“Proof” Directed by: John Madden

Starring: Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal and Hope Davis

Running time: 101 minutes

Best suited for: those who appreciate intelligent psych-dramas; Paltrow, Gyllenhall and Hopkins’ fans

Least suited for: the actionadventure freak Acorn’s Rating Guide:

Hollywood often loves to smudge the line between brilliance and insanity. “Proof” is one such blur of reality, a nearperfect psychological drama, a character sketch of rare depth and ambiance. This is the story of Catherine Llewellyn, the daughter of a distinguished mathematician, who has spent her last few years caring for her father, Robert, watching his gradual descent into madness. She must now cope with Robert’s recent death as well.

Catherine is a grad-school dropout who’s inherited her father’s mathematical genius, but Catherine fears she’s also inherited his mental instability. When she begins to converse with her father’s ghost, we wonder if her mind has already begun to crumble.

On the periphery of Catherine’s existence is her manipulative sister, Claire, who’s flown to Chicago from her home in New York for the funeral, and Hal Dobbs, a young and self-proclaimed geek, a protégé of Robert’s who implores Catherine to examine the 100-odd personal notebooks that her father managed to fill during his declining years.

Hal hopes to discover some new facet of Robert’s genius that might have been overlooked or that, with his death, might forever be lost. Her father did have, Catherine admits to Hal, some prolonged lucid moments, as recently as months before his death.

“Proof”—co-written by David Auburn and based on his longrunning play—moves slowly, but with a gradual, methodical intent. For those confident enough to endure a smattering of mathematical jargon with their weekend’s entertainment, you should find a discreetly riveting glimpse into the mind of a tormented young woman who questions her own sanity.

This is a film no less engaging than “A Beautiful Mind” or “Good Will Hunting,” but without the latter’s bar-hopping camaraderie, as Catherine’s existence is one of utter isolation. She is a woman who prefers the comfort of her father’s apparition to the company of the living.

Claire has been spared her sister’s psychological ambiguity, but she is every bit as stubborn as Catherine is fragile. Claire not only wants to whisk her sister away from her father’s rambling brownstone, but also admits that’s she arranged for Catherine to meet with a number of “people” —and one can only assume that Catherine’s incarceration in some upstate psych ward is not far removed. If Claire’s intentions come across as honorable at first, her darting, fake smiles and barely perceptible facial ticks gradually belie her own well-concealed neuroses.

The film takes off when Catherine admits Hal into her father’s inner sanctum, allowing him access to haphazard piles of the mathematician’s unseen work. Hal finds nothing of value, but the two begin to form a tenuous relationship and Catherine ultimately shows him one additional notebook that she’s secreted in her father’s locked desk. Hal realizes that the book is different from the others—that it may indeed contain a rambling yet radically important mathematical formula. He excitedly insists they publish the information for the academic community to ponder.

In a moment of panic, Catherine blurts out that it was she, not her father, who penned the lengthy formulation. But in her delicate mental state, even Hal can’t bring himself to believe that Catherine, an untrained and hardly stable dropout, has penned the equation. Even Catherine herself can’t be certain, and her mind swirls between what is real and what is not.

If there is a missing equation in this otherwise flawless formula, it’s in Hal’s abrupt loss of faith in Catherine—and, later, of Catherine’s in Hal. Until these moments, both characters are so subtly layered in shrouds of rich texture that such outright doubt seems forced, out of place. Granted, “Proof” was originally staged for theater—and one can sense a hushed, collective audience gasp as fragile personalities collapse. But both Catherine and Hal are so nicely portrayed that those few moments come across as loud cymbal crashes in an oth

One’s knowledge of mathematics is as important to appreciating this film as one’s knowledge of statistics is to the recent, superb “Kinsey”—which is to say, not at all. This is less a story of numbers than it is one woman’s search for her own clarity, for her own sanity. Paltrow plays Catherine with a marvelous blend of waiflike frailty and belligerent torment—regret for both her father’s wasted years of mental anguish and for her own instability. But neithePaltrow nor Gyllenhaal play their roles as doomed fatalists, and the film churns and swirls far above melancholyattached always to a slendethread of hope. In a nutshell: For those unafraid to tackle an intelligentemotionally driven and occasionally uncomfortably realistic film, I highly recommend “Proof.” Both Paltrow’s performance and Gyllenhaal’s deserve to be seen and appreciated. And Hopkins, even ethereal, is as guileless as everThis is one terrific film.