Let no one who is not a geometer enter here.
According to legend, Plato posted this sign above the door to his Academy in Athens to show just how much he valued the beautiful minds of mathematicians. Judged solely on their performances in the new film Proof, Gwyneth Paltrow and Jake Gyllenhaal might have had trouble slipping past Plato’s bouncer. Anthony Hopkins, in a brief acting turn here, might likewise have needed a designer toga plus all his thespian’s bluster.
Paltrow reprises her London stage role as Catherine, the troubled, depressed daughter so much like her mathematician father Robert (Hopkins) that even their handwriting looks alike. Gyllenhaal plays Robert’s former graduate assistant and Catherine’s current love interest, Hal. But neither Paltrow nor Gyllenhaal really proves to the audience that his or her beauty goes past the epidermal. Indeed the two actors’ physical attractiveness (to us in the audience though not apparently to each other) militates against their success as this particular couple. Paltrow’s Catherine is supposed to be twenty-seven and looks older, though still way too attractive to be a math geek; Gyllenhaal’s Hal is supposed to be twenty-four and finishing his dissertation. He comes across as youthful enough to be conceivably starting graduate school, but way too Hollywood for us to picture him teaching college students, much less writing anything.
Like its source, David Auburn’s screen adaptation of his eponymous play explores the thin line in certain gifted people between productive genius and hopeless insanity. One-upping Russell Crowe’s solitary struggle with schizophrenia in 2001’s A Beautiful Mind (the play Proof actually opened on Broadway in 2000), we here have a case of two minds in jeopardy. Both father and daughter teeter on the all-important divide between mental health and illness, a demarcation at times so fine that it approaches a geometer’s definition of a line: an imaginary construct of infinitesimally small points strung together and extending infinitely in both directions.
It is an interesting proposition to have the great mathematician’s heir apparent a female, burdened with the extra fears of nonconformity that society still imposes on all women and especially bright ones. Father or daughter (or possibly both of them) has written a brilliant new mathematical proof. Will Catherine follow her father’s path to mathematical glory or his descent into dementia? Directed by John Madden — co-creator of her luminous look for Shakespeare in Love (1998) — Paltrow can also channel her experience playing Sylvia Plath. But she does so a bit prematurely in Catherine’s narrative arc.
Hope Davis plays her conformist, disgustingly well-adjusted sister with gloating intensity (“Hope Gloats”). Anthony Hopkins treads heavily as the brilliant but wacko father. In his first scene we see him worried about Catherine’s being alone on her twenty-seventh birthday. His mental absenteeism from her life is evident, however, in his inquiring about a friend she hasn’t seen lately … since third grade.
Auburn and Madden’s efforts to make a talky uniset play “cinematic” are predictable (e.g., shots of characters gazing out from Chicago’s lakefront) but restrained. We begin with a noticeably cinematic exterior shot of a house in the rain, the camera panning over and zooming in to locate a silent figure — Catherine — channel surfing from the sofa. Her face is nearly catatonic, and we suspect immediately that this depression may be more than a routine funk. The mood of futility having been established — there’s nothing like a quick shot of Jimmy Kimmel to telegraph the setup “main character mindlessly watches TV” — Robert (Hopkins) enters causally, POV Catherine, for a buck-up birthday chat, as mentioned above. They banter about her absent friends, her sister Claire. “Claire is not my friend. She’s my sister,” quips Catherine. The banter shifts over into talk of being “bughouse” — family slang for crazy — and whether such craziness is “strictly hereditary” or no. It is a careful setup for Dramatic Moment # One, legitimately lifted whole cloth from the play. Robert mentions he’s crazy, adding, as if an afterthought: “Crazy and dead.”
It’s only at this moment that we realize that we are caught in Catherine’s restricted POV, and that girls who see and naturalistically interact with dead people probably are not themselves 100% hunky dory. Though the surprise revelation also packs a wallop in the stage version of Proof, there’s nothing more seductive than film for conveying a restricted point of view. M. Night Shyamalan, after all, has based a whole career on this insight.
