*Good Will Hunting*. If you haven't seen it, go watch it. It's a really good movie.

One problem that movies like

*Good Will Hunting*often have is that they have to either make up a new math problem, use an existing math problem, or be really vague about what the problem actually is. The movie

*Proof*takes this last approach. Gwyneth Paltrow's character solves "a really important problem." For mathematicians like me, this approach is kind of agonizing. I want to know what the problem is! But the other approaches can be worse.

The book

*Uncle Petros and Goldbach's Conjecture*actually names the proof. Goldbach's Conjecture is one of the big unsolved conjectures in mathematics. If anyone actually solved it, it would be a

*huge*deal. So right from the outset you know one of two things about the outcome of the book: either he doesn't solve it (a bit of a letdown) or he solves it but for some reason never tells anyone his proof (even more of a letdown). I'll tell you this much: it ends in one of these two ways, and it

*is*a letdown.

*Good Will Hunting*takes an approach somewhere between making up a math problem and being really vague. The first time I saw it, I was really impressed by the idea that Matt Damon's character could solve such a difficult problem. But, upon closer inspection, my admiration dwindled. On the very first day of graph theory class, my professor put in this movie and said, "Now pay attention."

When the big math problem is first introduced in the film, the professor says, "I also put an advanced Fourier system on the main hallway chalkboard..."

I happen to know what a Fourier system looks like (I wrote my thesis about Fourier series). Fourier series are a neat concept that only prove useful in a very specific setting. A Fourier series is a sum of sines and cosines used to approximate some function (like f(x) = x). The formula should look something like this: