The play takes place on the back porch of a house belonging to the math professor, Robert. Located in the Hyde Park section of Chicago--the neighborhood that is home to the University of Chicago--the house reflects the condition of its owner. A handsome old building, large and dignified, parked in the middle of a thriving university community, it has become shabby and disheveled, a local eyesore. Like the dotty chemistry professor who stands out so vividly in David Auburn's memory, this house is both picturesque and disquieting. And as the play begins, has become a kind of mausoleum-in-the-making for Catherine, who, it seems, plans to remain there for the foreseeable future. And the house becomes the focus of conflict when Claire announces her intention of selling it as a way of jolting Catherine out of her mental and spiritual torpor. As the play ends, however, she and Hal seem to be agreeing that, old and drafty though it be, it is a "nice house," and one that might in fact make a home for a mad professor's sane daughter.
The play begins on the eve of Catherine's twenty-fifth birthday, which she is quietly celebrating with her father, Robert, a brilliant mathematics professor at the University of Chicago. Catherine lives with her father, in the same house where she grew up, and where she has become Robert's caretaker, sacrificing, as many daughters do, her own life to the needs of a sick parent. As they fumble with a bottle of champagne, we learn that Catherine has been experiencing a string of listless days and nights and exhibiting symptoms of what may be the onset of the insanity that derailed and eventually destroyed her father's career. She is now at the age when the disease began to afflict Robert, and she shares many of his personality traits, particularly his freakish talent at math. As Robert tells her, "You knew what a prime number was before you could read."
While she is nearly paralyzed with anxiety over the possibility of her impending breakdown, her father tries to reassure her that she is demonstrably sane. After all, he reasons, she is asking herself whether she is losing her mind. By contrast, "A very good sign that you're crazy is an inability to ask the question, 'Am I crazy?'" Ever the logician, his daughter catches him up on the flaw in his argument. If, as everyone knows, Robert is crazy, and if he also questions his sanity, then merely asking the am-I-crazy question proves nothing. (This bit of reasoning is, in fact, the first "proof" in the play.) But Robert trumps his daughter with an irrefutable rejoinder. The reason he can admit he's crazy is not because he is sane, but because he is dead, and has been for a week.
With this shocking bit of exposition we move into the second half of the scene, wondering to what extent Catherine's conversation with a dead man demonstrates her madness. After all, she could simply be dreaming, as we all do, about a loved one who has passed on. Nothing crazy about that. Or she could merely be experiencing a waking fantasy, a kind of daydream, especially vivid perhaps, but not necessarily insane. Or she could be having a psychotic delusion. Which is it? The rest of the play is spent answering this crucial question.
Before Robert disappears, we learn that his funeral is to be the next day, and that his other daughter, Claire, is flying in from New York to join her sister for the ceremony. That Catherine's birthday coincides with her father's funeral raises pressing questions. Does it suggest that her father is putting a curse on her, bequeathing her his madness as an inescapable consequence of her birth? Or does it mean that Catherine is about to make a fresh start, passing from under her father's shadow into a new life of her own? Robert's parting words are not reassuring. "For you, Catherine," he says, the fact that she has been conversing with a ghost, "could be a bad sign." And with those disturbing words, he departs.
To be followed onstage immediately by Hal, one of Robert's former graduate students who has been sorting through his professor’s papers upstairs in the study. Hal adored Robert, whose advice put him on "the right track with my research" when he was "this close to quitting" his work on his Ph.D. He is awestruck by Robert's professional accomplishments, reminding Catherine that when her father "was younger than both of us he made major contributions to three fields." Thus, he is determined to sift every shred of paper Robert has left behind on the slim chance that he will find even a morsel of brilliance. So far, sadly, he has found nothing but gibberish, the worthless scraps of Robert's insanity.
Hal plays in a mathematicians' rock band, thus giving the lie, he says, to the stereotype of the math student as "geek, nerd, wonk, dweeb, Dilbert, paste-eater." On the contrary, Hal seems charming, friendly, concerned about Catherine's well-being, and even a bit flirtatious. Indeed, he invites her to join him at the bar where his band is playing just to get her out of the house that is so haunted by memories of her father.
