Proof

In another case of a Miramax movie made in 2003 that is just getting released, Proof marks the second pairing of John Madden and Gwyneth Paltrow after the Academy Award winner Shakespeare in Love, and once again the result is wonderful. While not as good as A Beautiful Mind or Good Will Hunting, the only other movies about a similar subject, math, that come to mind right now, the movie has excellent performances from all its four main characters and at just 1 hour and 40 minutes, it never bores us, keeping the story flowing perfectly.

Gwyneth plays Catherine, the daughter of Anthony Hopkins' Robert, a brilliant mathematician, the best of his generation, who's been declared crazy and so Catherine as been taking care of him for the past 5 years, leaving school and having no social life at all in the process.
Catherine is also a great mathematician, so when his father dies, her sister Claire (Hope Davis) comes back home for his funeral and also to try and take care of her, as she thinks she's going crazy just like their father. And she kind of is.
Also in the picture is Hal (Jake Gyllenhaal), one of Robert's students, who falls in love with Catherine, and at the same times wants to research Robert's more than a hundred notebooks hoping to find whatever it is the beautiful mind has supposedly been working on when he was out of his mind.

This is Gwyneth's best performance to date, and have in mind she won an Oscar already. She is so believable in the role, helped by David Auburn and Rebecca Miller's smart screenplay that gives her and all the characters great dialogue, specially when it comes to math.
Catherine never goes crazy, but she does show some signs, and while Gwyneth does not show it like Russell Crowe (who got robbed at those Oscars) did, her more quite performance is equally magnificent.
The one showing more Crowe-like signs is Hopkins, who is crazy and fatherly and sweet all at the same time. Davis and Gyllenhaal also give very good supporting performances with some great dialogue from both of them, specially whenever Hal talks about his fellow geeks.

Because of my love for math I knew I was going to like this movie, but the amazing performances and smart dialogue made me love it. Proof is intelligent but not confusing, funny when needed and then perfectly realistic in its drama, an overall excellent movie, with Gwyneth Paltrow giving a performance that puts her at the lead of the Oscar race.