Themes
Key
LitCharts assigns a color and icon to each theme in Proof, which you can use to track the themes throughout the work.
Genius and Mental Instability
Family and Heredity
Sexism
Proof, Trust, and Credibility
Caretaking and Sacrifice
Summary
Analysis
Exhausted, Catherine sits in a chair on the back porch of a house in Chicago. Her father, Robert, stands behind her, but she doesn’t realize that he is there. It’s nighttime, and both she and her father are rather messily dressed. Suddenly, he asks Catherine if she can’t sleep, startling her.
Catherine’s exhaustion and her haphazard outfit suggest that she is going through a hard time. Robert is also messily dressed, which may suggest that he also doesn’t have the time or energy to care about what he’s wearing. The fact that Catherine and Robert are alike in their haphazard dress may suggest that the two characters are similar to each other in some unspecified way, but, at this point, the audience doesn’t know what this similarity would be.
Themes
When Catherine asks Robert why he’s there, he says he’s “check[ing] up” on her. Catherine is waiting for his student, who’s upstairs in Robert’s office, to leave. Robert reminds Catherine that the man is no longer his student, but a teacher in his own right.
In this passage, Catherine comes off as a bit confused. She’s clearly surprised by Robert’s presence, which may suggest that he’s not supposed to be on the porch at all, or it may mean that he should be asleep (it’s late at night). She also mistakenly identifies the man in the house as her father’s student (he’s actually a teacher now), which may indicate that she’s not up to date with what’s going on around her. In general, Catherine seems to be out of sorts. Catherine’s confusion establishes an atmosphere of uncertainty, making the audience feel unsure of what’s going on.
Themes
Since it is past midnight, Robert gestures toward a bottle of champagne while wishing Catherine a happy birthday. As she pops open the bottle, she says that she feels old—she’s twenty-five years old. Robert forgot to bring glasses, so Catherine takes a swig from the bottle then pronounces the wine disgusting. Not insulted, Robert says that he’s proud to not be a wine snob, as he finds “those kind of people” to be annoying. Catherine offers Robert some of the wine, but he declines.
Robert and Catherine appear to have a close and amicable relationship. Catherine feels comfortable enough with him to drink straight from the bottle in front of him and, when she pokes fun at Robert’s poor wine choice, he isn’t offended, but instead joins in the gentle teasing. Catherine shows that she has some anxieties about getting older (she isn’t happy that she’s turning twenty-five), although the audience doesn’t know why yet.
Themes
Robert asks Catherine what she will be doing on her birthday, and she says that she’ll be drinking the wine he purchased. He asks whether her friends will celebrate with her, but Catherine tells him no; she doesn’t have any friends. When Robert brings up an old friend of hers, Catherine exclaims that the girl, Cindy Jacobson, was her friend in the third grade. Robert asks about Claire, which Catherine dismisses. Claire doesn’t count because she is Catherine’s sister, whom Catherine doesn’t even like.
Robert is now the one who seems behind-the-times—he thinks that Catherine is close to someone that she hasn’t seen since childhood. The fact that Robert doesn’t know some key details about Catherine’s life (he doesn’t know she doesn’t have friends or that she doesn’t like her sister) seems at odds with the fact that they seem to be quite close. This confusion adds to the general atmosphere of uncertainty. Additionally, Catherine’s not having friends suggests that she either is an unfriendly person or that she doesn’t have the time, energy, ability, or inclination to make friends. Again, the audience doesn’t know why. Another important fact about Catherine is that she isn’t close to her sister, which Robert again seems ignorant of. This implies that there may be a rift in the family; while Catherine and Robert are close, Claire doesn’t seem to be in the picture as much.
Themes
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Confused, Robert says that he thought that Claire was coming. But Catherine explains that Claire is arriving the next day. After a moment, Robert advises Catherine to do some math, as that’s what helps him when he’s up late. But Catherine refuses and instead offers him some wine, which he declines again. He reminds Catherine of her talent—she “knew what a prime number was before [she] could read”—and tells her that, while she is going through a rough time, she shouldn’t be lazy.
