Gwyneth Paltrow, in her powerful performance in Sylvia, caught the scary tenor of mental illness the way that Sylvia Plath, in her forcefulness and creeping rage, kept crashing through the fragile foundations of a weak identity. In Proof, Paltrow plays yet another young woman who is being gnawed at by termites of instability, only this time out, her performance, rather than startling, is merely competent: earnest and overly familiar. She's one more depressive mope in dirty lank hair and an oversize wool-knit sweater, whining about how unfair the world is a character who, for all of her meticulously embedded quirkiness, borders on type.
On the eve of her 27th birthday, Catherine (Paltrow), the heroine of David Auburn's thin if celebrated Broadway play, is a nervous, stammering, misfit wallflower who has spent most of her adult life caring for her brilliant mathematician father. Robert, played by Anthony Hopkins in snowy white hair and beard, with an avuncular manner of brainy excitement, did revolutionary work in his early 20s and then suffered a massive breakdown; he may have been institutionalized. He has maintained a casual, on-and-off relationship with reality ever since, and Catherine may or may not have inherited both her father's tendencies: his genius and his insanity.
Proof has been reworked for the big screen, with restructuring and added dialogue, by Auburn and Rebecca Miller, and the director, John Madden (Shakespeare in Love), has opened up the action so that it now flows through airports and Armani boutiques and bustling university corridors. Yet Proof remains one of those clever, facile plays that tries to be ambiguous and tidy at the same time. It's like The Glass Menagerie rewritten by Aaron Sorkin.
The movie opens just after Robert's death, when Catherine, still living in her father's messy, book-laden cocoon of a college-town clapboard house, plays host to two visitors, both of whom she regards, in her muzzy paranoia, as intruders. There's Hal (Jake Gyllenhaal), a handsome young grad student who studied under Catherine's dad and is now looking through his notebooks, searching, amid the psychotic scribblings, for any lost nuggets of mathematical theory he may have left behind. The aspiring prof also plays drums in a rock band, which allows the movie to include at least a scene or two that consists of something other than dolefully dry debate. Then there's Claire (Hope Davis), Catherine's sister, a New York yuppie who, in her patronizing desperation to save her sibling, would like to neaten up every loose end within reach, including...Catherine's hair.
The two have a conversation in which Claire pushes the wonders of jojoba, a substance Catherine has apparently never heard of. It's the sort of pointed stage dialogue that revolves around overly ordered dichotomies: chatty, well-groomed consumer princess versus morose, unkempt academic beatnik. Yet all I could think was, Is Catherine so out of it that she has never even glanced at the label of a shampoo bottle? Proof flirts with hefty themes, yet too often it barely tethers them to a recognizable, lived-in world.
Nosing around Robert's notebooks, Hal doesn't find a lot, at least not until Catherine directs him to a solitary notebook in a locked desk drawer. It contains a visionary proof, a theorem of more than 40 pages that could be the proof, as well, of Robert's restored sanity. Yet did he write what was in the notebook, or was it Catherine herself? And if she wrote the proof, is it also proof that she inherited his gifts, or confirmation that she's doomed to repeat his slide into madness?
The link between higher mathematics and mental derangement had genuine resonance in A Beautiful Mind, but in Proof the connection is far too axiomatic. Auburn withholds key information about his characters, then passes off the missing puzzle pieces as ''mystery.'' In flashback, Hopkins plays Robert as a saint of knowledge, desperate to get ''the machinery'' his grasp of higher numerical systems working. His instability, on the other hand, is portrayed in a cut-rate fashion. Paltrow, speaking in a dishrag whimper, works to give Catherine a tremulous vulnerability, but she lacks the obsessiveness of a numbers-driven personality. The movie turns the issue of who authored the proof into a gimmicky, diminished game of did-she-or-didn't-she?
It's hard to quarrel with the way Proof depicts mathematical genius as an unknowable abstraction. Otherwise, we might need advanced degrees to watch it. If only the film didn't carry that same intellectual shorthand over to its portrayal of mental illness, as though insanity were a light switch that could be flipped on or off. Proof is watchable but second-rate, the minds it depicts too finite to be beautiful.