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.
Click here to find out what approach Good Will Hunting takes!