Catherine is skeptical of this attention. She has no desire to have a stranger rooting around in her father's papers, especially not a worshipful ex-student who knows nothing about the grim facts of Robert's madness and her thralldom to it. Moreover, she suspects that what Hal really wants is to find an undiscovered idea which he can filch and pass off as his own in order to further his academic career. In fact, she is so distrustful of Hal's motives that she insists on searching his belongings before he leaves to assure herself that he is not stealing one of Robert's notebooks. Perhaps, she thinks, he has found some bit of legitimate work produced in one of her father's rare moments of sanity.
Hal reacts with a mixture of indignation and condescension, resentful of Catherine's suspicions, and dismissive of the idea that a layman like her could even recognize legitimate work if she saw it. Enraged by his skepticism about her knowledge of math, she tears open his backpack--and finds nothing incriminating in it.
This momentarily dispels the tension between them, and Hal resumes his efforts to make friends with Catherine, inviting her to join him during his daily jog along the lake. Catherine remains resistant to his overtures, though less frostily that earlier. As he is on his way out the door to catch up with his rock band, she hands him his coat, out of which falls one of her father's notebooks.
Hal tries to explain that he took that particular document, not because of its mathematical content, but because it contains a long entry in which Robert praises and thanks his daughter for the care she has given him and for the sacrifices she has made on his behalf. That entry is dated exactly four years earlier, on the eve of her turning twenty-one. Hal, he says, had planned to wrap it up and give it to Catherine on the following day, a posthumous birthday present from her dead father. But Catherine is so enraged by the idea of Hal's theft that she calls the police to report a robbery. As Hal leaves, placing the notebook in her hands, police sirens are wailing outside, and a weeping Catherine has buried her head in her hands.
The next scene begins on the following morning as we meet Claire, Catherine's sister, freshly arrived from New York. "[S]tylish" and "attractive," focused, efficient, cheerful, Claire seems the complete opposite of the disheveled and distraught Catherine. She repeatedly asks Catherine how she feels, plainly concerned that her sister is succumbing to their father's illness. She asks disbelievingly about Hal, who she seems to think might be merely a figment of her sister's imagination. And she proposes that Catherine leave Chicago and join her and her future husband in New York. Catherine is quick to see this idea as a way of putting her under her sister's surveillance, perhaps even as a first step to committing her to a mental institution. And so she bursts out in a resentful response:
I really don't need this, Claire. I'm fine, you know, I'm totally fine, and then you swoop in here with these questions . . . . I mean it really pisses me off so just SAVE IT.
At which point Hal has arrived on the scene, vindicating at least one element of Catherine's account of her life, and ending the scene.
Robert's funeral is over, night has arrived, and inside the house, as Scene Three begins, a post-funeral party, organized by the ever-buoyant Claire, is in progress. Catherine and Hal are talking about the eccentricities of mathematicians and the peculiarities of the profession. "Mathematicians are insane," Hal says, and mathematics is a "young man's game . . . your creativity peaks around twenty-three and it's all downhill from there. Once you hit fifty . . . you might as well teach high school." Now past twenty-three, and conspicuously not a man, Catherine it would seem is definitely beyond the pale of mathematical distinction. She does know of one woman renowned in the field, Sophie Germain, about whom her father once gave her a book, and has memorized a famous passage from it about women and mathematics. When she quotes it Hal, a little drunk, kisses her. And as the scene ends Catherine is kissing him back and conceding that he seemed, when she first met him, "not boring."
The following morning, having slept with Hal, Catherine gives him a key to a drawer he has yet to explore in her father's desk. As Hal eagerly runs off to see what it contains a badly hungover Claire arrives to inform Catherine that she is selling the family house, leaving Catherine no choice but to come to New York and live under her wing. As the sisters quarrel over this development, Hal returns to announce that in the drawer he found a notebook containing "a very . . . important . . . proof . . . [of] a theorem . . . a mathematical theorem about prime numbers . . . something mathematicians have been trying to prove since there were mathematicians, basically." This proof, he declares, is "some of the most important mathematics in the world" and it was done when everyone assumed that Robert was insane. To which Catherine objects that Robert's sanity is irrelevant since in fact she herself is the author of the proof, ending Act I with a major revelation.