Claire’s absence is confirmed in this passage—she doesn’t live with Robert and Claire, and her trips to visit are planned, which shows that she isn’t close enough (emotionally or geographically) to casually stop by unannounced. Meanwhile, Robert’s advising Catherine to do math—it’s what helps him when he’s up late—shows his love for math. By refusing, Catherine appears to not be as interested in math, but it becomes clear that that’s not because she has no talent for it—according to Robert, Catherine has had a talent with numbers since a young age. Robert also reveals that Catherine has been going through a rough period, which could explain the exhaustion and confusion that she has exhibited so far. The reason that Catherine is in a bad place is unclear.
Themes
Catherine insists that she’s not lazy—she’s been busy taking care of Robert. But Robert enumerates her bad habits: she sleeps late, eats poorly, doesn’t work, doesn’t clean, and rarely gets out of bed. Catherine makes a joke, but Robert won’t let it go, bluntly telling her that she has wasted many days, which means that she’s also lost any groundbreaking ideas that she could have had during that time.
Catherine’s exhaustion may be due to the fact that she’s been caring for her father. All the same, Robert believes that Catherine has been lazy and isn’t living up to her potential. His insistence that she is mathematically talented suggests that Catherine is either extremely talented, or Robert just thinks she is. At the same time, Catherine is clearly struggling with her mental health; all of the “bad habits” that Robert references can actually be interpreted as signs that her mental health is poor. So, Catherine may be brilliant, and she may be living with poor mental health.
Themes
When Catherine admits that she has “lost a few days,” Robert sharply asks how many—he knows that she counts them. Catherine claims not to keep track, but Robert keeps pushing, and she finally admits that she’s lost 33 days plus a chunk of today, which is a “depressing […] number.”
Not only is Catherine’s mental health so poor that she has spent more than 33 days’ worth of time too depressed to get out of bed, but she is so intuitive with math that she keeps track of the time she has spent holed up in her room. She easily calculates the amount of time she has “lost” to her mental illness, which supports Robert’s belief that she has a talent for math.
Themes
But Robert says that if each day were a year, the number would be quite interesting. Catherine reluctantly acknowledges that it would be 1729 weeks, which is “The smallest number expressible […] as the sum of two cubes in two different ways.” Delighted, Robert proclaims that “Even [her] depression is mathematical,” taking it as a sign of her potential.
Catherine’s mathematical talent seems even more apparent in this passage, in which she performs some impressive calculations on the spot. Robert interprets the coincidence—the number of days that she “wasted” is a mathematically significant number—as a sign of Catherine’s potential. But his remark that “Even [her] depression is mathematical” has a greater thematic meaning—it suggests that Catherine’s mental illness to is inseparable from her brilliance.
Themes
Catherine feels that she hasn’t “done anything good,” particularly in comparison to Robert, who was already famous when he was her age. He confirms that by 25, he’d already done his best work. After a pause, Catherine reminds him that he couldn’t work after he got sick. But Robert insists that he was at his sharpest then, which makes Catherine laugh.
Catherine’s anxieties about getting older are partially explained: she’s worried that she won’t live up to her father’s legacy. While she feels that she hasn’t made any discoveries or contributions (presumably to the field of mathematics), Robert had already done a considerable amount of work that had made him famous by the time he was her age. Apparently, his successful period was cut short when he became sick—this sickness may also be the reason that Catherine has been taking care of him.
Themes
Robert felt an amazing clarity after getting sick, and Catherine asks whether he was happy then. He says yes—he was “busy.” Catherine points out that busy and happy aren’t the same, but Robert “[doesn’t] see the difference.” He would work all day and find “secrets, complex and tantalizing messages” all around him.
Robert is obsessed with his work—to him, being busy is the same thing as being happy. For Robert, working feels like finding “secrets, complex and tantalizing messages,” a description that suggests that his brilliance is tied to his ability to perceive connections and meaning that are “secret,” or unseeable, to other people.
Themes
Catherine abruptly asks when “it” started. As Robert explains that he was in his mid-twenties, he realizes that this is what Catherine may be dreading this year; she’s afraid to go “bughouse” like he did. But he says that there are lots of factors beyond heredity—just because he got sick doesn’t mean she will.
This passage partially explains Robert’s illness, as well as why Catherine is anxious about turning twenty-five. Robert evidently became ill with a severe mental illness, which is likely the reason that Catherine has been taking care of him. Robert’s sickness set in around Catherine’s age, giving her another reason to feel stressed about her birthday—not only does she feel unaccomplished when compared to Robert, but she’s also worried about inheriting his mental illness.
