Catherine (Gwyneth Paltrow)’s father, Robert (Anthony Hopkins) has just died. He was a brilliant professor of mathematics who in his early years did some incredible proofs that had an impact on mathematics and applied science. One of Robert’s doctoral students, Hal (Jake Gyllenhaal) goes through her father’s office the day before the funeral. He finds a notebook with what seems to be a new proof. Catherine thinks he only wants to publish it to become famous, something he denies.


Claire (Hope Davis), Catharine’s sister, arrives for the funeral. She intends to only stay for a day. She thinks Catherine is unstable, having quit school to care for her mentally ill father. Meanwhile, Catherine has flashbacks about her father; he also appears to her. 


Catherine has a melt down during the funeral and while the funeral gathering afterwards winds on, she and Hal have a brief fling. Afterwards, Catherine accuses Hal of sleeping with her just to get the notebook. He tells her he was only getting it to gift it back to her. She doesn’t believe him. It is revealed that Catherine is herself a world class mathematician when the author of the ‘proof’ Hal discovers is put in doubt by the people who are closest to Catherine: Hal and Claire.


[proof]  is adapted from a play by David Auburn, but the transfer to the screen works. (Some plays that are made into movies are mind-numbing because of too much dialogue instead of dependence on visuals to tell much of the story: case in point 2004’s Closer; so tedious.) Other elements signal a play: the simplicity of the scenes: most of the action takes place in the house. Director John Madden (Shakespeare in Love) keeps the dramatic tenor of the film even throughout, between plot and characters (one of which is higher mathematics), even when the characters themselves are anything but even.


[proof] is about higher math but it also asks questions about love: how do you prove it? How do you disprove it? In math can you “trust” an answer? In life, can you trust the word of another, even when there seems to be proof that would contradict their assertions? Can you trust a mad man, or a mad woman? Can you trust love between a parent and child, siblings, a man and a woman? What kind of proof do you need? When is it time to have faith, to believe? What proof do you need? Proof, then, is also about epistemology: how do we know?


The math elements of the film are fascinating especially to a non-math person such as myself. There is a shot of a book called “discreet mathematics” in the film that sent me scrambling to find out what it means. Ask Jeeves; I did. Some parts are reminiscent of A Beautiful Mind, but not enough to be distracting. If anything, I think the links between CBS’s Friday night crime drama, Numb3ers were more obvious (Numb3ers is of my favorite shows). We are never quite sure if the character of Catherine, played convincingly by Paltrow, is ill or not, and the mystery of the proof’s authorship kept me hooked, even if I had no idea what it proved – or not. [proof] is a “small” film that keeps its focus. I enjoyed [proof] very much.

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