Act II takes us back four years, to Catherine's twenty-first birthday. Catherine has decided to take up the thread of her own life after having devoted herself up to now to her father's well-being. Convinced that her father has recovered, she has enrolled at Northwestern University, where she will resume the study math in a matter of weeks. Robert is surprised and hurt, and he begins to argue with his daughter about the wisdom of her decision, at which point Hal, then Robert's student, arrives. They suspend their argument, Robert counsels Hal on his graduate school woes, and eventually he and Catherine decide to celebrate her birthday by going out to dinner. As she gets ready to leave, Robert begins an entry in his journal--the entry Hal discovers four years later expressing his love and gratitude for his daughter's years of care. What we learn from this scene, then, is that Robert's illness has stood in the way of Catherine's aspirations as a mathematician, but that as recently as four years ago, she was determined to pursue her professional aspirations.
The next scene returns us to the present, "an instant after the end of Act One" following Catherine's blockbuster revelation that she, and not Robert, is the author of the mind-boggling proof Hal has just found. Her claim, it seems, it too improbable to be believed. "[T]here's no proof that you wrote this," Hal declares, pointing out Catherine's amateur status as a mathematician, her lack of formal training, and the fact that the handwriting of the document closely resembles her father's. Above all else, it is inconceivable to him that a young woman who took a few courses in college could have equaled the achievements of a man who "was the best," who "revolutionized the field twice before he was twenty-two." Stunned and furious, feeling absolutely betrayed by the skepticism of a man she has just slept with, Catherine tries to rip the pages out of the notebook and destroy the proof. Claire struggles to wrest the precious document from her, and as the lights fade on the scene, Catherine throws the notebook to the floor and stalks off.
The next day Hal returns to beg Claire to give him the manuscript so he can have his colleagues at the University analyze its content in an attempt to determine its author. Reluctantly, Claire agrees, and Hal leaves bearing the precious notebook.
The scene switches back again to the past, this time about three and a half years earlier, following Catherine's first semester at Northwestern. She returns home to find her father sitting on the porch in mid-December. He claims to be overheated from the working of his brain, now feverishly operating on mathematical problems since his sanity has returned. He begs Catherine to return home to work with him, and by way of persuading her, hands her one of his notebooks containing his most recent efforts. When she begins to read it, however, she discovers it is all nonsense, and that her father has fallen ill again. She will indeed have to return home, but not to do math.
Back again in the present, a week after Hal has taken the manuscript containing the proof, Claire and Catherine are preparing to leave Chicago for New York. Catherine has apparently surrendered to her sister's plans, and is listlessly succumbing to a future of dependence. At this point Hal arrives. Having closely analyzed the proof, he now understands that it works. But more momentously, he is convinced that it is indeed the work not of Robert but of Catherine. As he explains, the techniques used to solve the problem involve ideas and methods only recently developed--too recently for Robert in his condition to have known about them, much less made brilliant use of them. Catherine at first is unforgiving of Hal's previous skepticism. But little-by-little, Hal elicits her forgiveness, and persuades her to hold on to the house, and to stay in Chicago and do mathematics. Finally they begin to work together, refining the proof, both convinced that Catherine can stand on her own as a mathematician and a sane human being.
CATHERINE. Near the end of the play Catherine and Hal have this brief exchange:
Much of what makes CATHERINE tick is contained in those four lines. She is emphatically her father's daughter, having inherited his mathematical genius. But she is also terrified of being swallowed up by her father through the other inheritance--his madness. Robert's legacy to Catherine is simultaneously a gift and a curse, and caught between the conflicting terms of this bequest, she finds herself paralyzed by fear at the beginning of the play. Like Hamlet, she has a "to-be-or-not-to-be" problem: in her case, the question is whether she will become her father.
As Robert's ghost reminds her in the first scene: "You sleep till noon, you eat junk, you don't work, the dishes pile up in the sink. If you go out it's to buy magazines. . . . And those are the good days." He chastises her for "the work you lost, the ideas you didn't have, discoveries you never made because you were moping in bed at four in the afternoon."
Given these symptoms of incipient break-down, she is understandably appalled by her father’s legacy. Perhaps this is why she hides her brilliant proof in a locked drawer at the bottom of Robert’s desk—as an act of sympathetic magic. If she buries the talent left by her father, she will also bury the madness that goes with it.
