Take a moment and think of mathematics: of its symbols, its obscurity, the gobbledygook found in its reams of incoherency. Remember the eccentricities of its practitioners and worshipers, the gibberish they pass off as speech. Think of how these things alienate the rest of the world from mathematics, that most charming and fascinating of all human pursuits.
For mathematics is not so much a game, like chess, with strange rules of movement, simple yet totally impenetrable. It is a place, the most ideal of all places, because it offers certainty when elsewhere there is only doubt. How terrifying it must be for someone asked to leave that world for the first time.
In Proof, that person is Catherine (Gwenyth Paltrow), the daughter of a former giant among mathematicians who in his later life becomes feeble and insane. Catherine has spent the last five years caring for her ailing father at the expense of her own education and self-discovery. Now he's dead, leaving Catherine burdened by the genius and instability he has bequeathed her.
He also left her the piles of notebooks, glutted with writing because of his graphomania. Amid the rubble there is an extraordinary proof, one that would revolutionize the world of mathematics. Catherine claims it's hers. Her sister, Claire (Hope Davis), and Hal (Jake Gyllenhall), a doctoral graduate who loves Catherine, believe it's her father's. The question of its authorship is the main conflict in the film. Its answer may prove that her father had moments of clarity despite his infirmity or show that Catherine is heir to the mantle her father left behind.
How Proof resolves this is left for the reader to discover. The scene that settles the authorship's identity is poignant and truly heartbreaking. It is a moment of extraordinary dimension and poetry about the love between parent and child. The resolution should make it clear why this film is one of the most moving films of the year.
This is a film that never moves too fast to miss the nuance of its character or too slow for its details to stagnate.
Catherine is fractured, and her edges are sharp, like smashed porcelain. She doesn't like to be touched, not because she's afraid she'll cut someone, but because she's afraid they'll cut her. That the film begins on her birthday is symbolic not of new beginnings but of first words. The movie is about Catherine being asked to speak to a world that might not understand her for the first time.Paltrow resonates in her performance and is brittle rather than her usual ethereal.
The character of Claire is especially unfortunate, because she is a currency analyst who works 100 hours a week in New York to support the family. By any other metric, she is extraordinary. But in a family that measures success in terms of genius, her life is as impressive as someone who's mastered the art of walking and chewing gum at the same time. Davis discovers the complexity of the role.
Proof is a film that understands mathematicians, their insecurities, their worries, the way they think and the depth of their humanity. There is a term ascribed to works that have a clear and beautiful insight into their subjects -- elegance.
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