Robert has died from an aneurysm leaving behind 103 notebooks “full of bullshit,” according to Catherine. But we are told he has had (or has he?) occasional lucid moments — even moments when he could return to his proof-making profession. This means each now-posthumous jotting needs to be checked for brilliance, a process that has been eagerly undertaken by Hal (Gyllenhaal). Catherine suspects handsome Hal’s motives and honesty, especially after he starts coming on to her. Is he out to steal gold nuggets he may find in the dreck of dementia? He admits himself to being a second-rate mathematician: “The Big Ideas aren’t there.” We suspect Hal of being a Salieri figure who has glommed onto a true mathematical Mozart (Robert and/or Catherine) for career-building purposes.
After Hal’s departure, enter Claire the Good, Sane Sister who has turned her hereditary gift for numbers into a career in currency analysis. Davis is perfectly prissy, competent, and bustling. Engaged to a man named “Mitch” and determined to condition her lackluster sister’s hair, Claire swears by Jojoba and mood-altering shopping sprees. Wearing a marvelously character-revealing textured lavender coat, Claire forces her moody stay-at-home sister out to shop for a dress for Daddy’s funeral. Claire’s overly lengthy inquisition about Catherine’s lifestyle, improbably set in a trendy clothing store, is one of the few false notes in an otherwise competently acted (if poorly cast) film.
Catherine indeed buys and wears the little black dress, albeit hidden under a denim jacket at the funeral proper. She interrupts the stodgy proceedings — a colleague intones that Robert’s “work will endure” — with decidedly disruptive remarks such as “He stank … I had to make sure he’d bathe … ” and “I’m glad he’s dead.” These are not the filial eulogy remarks of a happy, well-balanced camper.
Later at the wake, the liquor flows, and the little black dress — now free of its denim cover-up — has a chance to work. Catherine and Hal become lovers: he tender, she fragile. Besides yielding up her figurative chaste treasure, she gives him the key to a drawer where he finds another notebook, this time full of academic gold.
“It’s a very important proof!” Hal jubilates. He asks her where she first found it. It’s a setup line for Dramatic Moment # Two — again borrowed directly from the play.
“I didn’t find it,” says Catherine. “I wrote it.”
The problem for the remainder of the film is “Who wrote the proof?” and “How can he or she prove it?”
There’s another good use of specifically filmic technique to flashback to Robert’s time of relative lucidity, back when he was still alive and under Catherine’s care. We arrive, POV Catherine, at home one evening to a deadly silent house. Out in the snowy backyard, with snowflakes still falling about him, sits Robert “on fire” with inspiration despite the 30-degree chill. Our relief at locating him, like Catherine’s, is palpable. He insists that she read aloud, right there in the snow, the marvelous proof he has been working on. She reads.
Earlier in the film we have heard the pithy statement, “Mathematics isn’t jazz.” And we are certainly not meant to mistake Robert’s febrile rantings — e.g. “The future of heat is the future of cold” — for mathematics. He has truly lost his beautiful mind. But perhaps the master mathematician has merely found a new calling: novice poet.
The beauty of this film is its careful equipoise between outmoded disciplinary boundaries and … perhaps just perhaps … some wonderfully creative interdisciplinary future. Maybe mathematics is more like jazz than we thought — irrational numbers for irrational souls. Postmodernism, along with its talking critical partner deconstruction, makes us rightly question whether anything can be proven. Proof (with a capital “P”) gives way to lowercase proofs; just as Truth (capital “T”) gives way to truths. There are, of course, older precedents for this view of art as science and science as art. Thomas Mann — the twentieth century’s master of dangerous Faustian terrain — looked at the problem of Dionysian madness and illness coupled with Apollonian reason in genius philosophers such as Nietzsche and musicians such as Arnold Schönberg. The French Symbolists and many Romantics certainly trod the boundary between brilliance and dementia. Playwright Auburn, in tune with the popularity of science and technology in the movies and corporate America (cf. Good Will Hunting, 1997 and others), simply makes his Faustian strivers — his dancers on the thin line between genius and insanity — “mad” mathematicians.
We have always known that real genius knows no boundaries of discipline, age, or gender. Despite the unconvincing pairing of Paltrow and Gyllenhaal, this film succeeds in offering welcome proof of this old/new truth.
Quod est demonstrandum. Q.E.D.