if one’s difference from the other is a slightly different angle between vertices or a different rotation between the trees), and must not have any vertices with any reducible vertices(those with only 2 lines/edges going through them). So now you can do this problem, it just takes a bit of thinking. The trees at the end should look like these:

http://stanford.edu/class/archive/cs/cs106x/cs106x.1142/lectures/GoodWillHunting.pdf

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I happened to find another website which breaks down the math problem done in Goodwill Hunting. This person who solved it broke it down to teach one to solve a problem and it looks extremely challenging but if you look a little bit harder, its’s honestly not bad. I find it fascinating how many different ways you can design an n=10 tree. I attached an image this website included to show some more patterns you can find. This link also has an image demonstrating n=11 and n=12.

https://thespectrumofriemannium.wordpress.com/tag/homeomorphically-irreducible-tree/

It is so crazy that a big name move like “Good Will Hunting” uses an actual math problem in it, instead of just making up a equation to fit the plot of the story. Similar to the OK GO video where they hired a mathematician to figure out the timing on “The One Moment” video. It just shows that math is literally all around us in the real world, not just taught in school. Movies like “Good Will Hunting” and “Interstellar” were all big Hollywood movies that had serious math in them. The producers and film makers hired mathematicians to make the movies legit as possible. When watching these movies you don’t really realize that these equations are correct, but a lot of hard work and research is put into making them as accurate as possible.

I think it is very interesting when movies are created on big problems that were solved. It feels like you can connect to the problem and get the background of what to happened. I remember taking a class on AI and they were talking about the Turing problem. Then I ended watching the movie the imitation game about this problem. It helped me understand the problem and how it was solved. The movie did a way better job of explaining it then my teacher did so it finally made sense.