As Hal notes, madness does seem entwined with mathematical genius. And Catherine knows only too well what it means to be insane. Her whole life has been devoted to nursing her sick father. As she tells Hal, "I spent my life with him. I fed him. Talked to him. Tried to listen when he talked. Talked to people who weren’t there . . . Watched him shuffling around like a ghost. A very smelly ghost. He was filthy. I had to make sure he bathed. My own father.” Traumatized by this experience, dreading the possibility that she will turn into another such wretched figure, she withdraws from life. She has no friends, no contacts outside her father’s broken-down house, no career, no social world of any kind.
Until Hal comes along. Her passion for him seems to be the first experience she has had of powerful human connection beyond her mad father. Unlike Claire, who is constantly reminding Catherine that she is sick, Hal brings the message that she is healthy--even, in all the best ways, normal. As he says to her on the morning after their first lovemaking, “I want to spend the day with you if possible. I’d like to spend a s much time with you as I can unless of course I’m coming on way too strong right now and scaring you in which case I’ll begin backpedaling immediately . . .” In response to this sudden avowal she, “laughs. Her relief is evident. . . . They kiss.”
It is because Hal makes Catherine believe that she is lovable, and therefore healthy--which means sane--that she reveals to him the hidden proof. Hal makes it possible for her to believe, perhaps for the first time, that she can be a genius without being crazy.
Which is why she is so distraught and enraged when Hal initially refuses to believe that she wrote the proof. By questioning her authorship, he questions her newly-forged, and extremely fragile, synthesis of genius and sanity, the combination that eluded her father. Worse still, to believe that she would lie about the proof is, in itself, to take her for a mad woman. One would really need to be crazy to make such a crazy claim. "You should have trusted me," she says to him reproachfully. And there is a still worse possibility. Maybe, she suggests, Hal is merely pretending to disbelieve her, perhaps even intending to claim authorship himself. If that were the case, his attraction to her would also have been false, and her normalcy merely an illusion.
But Hal comes around in the end, and Catherine re-emerges from her shell, a sane genius ready to take up her work and life.
HAL. The most important fact about Hal is that he is not a genius. In fact, he provides a fairly precise estimate of his gifts: “if I came up with one-tenth of the s**t your dad produced I could write my ticket to any math department in the country.” This tithe of talent, however, is a cloud with a silver lining. He may enjoy less than a tenth of Robert’s ability, but he suffers nothing of his curse. We see this in his after-hours life in a rock band, a robust symptom of his utter sanity. As he says of his fellow musicians, “They play sports, they play in a band, they get laid surprisingly often.” Presumably the same goes for him, too.
Thus, unlike Catherine whose gift is wrapped in dread, Hal enjoys his ordinariness as an unmixed blessing. He also recognizes and admires the extraordinariness of others. He all but worshipped Robert, as his pious sorting of the professor’s papers indicates. And he stands in awe of Catherine’s untutored genius. If Catherine is a kind of Hamlet, struggling with the problem of being or not being her father, then Hal is her Horatio—competent, firmly grounded, fully aware of the rareness he serves.
CLAIRE. A financial analyst, Claire is also good with numbers. But not that good. “I probably inherited about one-one-thousandth of my father’s ability,” she tells Hal. And she hastens to add, “It’s enough.” Like Hal, then, she too is no genius. And from that last sentence we get the impression that she’s glad of it. Instead, she is good at life. She is a fixer. When she arrives from New York, she finds a house without food. She quickly remedies that, supplying bagels and fruit. She also finds a sister without spirit or purpose, drinking cheap champagne by herself on her birthday. That problem, too, she tackles, inviting Catherine to live in New York where they can be near one another, and where Claire can keep a helpful eye on her sister. More immediately, she organizes a party—probably the first social gathering in that forlorn house in decades— an event in the course of which Catherine finds herself, also possibly for the first time in years, kissing a man.
She dreads the family curse of madness, but on her sister’s behalf. And so, unlike Hal, she has a difficult time seeing Catherine as normal. She can’t get beyond her sister’s eccentricities, always interpreting them as symptoms of an illness about to strike. We see this anxiety during their first scene together as she asks how Catherine feels at least a half-dozen times in the course of as many minutes. She even initially doubts that Hal exists, hinting that he may be merely a figment of Catherine’s imagination, a delusion like her father’s non-existent friends.