Themes
Robert reassures Catherine that she’s just going through a rough spot and, if she just “get[s] the machinery going” again, everything will be fine. He adds that the mere fact that she is talking to him about this is a good sign, since “Crazy people don’t sit around wondering if they’re nuts”—and he would know.
Just as Robert is convinced that Catherine has inherited his mathematical talent, he is certain that she hasn’t inherited his mental instability. To comfort her, he gives her a seemingly good argument, that “Crazy people don’t sit around wondering if they’re nuts.” As someone who has experienced mental illness, he seems to be a credible source.
Themes
Catherine seems to believe Robert, but then she interrupts him: his argument doesn’t make sense. He just called himself “crazy,” even though he also said that “a crazy person would never admit that.” Robert replies that he can only admit it because he’s dead, which Catherine confirms: he died from heart failure a week ago, and Claire is coming to Chicago for the funeral. Catherine asks what it means for her that she’s talking with her dead father, and Robert replies that it might be a bad sign.
Robert’s argument crumbles with the revelation that he’s actually dead—Catherine is either drunk, hallucinating, or missing him so much that she is imagining that he’s there. But this moment severely undercuts Catherine’s credibility. The audience suddenly realizes several things: one, Catherine may not be a reliable witness; two, maybe she really has inherited Robert’s mental instability; and three, the audience cannot trust what they see, since Robert appeared to be a flesh-and-blood person but is actually a figment of Catherine’s imagination.
Themes
Hal enters the room, startling Catherine. As he apologizes for staying so late, Robert disappears. Noticing Catherine’s champagne bottle, Hal asks whether she is drinking alone. She says yes and offers him the bottle, but he says he needs to drive. When he asks if he can come back tomorrow, Catherine reminds him about the funeral. Apologetic, Hal asks whether he can come Sunday.
When Hal enters, Robert disappears, which confirms that Robert isn’t actually there, and that Catherine had only imagined that him. Now that Robert is no longer there, Catherine’s drinking takes on a more somber significance. She’s drinking on her own, which can be a sign of poor mental health.
Themes
Incredulous, Catherine asks how much more time Hal needs; he has already had three days. But Hal says he’ll need at least another week to go through everything in the office. So far, he’s been sorting the notebooks—Robert dated them all. But when Hal suggests that he bring the books home, Catherine refuses. According to her, he’s just wasting his time, as the books contain nothing but nonsense—Robert was a graphomaniac, which means he wrote compulsively. But Hal insists that someone has to look through all 103 notebooks that Robert left behind to make sure that there isn’t anything genius.
Hal, who is Robert’s former student (the one mentioned at the beginning of the play), demonstrates that he is a rigorous and pushy person. He is a dedicated mathematician who wants to know for a fact whether Robert’s notebooks only contain gibberish. By painstakingly going through each notebook, Hal demonstrates his skepticism and a belief in the supreme value of evidence. He isn’t just going to take Catherine’s word that there’s nothing valuable in the books—he’s going to look in each one in order to have definitive proof of whether Robert only wrote nonsense. At this point, the audience may support Hal’s skepticism toward Catherine, given that Catherine is not the most reliable character (she just hallucinated her dad’s presence). At the same time, his refusal to take Catherine at her word doesn’t make her inclined to be kind to him.
Themes
Hal tells Catherine that he has to go see some friends from the math department play in a band. Their songs are math jokes, including one called “i,” or “Imaginary Number,” where they stand silent, not playing anything. Catherine calls them nerds, and Hal agrees, but he adds that they are nevertheless cool: they are professionally successful, socially adept, and sexually active. Catherine snidely guesses that he’s in the band, which he admits.
Catherine proves herself to be quite perceptive—she can immediately tell that Hal is in the band that he tries to casually talk up.
Themes
When Hal invites Catherine to come with him, she refuses. He suggests another day, but she rudely reminds him that he has a job and band practice, so he must be busy. Hal admits that he doesn’t have much time, but he wants to take her out. After a pause, he says that he loved her father, who helped Hal through a rough spot during his Ph.D. program. That was a few years back, during a “lucid year” that Robert had. Hal adds that if he could do even a fraction of the work Robert did, he could have a job at any math department.
