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Take Catherine (Gwyneth Paltrow). A potentially brilliant mathematical mind in her own right, she has spent the past few years caring for her father (Anthony Hopkins), who was brilliant in his younger days but who has paid the karmic price that drama demands of genius, and has spent the past twenty years at the mercy of compulsion and dementia. After his death, his former grad student Hal (Jake Gyllenhaal) comes to their house to see if he left anything interesting behind, while older daughter Claire (Hope Davis) arrives to take care of funeral arrangements and look after Claire, whose fragility suggests that she might have inherited their father's instability along with his genius. Catherine points Hal to a notebook containing an extraordinary proof, but also claims that she, rather than her father, had worked it out.

Though set against the world of mathematical academia, math itself has very little to do with the story. In theory, the disputed proof could have been a poem or novel, but it works much better with numbers; they're objective, and the personality of the author shows through far less clearly. Besides, it makes for a nice later contrast, as "proof" becomes a play on words: A theorem can be shown to be objectively true, but eventually Hal must make a leap of faith as to its authorship. And that involves not just examining the work, but examining Catherine.

Gwyneth Paltrow makes us wonder about Catherine - is she just collapsing under the strain of having had to tend to her mentally ill father for years without a break (and then the added strain of losing him and having to deal with her sister), or is her head just wired differently, so that she misremembers things (we've already seen her talking to her dead father)? What's better is that there's personality on top of that; she's not just a collection of weaknesses. Hal falls for her not just because she looks like Gwyneth Paltrow and knows her math; she's loyal and devoted, perhaps to a fault; her occasional sarcasm and hostility to her sister actually make her more appealing, because they reveal her as more than a beat-up rag doll.

Hope Davis probably has the film's most thankless role, but the one that's likely second only to Paltrow's in importance and difficulty. Her job, basically, is to make us kind of hate her for being normal, for being concerned about clothes and the will and not being incredibly rude. Sure, she's patronizing, but sometimes it's hard not to be when you don't know how to relate to somebody. Anthony Hopkins gives the kind of performance expected of him - intelligent with the attendant charm and distance. Gyllenhaal perfectly nails a certain type of nerd, passionate about things that seem completely abstruse to a layman but also outgoing, at least within the circle that understands his passion.

"Proof" is based on a play, but you might not be able to tell from the way it's shot; it doesn't hover around one room or location. It's a small gem of a film, worth seeing for how well it gets the audience inside these people's heads, despite theirs not being the sort of heads most people can easily understand.

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originally posted: 11/17/05 23:33:24
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