It is because she knows she will always be abnormal in her sister’s eyes that Catherine falls into a funk whenever Clair is around; it’s also why she resists the idea of moving to New York. Claire can repair every problem but her sister precisely because, to Claire, Catherine is nothing but a problem.
GENIUS AND MADNESS. Hal makes the blanket assertion that “Mathematicians are insane,” voicing an idea that pervades our culture. Exceptional talent, we seem to believe, goes hand-in-hand with craziness. We meet this idea in the classics and the comics, in the distant past and in the immediate present. Shakespeare tells us that, “The lunatic, the lover, and the poet” are brothers under the skin, while Batman battles one deranged genius after another in defense of Gotham. The story of Dr. Faustus, an intellectual whose thirst for knowledge drives him to the mad act of selling his soul to the devil, has fascinated us since the Renaissance. Indeed, in the hands of Goethe, this particular tale of deranged genius became Germany's very own national epic.
The deranged artist is a familiar figure—think of Van Gogh—as is the mad scientist, a character who haunts both fiction and reality: Dr. Frankenstein, meet Dr. Mengele. And Hollywood recently bestowed an Academy Award on a movie about an insane mathematician, a work mingling fact and fiction.
Why do we make this link between genius and insanity? Partly, as some of the examples above demonstrate, because it exists. Many gifted people have also been tragically deranged. Perhaps because the same twist in the brain that makes for exceptional talent also opens the door to mischief. After all, who can draw a clear line between extreme originality and madness? Innovative works of art or incandescently unconventional scientific theories have routinely been dismissed as crazy.
In Proof the main character fears for her sanity, in part because her father was mad, and genetics is, after all, a powerful predictor of one's own fate in life. But her fears are all the greater because she also shares her father's genius. Claire, intellectually undistinguished, has no worries about her mental health. And so we watch as a young woman struggles to be both brilliant, like her father, and normal, like her sister--to achieve the balance that our culture tells us may be impossible.
PROOF. The word "proof" comes to us from an Indo-European root meaning "through" or "forward." From this root comes one of the word's primary English meanings: a test or trial in which a person or object is put through an ordeal, or placed in a forward position in the face of danger. Thus we say of someone, "He has been proven in battle," and we use phrases such as "bullet-proof" or "rust-proof," or "the proof of the pudding is in the eating."
A second sense of "proof" means the deployment of evidence or reasoning to establish a fact or validate theory. A "proof" in this sense is a demonstration that something is actually the case.
The meaning of "proof" in Proof continually oscillates back and forth between these two senses, sometimes figuring as a test or ordeal--that is to say, an emotional trial--and at other times appearing as an exercise in logical demonstration.
As the play begins, Catherine's "proof"--her logical demonstration of a theory about prime numbers--is a fait accompli, sitting in a drawer in her father's desk. And having gone through the intellectual ordeal necessary to construct this "proof," she has now "proven" herself as a worthy contestant in the mathematicians' struggle for knowledge. She has earned her intellectual spurs.
However, she must still "prove"--that is, establish the fact of--her genius to Hal, who is initially skeptical, and who thus "proves"--by failing the emotional test--to be less than fully worthy of her love and trust. Meanwhile, Claire is constantly scrutinizing Catherine, looking for "proof"--logical evidence--of her sister's illness, while Catherine simultaneously seeks "proof"--through testing herself at love--of her own sanity.
What we see from this shuttlecocking back and forth between these related but distinct senses of the word is that the two kinds of proof come from different zones of human experience, one cognitive, one ethical--and both essential for sanity.
QUESTIONS FOR DISCUSSION.
1. Do you know people who are unusually gifted? Are they also odd, or strange in any ways?
2. Can you think of examples of well-known people who seem both crazy and very talented?
3. Can you think of children who have inherited the talent, or the problems, of a parent?
4. Can you see resemblances between parents and children in your family? Among your friends? In the world at large?
5. Why do you think the playwright chose to write about a mathematician and his daughter, rather than, say, a biologist or an economist?
6. Do you think Catherine should move to New York to be close to Claire?
7. Do you think Catherine should move out of the house?
8. Why do you think Hal is interested in Catherine?
9. Discuss the difference between "proving yourself" and "proving a theory."
10. Why do we never hear anything about Robert's wife and Catherine's mother?