Catherine’s rudeness demonstrates her prickly character. Yet her rudeness is somewhat justified—Hal has been extremely pushy about seeing Robert’s old notebooks and won’t listen to Catherine’s insistence that the notebooks only contain gibberish. His not trusting her has hurt his chances at building a relationship with her. Additionally, he comes off as a bit tone deaf; Catherine’s father has just died, so his insistence on taking her out on a date feels rather disrespectful.
Themes
Catherine abruptly demands to see Hal’s backpack, but Hal insists that he wouldn’t take anything out of the house like Catherine suspects. Still, she accuses Hal of taking notebooks from Robert’s office in hopes of stealing Robert’s work to advance his own career. Hal swears this isn’t true, but she doesn’t believe him.
Catherine is interpreting Hal’s respect for her father as evidence that Hal is trying to steal one of Robert’s notebooks to publish under his own name. At this point, the audience is hesitant to believe Catherine—her hallucination of her father has deflated her credibility, so it seems like she may just be imagining Hal’s nefarious intentions.
Themes
Hal tells Catherine to calm down, that she’s being paranoid—after all, she herself just said that the notebooks were all gibberish anyway, so what would he steal? Catherine agrees and says that Hal has no reason to come back, since he agrees that the notebooks are worthless. Exasperated, Hal insists that someone needs to make sure.
Hal points out a flaw in Catherine’s logic, but he does so in a sexist way Not only does he patronizingly tell her to calm down—men have a history of gaslighting women by telling them to stop being “hysterical,” even when they have good reason to be upset—but he also keeps refusing to listen to Catherine, even though she, as Robert’s daughter, likely knows more about Robert’s notebooks than he does. At the same time, his dedication to looking over all the notebooks firsthand emphasizes how he values the role of evidence in trying to determine the validity of a claim. He wants proof that what Catherine says is correct—he won’t just take her word for it.
Themes
Catherine interrupts, saying that she lived with Robert—since her mom died, she’s the one who had to watch him descend into madness. He talked to invisible people, neglected his hygiene, and believed that aliens were sending him messages through the Dewey decimal numbers on library books. When he started writing dozens of hours a day, Catherine had to drop out of school. She tells Hal that she is glad that her father is dead.
Catherine made many personal sacrifices (such as quitting college) in order to take care of Robert. On top of her sacrifices, she had to go through the trauma of witnessing her father’s mental deterioration. At this moment, Catherine feels resentful toward her father but, given her genial imaginary conversation with him earlier (and the fact that she decided to give up so much in order to care for him), it actually seems that she isn’t “glad” that Robert’s dead. Quite the opposite—she may be missing him so much that she imagined having a conversation with him. It’s unclear why she imagined Robert, which adds another layer to the atmosphere of uncertainty in the play. In this passage, Catherine also describes Robert’s mental health in more detail. He suffered from mental delusions and often saw things that weren’t there.
Themes
Hal tries to empathize, but Catherine curses at him and insists that he doesn’t know her. She just wants to be alone. Hal argues that he won’t be the only protégé who will come around—people are already looking over Robert’s old work and they will definitely want to know what’s in the notebooks.
Catherine is clearly grieving, which makes Hal’s pushiness about seeing the books even more disrespectful. He comes off as selfish and tone-deaf—he prioritizes finding evidence of Robert’s genius over respecting Catherine’s feelings. Unsurprisingly, Hal’s persistence about reading the books annoys Catherine, showing how the (often unfeeling) search for proof can damage human relationships.
Themes
Suddenly, Catherine says that she will be the one to look through the books; Robert was her father, after all. But Hal says she doesn’t have the skills required to determine what isn’t nonsense. When Catherine insists that she does, Hal says that she only knows whatever basic math Robert taught her, which won’t be enough to decipher her father’s work—it would take a professional.
Hal doesn’t know Catherine well at all, so his insistence that she doesn’t know enough math to understand Robert’s worth is founded on what Hal does know about her: her gender. By underestimating her abilities, Hal appears to be employing the sexist stereotype that women are not smart enough to keep up with advanced mathematics. Hal takes it upon himself to act as gatekeeper to Robert’s books, locking Catherine out of the opportunity to go through her own father’s work.
