Is there some compelling reason why the mathematical field of combinatorics was featured in “Goodwill Hunting”? Is it considered particularly difficult or especially exotic or impressive looking so as to wow the viewing audience?
Hmm… Im not sure how much research they did into the issue but I would think combinatorics is a field where there are quite a few easy problems with hard answers.
That is, problems that dont require all that much theory to understand but are fiendishly difficult. It would be more plausible that someone could be “discovered” in such a field rather than a more techinical one.
What Shalmanese said. Plus, the notation is fairly unfamiliar to most people, so it looks more advanced.
If I may be nitpicky:
The film’s title is Good Will Hunting. Will Hunting is Matt Damon’s character’s name.
I saw a clip of the sequel “Hunting Season”. I liked it.
“Applesauce!”
What is combinatorics math, and what is it used for? What would be the most basic of questions in this branch of math? - Jinx
Combinatorics is more or less the art of figuring out how many elements are in a set without enumerating them*. The most basic questions are along the lines of “How many possible poker hands are there?” Questions can become much more advanced, but at bottom, they all relate to counting.
There are a few other areas of modern combinatorics, but they really all relate to the art of counting.
*There’s also a branch of combinatorics devoted to creating algorithms to enumerate the members of a set, but I won’t mention that cause it could lead to confusion.
A) Let’s not forget the script was written by Ben Affleck (sp?). He must have had some personal experience with BOTH mathematcis (or a liking of math) AND knowledge of a subtle personality disorder which manifests itself as “fear of abandonment”, for one …or he was very well advised. Personally, I am amazed he could tackle such a subtle topic as this personality disorder and do a fairly decent job depicting it - in a nutshell.
B) As for the math shown in the film, they could have just as easily have shown a Control Theory problem. The math can get ugly there, too. But, then again, the camera purposely shows so little… - perhaps it is intentional to keep the audience from recognizing the math problem might only be a bunch of jibberish.
- Jinx
Another factor: The NSA wanted to hire Will as a codebreaker. If I’m not mistaken, combinatorics would be relevant to codebreaking, no? The scriptwriters, for dramatic reasons, wanted Will to specialize in something of value to the Feds.
As for the camera showing little, I’d be a little less cynical. For starters, there are a lot more people in the audience who would be bored by too much mathematics, than would be excited by it. Besides, suppose you do show all the steps? Then you’ve either got to develop the same revolutionary breakthroughs that Will did, or have all the math nerds who are in the audience say either “That’s wrong” or “That’s trivial”.
The Math stuff I paid attention to was indeed quite trivial. Basic trig relations in matrices and such. The physics diagrams were also apparently no big deal.
Yep, as said, you can start learning combinatorics with virtually no previous math experience, unlike calculus, for example, where you need algebra, linear algebra, and trig skills. Combinatorics is extremely logic based. I remember when we first started “counting” in our discrete math class: “Ok class, today we’re going to learn various methods of counting,” says the prof. We weren’t laughing by the end of the next lecture.