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PLOT: A young woman attempts to understand her own life and her future in the aftermath of her father's psychological decline. There's a mystery at the heart of the story, to be sure, but this is pure character study.
Dad's crazy, and as for his daughters, Catherine speaks to the dead and Claire obsessively makes lists of everything. You can do the math.
Or can you? Proof is a story about a woman's struggle to understand who she is and where she's going, given that her life has been led very much in the shadow of her genius father.
Robert (Sir Anthony Hopkins) is a brilliant mathematician, a man whose discoveries early on in his career gave him an international reputation.
But Robert struggles with mental illness, and in middle age the symptoms of schizophrenia have overwhelmed his life. His bright daughter Catherine (Gwyneth Paltrow) has given up her university studies to stay home and care for him.
Her sister Claire (Hope Davis) thinks it's time Catherine left their childhood home and came to live with her in New York. What Claire doesn't much talk about is her suspicion that Catherine may have inherited much of their father's madness.
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That Catherine may also have inherited dad's genius for mathematics is another element in the story.
Proof is an intense investigation into the nature of various relationships -- with work, family, love. All the events in the story are vaguely ambiguous and the characters are rather suspect in some crucial way: For example, Jake Gyllenhaal plays a student of Robert's and he's also attracted to Catherine, although she wonders if it's just her father's work he's after.
Likewise, Catherine herself is either going mad or else she's got a unique relationship with the truth.
And Claire, the bossy sister who has embraced a Martha Stewart-like domestic life, is either a caring older sibling or a jealous controller. It's not that simple, of course, but there is a layer of betrayal in Proof and the characters are such that it actually puts you on edge watching this thing resolve itself.
A Proof in the world of mathematics is a certainty, a formulation in which a hypothesis can be proved by mathematical deduction to be true. (You may be very sure we had to borrow that last sentence from people who understand this sort of thing.)
Proof concerns the less-certain world of the emotions, and the ways we look for meaning and certainty in that area of life. Catherine, more than once, makes an important distinction between mere evidence, and proof.
The narrative moves back and forth between past and present in this story.
Parents and children swap roles with the passage of time. The performances are astounding; Hopkins and Paltrow together will break your heart.
Prior to making the film, Paltrow played this role in Proof on the stage. As well, she is directed here by John Madden, who directed her Academy Award winning performance in Shakespeare In Love.
It adds up.
BOTTOM LINE: Based on the highly successful stage play, this is a story about family, love, betrayal, madness and mathematics. The performances are all just about perfect.
(This film is rated PG)