Themes
Catherine suddenly snatches Hal’s backpack and rifles through it. But there’s no notebook there, only various personal items. Embarrassed, Catherine tells Hal that he can come tomorrow. After a brief pause, Hal advises Catherine to go see a doctor or get into exercise, both of which helped him after his mother’s death. Hal invites her one last time to the show, but she refuses.
Hal doubting Catherine’s abilities makes her snap and snatch his backpack to search it, demonstrating how skepticism can harm interpersonal relationships. When the audience sees that Hal’s backpack doesn’t contain any notebooks, Catherine’s credibility deflates further—she seems paranoid for having suspected Hal. At this point, it seems like she may be a bit unstable, perceiving things (like Hal’s intention to steal) that aren’t actually there.
Themes
As Hal gets up to leave, Catherine realizes that he has forgotten his jacket. But when she picks it up, a notebook falls out. “I’m paranoid?” she says to Hal before yelling at him to get out of her house. He insists that he wants to explain something, but she dials the police. As she tells the police that there’s a robbery in progress, Hal tries to say that he borrowed the notebook not because of any math, but because of something Robert wrote about Catherine. As he starts to read, Catherine hangs up the phone.
Catherine’s suspicions appear to be valid after all—Hal really was trying to steal one of Robert’s notebooks. At this point, it appears that her perception was correct, a fact that redeems her credibility for the audience. She seems less unstable, and more astute. Hal, meanwhile, totally breaks her trust by lying about not taking a book from Robert’s office. In response, Catherine calls the police, which shows how damaging doubt is for relationships; now that she knows she cannot trust him, Catherine has no interest in maintaining so much as a friendship with him.
Themes
Robert wrote that it was “a good day,” since Catherine had some good news—Hal doesn’t know what this refers to, but he thought Catherine might. Catherine asks when Robert wrote this, and Hal speculates that it was during his remission—Robert also wrote that while the “Machinery is not working yet,” he can be patient. Hal clarifies that “The machinery” is what Robert called “his ability to do mathematics,” Catherine brusquely says she already knows.
Hal begins to rebuild his credibility by giving Catherine definitive proof that he wasn’t taking the book with the intention of stealing Robert’s ideas. The book that Hal has taken is one that contains a journal entry, so it’s unlikely that Hal was trying to take it for nefarious reasons, although he has yet to give an explanation for his theft. Additionally, Hal again exhibits sexist behavior when explaining Robert’s terminology (his use of the phrase “The machinery”) to Catherine, who, as Robert’s daughter, would certainly already know. It is likely that Hal (who has already stereotyped Catherine as less intelligent because of her gender) is overexplaining to Catherine because he assumes that she, as a woman, knows less than he does, even though she is certainly a better source for knowledge on this topic (her father) than he is.
Themes
In the rest of the entry, Robert writes that he feels better when talking to students and doing “all the activities of ‘normal’ life,” like going out to restaurants and going outside. He also expresses gratitude for Catherine’s aid and sacrifice, acknowledging that he wouldn’t be improving if she hadn’t chosen to take care of him at home. Robert plans to take Catherine out to dinner that night for her birthday. Hal remarks that the entry is dated September 4, which is the same day as today.
Robert’s journal entry shows one way that Catherine’s decision to sacrifice much of her life to take care of Robert was a good decision. Robert believed that he wouldn’t have been able to recover had it not been for Catherine’s in-home assistance. By prioritizing his needs over hers and by listening to his desires, Catherine was a good caretaker to her father.
Themes
Hal hands Catherine the notebook, acknowledging that he shouldn’t have tried to “sneak it out,” even if his intentions were honorable. He wanted to wrap it for her and give it back as a birthday gift, which he now thinks was a stupid idea. He wishes her a happy birthday and then leaves. Catherine sobs for a moment, but she stops and curses when a police siren wails.
While Catherine was right in her instinct that Hal was trying to take one of Robert’s books, she was totally wrong in his motives, which he has proven to her by showing her that the notebook contains only writing. Her skepticism further damages the chance that she and Hal will have a relationship of any kind, as he now sees his attempt to connect with her as a foolish one, since her response was anger and distrust. Once again, Catherine’s credibility diminishes in the eyes of the audience—they have yet another reason to not trust her. At the same time, her misinterpretation of Hal’s actions suggests that she may be slipping into the same state of mental delusion that her father had—she is perceiving things that aren’t real—which may be proof that she has inherited his illness.
Themes
