As John Madden says, the film's central issue is 'validation', in emotional and familial, as well as mathematical and metaphorical, frameworks.
ProofDirector: John Madden
Cast: Gwyneth Paltrow, Jake Gyllenhaal, Anthony Hopkins, Hope Davis
MPAA rating: R
First date: 2005
US DVD Release Date: 2006-02-14
Sometimes in my head I think it works, and then sometimes, I think it's just crazy.
-- Catherine (Gwyneth Paltrow), Proof
In order to tell the story in the film cinematically, you needed to make a creative tension between the information that was available from the narrative in the past and the information that we were getting from the narrative in the present.
-- John Madden, commentary, Proof
"Beginnings of films are interesting," muses director John Madden as rain drops onto scenery in the early moments of Proof. "The way the information first hits an audience, I think, is always pretty critical. You're waiting to understand the terms, the rules, the conventions, somehow." The camera pans through the rain to a house exterior, where inside, a tv blares, channels flipping: something that fights stains, something "designed with women in mind," and Jimmy Kimmel. The images are terse and abstract, making their point in a way that suggests Madden doesn't need to explain what he's explaining. It seems obvious. "I just wanted to create a sense of blankness," he says, "a sort of clean slate... just a mind drifting."
But a cut to the sad face of Catherine (Gwyneth Paltrow) makes you look again, and the dreary wet night clichés shapeshift into another set of "terms." She looks more defeated than adrift, lit blue by the tv. A brief flashback shows Catherine in happy golden light, riding her bicycle with big smile and hair pretty in the breeze, and clarifies Madden's point by contrast. She was once this other way, and now she remembers it. "That," says Madden on the DVD commentary track," allows me to introduce a kind of problem I suppose, is one way of putting it, like a contradiction, which is what this colorful world, which is about energy and movement, has to do with this monochromatic world, which is about blankness and stasis, and somebody not able to move forward or backward, and also sets up this language which is going to be used much later, which is moving forward and backward in time."
While this movement is occasionally clumsy in Proof, adapted from David Auburn's play (directed on the London stage by Madden, starring Paltrow, a collaboration that he says he initially suggested as a means for Paltrow to explore her terrific acting "instincts"), it can also be provocative. Though the DVD's other extras (three deleted scenes and the nine-minutes-long "From Stage to Screen: The Making of Proof") are not so enlightening, the director's commentary track complicates the text and enriches the context.
Proof's premise has to do with Catherine's state of mind following her father's death. A brilliant, renowned, and insane mathematician, Robert Llewellyn (Anthony Hopkins) admits that he's crazy, even while asserting that he could never have admitted same while alive. In his first scene, a conversation with Catherine, he reminds her that he is, indeed, dead. Oh, she pauses. But still, this is not proof of anything specific, is it?
Throughout the film, Catherine struggles with her relationship to Robert, his legacy (personal and professional) and her memories of him, helped along by his former student, the very enthusiastic Hal (Jake Gyllenhaal), who asks to pore through Robert's 103 notebooks in search of his last great work ("I'm prepared to look at every page"). Catherine resists, observing that her father was a graphomaniac, that the pages are likely filled with "bullshit," and that he has to be "crazy" to want to read them.
While Catherine and Hal haggle over the notebooks (and he invites her to come see him play in his rock band, made of math students -- an outing that involves sensual as well as intellectual pleasures), the camera frames them to show distance and impending intimacy, set against Robert's full bookshelves and fluttery curtains and piles of papers. Describing his decision to use an "observational style" for the film, Madden says he toyed with the idea of using a handheld camera, but thought this typically more subjective mode would be "too intrusive." Aware of the risks of transferring a play to the screen (the tendency to imitate the proscenium arch, for instance, with actors hitting marks), he says the steadicam work "is keyed, really, to the kind of provisional state of mind she is in. it's a very subtle thing, but it lends a kind of quality of immediacy." Such immediacy makes "proof" -- of loyalty and love, perhaps -- feel fragile. Proof in the film is mathematical and documentable. It is also a matter of faith.
This is Robert's word for it. A genius who completed his own math-world-shattering work while in his 20s, Robert spent much of his later life writing out elaborate proofs about winter weather and his internal chill. While Catherine's sister Claire (Hope Davis) lives in New York City with a husband and a career, Catherine stays behind, tending to her father. Showing her own mathematical aptitude and a little lack of focus, she's worried now that she may have inherited her father's tendency to insanity.
In the sisters' relationship, Proof takes up questions of trust and doubt, grief and guilt, ambition and selfishness, competition and resentment. Claire, observes Madden, is "perhaps the character most susceptible to satire... She's the source of a huge amount of the humor in the piece, because of her tendency to mythologize herself." As she felt "the less preferred sister," she left Chicago, "terrified of illness and terrified of the madness that engulfs her father."
As Madden says, the film's central issue is "validation," in emotional and familial, as well as mathematical and metaphorical, frameworks. The film's central problem is the revelation of a proof, not quite elegant but exceptional and potentially math-world-changing, locked in drawer in Robert's home office. This "very important proof," says Hal, was written during a period shown in flashbacks, as Robert and Catherine worked on a problem, separately and at the same time, each writing out pages of proof, working late into nights and bent over desks in deep concentration. As their handwriting is similar, it's unclear whether the newly discovered proof is Robert's or Catherine's. She claims it is hers, but neither Hal nor Claire quite believes it. And so the film presents a knot of questions.
For all the nuance in this knotting, the film leaves the sisters caught up in a standard conflict, born of Claire's controlling inclinations and Catherine's alternating modes -- drift or explosion. Claire wants Catherine to move east with her, but Catherine doesn't want to deal with her jojoba and vegetarian chili. And then Catherine begins to disbelieve herself. Maybe, she worries, she is incapable of asking herself whether she's crazy, which might be all the sign she needs that she is.
Proof asks serious questions, probing the concept of sanity and the social categories imposed on subjective states. It suggests that sanity is a set of norms and expectations as much as it designates mental or emotional health. It suggests the distinctions between sanity and insanity might be fine and shifting, not fixed, and certainly not orderly. But as it asks you to believe in Catherine's claim to brilliance (visually, it tends to support her perspective, in her flashbacks as well as in her present interactions with Claire and Hal), Proof leaves little to your own figuring, not quite trusting you to be comfortable with irresolution or inelegance.