If you come to the movie Proof as I did, not having read or seen David Auburn's Pulitzer Prize-winning play, you may enjoy the first half as a melancholy romance streaked with humor. After all, it seems to be about a female math whiz (Gwyneth Paltrow) emerging from grief over the death of her addled math-genius dad (Anthony Hopkins) with the help of one of his former grad students (Jake Gyllenhaal).
Director John Madden and the screenwriters, Auburn and Rebecca Miller, sketch in the Chicago academic-math milieu with light poetic strokes, like Gyllenhaal's belonging to a band that "plays" a three-minute silent number called "i" - for "imaginary number." Math registers as numerical jazz - lively, improvisational, sexy.
Instead of introducing the usual romantic complications of a boring and determined rival, the filmmakers provide a meddlesome sister (Hope Davis) who wants to whisk Paltrow away to New York. Davis developed a professional and personal life while Paltrow stayed in Chicago and gave up everything to care for their helpless father.
Davis is wonderful. After her grungy turn in American Splendor and her dissatisfied middle-class wife and mother in The Secret Lives of Dentists, she proves her versatility yet again, wringing every possible laugh out of a character living by checklists and viewing muddle of any kind as a sign of potential instability.
Paltrow (at first) matches her - she brings a mulish strength to her usual swanlike profile. Even her whine has a resonance that makes her register as comic heroine, not potential victim. She's marvelous when she laments that Davis has swept in with "bagels and bananas and jojoba and `Come to New York' and vegetarian chili."
Gyllenhaal displays an easy masculinity, and Hopkins, in an opening fantasy sequence, is refreshingly chipper and restrained.
But just when you're ready to see Paltrow and her new and true love, Gyllenhaal, battle the conventional Davis and emerge triumphant, the movie becomes a trumped-up melodrama about how difficult it is to prove you're sane when everyone else believes the opposite. The trigger for this sad development is a brilliant proof that Paltrow says she wrote herself, though she dropped out of Northwestern's math department years before. (A proof is "a logical argument that establishes the validity of a statement.")
This mathematical breakthrough becomes a test of faith for Gyllenhaal, and evidence for Davis that her sister has inherited their dad's mental imbalance. The filmmakers use this gimmick as an excuse to sketch, in flashback, the increasing isolation and stress that comes from being the only caregiver for a parent. They go for pathos, with a vengeance.
Still, you never believe that Paltrow's character is insane, even when she herself does. She has too sturdy a core. Maybe that's what the play's fans mean when they say she's been miscast. I think the problem is that Auburn misjudged his own talent and sabotaged what could have been an unusual - and satisfying - comedy.
Starring Gwyneth Paltrow, Jake Gyllenhaal and Anthony Hopkins.
Directed by John Madden.
Time 99 minutes