Gwyneth Paltrow (Left) and Jake Gyllenhaal (Right) star in Miramax Films’ ‘PROOF.”
Photo Credit: ©2005, Miramax Films.

 
“Proof” opens looking in on a house at night. It’s raining outside, and the television is on. The window is cloaked in rain, obscuring the interior a bit. The scene cuts to the interior and reveals Catherine Llewelyn (Gwyneth Paltrow) flipping channels—sometimes the television’s. The scene abruptly changes to a university. Catherine bumps into someone, but before she can see who it is, her father, Robert (Anthony Hopkins), wakes her up. It’s her 27th birthday. They debate over her going out and doing something to celebrate.

Catherine and her father discuss his mental stability, the symptoms of which (as he recalls) started around the same age as she is now. He tries to reassure her, but she doesn’t believe him.

As I’m writing it, this description seems to give the impression of a disjointed beginning. It is. She feels confused, unable to tell apart her memories from her present reality. They are, in fact, so haphazardly jumbled (intentionally) that the viewer begins to feel the same disorientation that Catherine is experiencing.

She meets one of her father’s protegés, Hal (Jake Gyllenhaal), who is trying to track down any traces of critical research her father may have been conducting. Hal is a bit off, in a likeable way. He plays in a band made up of math nerds who, among other achievements, have recently penned a song called “i” (as in “imaginary number”). Think John Cage, but one minute and thirty-three seconds shorter.

She begins to suspect that Hal might be trying to steal her father’s work and take credit for it. When Hal is about to leave, she asks what he has in his backpack. They argue about it.

“Just because I’m paranoid doesn’t mean there isn’t something in that backpack,” says Catherine.

Catherine doesn’t seem crazy. She seems a highly-disorganized, yet brilliantly observant mind. I’m reminded, in a way, of something my college history professor, Mr. McCormack, told me. His office looked like a tornado (as did Einstein’s). He wryly explained, “But I know where everything is.”

That’s Catherine. She understands her life, her own sense of space and time. She’s very intelligent and consequently pragmatic—at times too much so. Her sister, Claire (Hope Davis)—extremely organized (she lives by her daily planner), obsessive—comes to attend the funeral. Catherine doesn’t care much for Claire’s self-obsession and perverse fascination with what is mundane in the grander scheme of the workings of the physical world. Claire is a “sophisticate,” or so she believes. Catherine, on the other hand, doesn’t bear the urge to engage in mindless and superfluous conversation simply for the sake of being social. When she tries to encourage Catherine to take better care of herself, Claire’s idea of doing so boils down to jojoba oil.

“It’s organic,” Claire says.

“It can be organic and still be a chemical,” retorts Catherine.

Catherine also explains that hair consists of dead tissue. How much “rejuvenating” effect can a hair product have on something that’s already dead?

Despite the dermatological oversimplification, I had to smirk at this because I’m very fond of the sciences and the rational thought process they encourage. I can relate to how terribly inept Claire’s product marketing-influenced screeds sound to Catherine. It also reminds me of a scene in “Little Man Tate” where Tate’s teacher asks the class how many numbers between 0 and 10 are divisble by two. It’s a humorous yet simultaneously depressing realization when Tate’s teacher is confused by his precocious response, “All of them.” Like Tate, Catherine is more troubled than enthused by her own intellect.

After a strange experience that began with a call to the police and ended with Hal’s band playing at a reception organized by Claire for friends of her and Catherine’s father, Claire provokes Catherine about what actually happened with the police. They recall vague details we, the audience, have not seen. She and Claire get into an argument over her condition. There are juxtapositions of different events throughout parts of the film that give the viewer, perhaps, a sense of what it’s like to be experiencing mental instability.

I find myself quoting a lot of lines in this film. Perhaps it’s because I haven’t heard well-conceived dialogue in so long. The dialogues here are key to understanding the mindset of these particular characters.

“Even your depression is mathematical,” intuits Robert. “Stop moping… do some work!”

Robert’s machinery, as he calls it, is his mind. When the machinery breaks down, he begins to ramble confusingly. This is a role for which Anthony Hopkins is well suited because his skill at rapid-fire delivery can pass simultaneously for intellectual exuberance and mental chaos. You are left, at times, to sort it out.

One thing I liked about this movie is the way in which the plot turns and delivers its revelation. The story is peppered with some hints along the way, and then the surprise drops very abruptly. The surprise, however, is not the point. It is the catalyst for some character development that constitutes the real substance of “Proof.” Had the buildup to the surprise been lengthy, a viewer might guess it anyway and miss the greater point of the film—the character study.

“Pi” and “A Beautiful Mind” only dabble in scientific method and never fully explore it. In “A Beautiful Mind,” the brilliance of Nash’s life’s work, his “Equilibrium Theory for Strategic Noncooperative Games,” for which he won the Nobel Prize, is worked into just one scene. “Proof” doesn’t attempt to feebly introduce a complex mathematical concept and then abandon it right when it gets interesting. It instead deals in the larger principles and philosophy of science and mathematics in a story whose central focus doesn’t rely upon the audience’s buy-in to the intricate details of any particular mathematical construct. The “proof” being tested in this film concerns Catherine’s own self-confidence amidst the double-shadows of her father’s sublime, yet mentally disturbed, genius–traits that she laments because they often smothered opportunities for a genuinely compassionate father-daughter relationship. Everything about Robert was methodical, calculated, like an equation.

There are two equations in this film that are to be solved for “x”. One missing variable is any fraction of her father’s work that may have harnessed his brilliance despite his long period of mental illness. The other is the question of whether or not Catherine has her father’s talent for mathematics, or his madness. It makes me wonder. There are so many geniuses throughout history whose minds were bursting at the seams. Is insanity a side effect of immense genius, or vice-versa?

A recurring theme in “Proof” is the scientific method. Though there are slightly differing definitions for a mathematical proof, and the term “proof” in the empirical (observable) sciences, they are related by the way in which they are substantiated: Falsification. Falsification is central to a proof. That is, if all attempts to disprove the theory have failed, then it is substantiated. In principle, this also means they can attempt to disprove the opposite.

Professor Bandari (Roshan Seth), Catherine’s graduate thesis supervisor, tries to harness her scattered genius.

“Mathematics isn’t jazz,” he says. He misses the point. Catherine, in one scene, described to Hal how her father would approach complex mathematical equations from oblique angles. The improvisational and fluid nature of jazz is precisely the metaphor for Catherine’s approach to mathematics and life. Life doesn’t always present us with finites and constants. So, maybe Catherine’s way of dealing with her own uncertainties is to remain fluid and improvise as she goes along. Can you disprove that it works?