Simply put -- and there's really no complex way to put it -- Proof tells the story of a morose young woman who fears she may have inherited mental illness from her father, a University of Chicago mathematician who made three landmark discoveries in his 20s, and who spent the time after that losing his mind.
We meet Catherine (Gwyneth Paltrow) on the night of her 27th birthday. Her dad (Anthony Hopkins) shows up for a visit, they chat a while, she pops the cork on his gift of cheap champagne, and he reassures her that as long as she can ask the question, she's not insane. Then he reminds her that he's dead.
This revelation comes as no surprise to us. Nor does much else in Proof, an adaptation of David Auburn's Pulitzer Prize- and Tony-winning play, directed by John Madden (Shakespeare in Love), and starring Madden's erstwhile blithe Shakespearean muse.
I didn't see Proof on stage, but I'll have to assume that Madden and Auburn stripped it down for the screen, leaving us with a love story, a family drama, some mathematical metaphors, and a central question that it pretends a bit too coyly not to answer. By the time the film ends, it doesn't really matter whether Catherine will go the way of her father. All that matters is that she and Hal will give it the old college try.
Hal is Harold Dobbs (Jake Gyllenhaal), her father's former grad student and now a young professor. He's known and desired Catherine since his doctoral days, and in the aftermath of her father's death, he's slogging through the old man's notebooks filled with copious scribbling, hoping to excavate a final great idea. When he discovers it, it's more than just genius: It's revolutionary. And, says Catherine, it's hers.
Did Catherine really come up with this proof, or does she merely think she did? Did she inherit her father's gift for numbers as well as his DNA for insanity? The question intrigues, although the answer satisfies a bit too much. Proof emits only the faintest whiff of science nerd when it should be thoroughly redolent with it: The script begs for more discussion of the relationship between our genotype and our phenotype, between numbers and the incalculable equation of the human heart. It's a smart and enjoyable movie, but it's also much too easy to work out with a pencil.
At its better, Proof explores a relevant life circumstance: Catherine gave up her youth to care for her sick father, and it takes a toll on her future and her sanity. This doesn't happen only in the rarified world of university mathematicians, and it plays out in Proof with poignant authenticity. Another layer of good drama begins with the arrival of Catherine's older sister, Claire (Hope Davis), who acts more like her mother. She makes lists of things to do, and she crosses them off as she does them. One of the things on her list is Catherine.
Madden balances plot, character and dialectic well in Proof, moving seamlessly from one element of the story to another. He opens things up visually, although virtually every moment of his film still feels like a scene from a play. At the end of act one, the figurative curtain falls so conspicuously that I almost felt obliged to go stand in line at the men's room.
Madden tweaks beautifully concise, intelligent, subtle performances from his three younger stars. As always, Paltrow's nasal voice takes some getting used to. But I guess that's just how she sounds, and at times in Proof, she's fiercely tragic and persuasively lost in her anxiety about Catherine's wobbly state of mind. Gyllenhaal, too, has a quirky voice and an earnest charm as the best-looking geek on the junior faculty, a drummer in a rock band made up of mathematicians whose most notorious original song is several minutes of silence. Best of all is Davis, an actress who can be delicate and ferocious in sublime unison. From the moment Claire enters the story and offers Catherine some coffee and a banana, you'll be ensorcelled by her cool, officious, doting menace.