Proof

At the start of Scene 1, it is nearly one in the morning, and Catherine, who is 25, is sitting on the front porch, “exhausted, haphazardly dressed. Eyes closed” (5). Her father, Robert, who is in his fifties and has a “rumpled academic look” (5) startles her. Catherine tells Robert that his student, Hal, is still at the house, going through Robert’s study. Noting that it is after midnight, Robert wishes Catherine a happy birthday and points to a bottle of champagne. They pop the cork, and Catherine drinks from the bottle. She tells Robert, “This is the worst champagne I have ever tasted” (6). Robert hopes Catherine has birthday plans, but she tells him that she has no friends to take her out. Robert suggests a girl who Catherine hasn’t been friends with since third grade, and then he suggests Catherine’s sister, Claire. Catherine tells him, “She’s in New York. And I don’t like her” (7). Additionally, Claire won’t be in town until the following day. Robert offers, “My advice, if you find yourself awake late at night, is to sit down and do some mathematics” (8).

Catherine is uninterested, and Robert points out that she was a math prodigy as a child and should use her gift. Robert chides her for her lifestyle, staying in bed all day, reading trashy magazines, and eating junk food. He calls those days “lost,” saying that she “threw them away” (8). Robert asks her how many days she has lost, prodding her until she reveals that she has “lost” exactly 33 days. They go back and forth, considering the mathematical properties of 33 and a quarter days or years. Robert tells her that she’s still young and has time to fulfill her potential. Catherine responds that by the time Robert was 25, he was famous. His productive days were limited, however, as he could no longer work after he got sick. He contradicts this, claiming that after falling ill he was clearer, able to work all day if he wanted. He could see mathematical formulas in everything around him. The symptoms started when he was 23 or 24.

Robert reassures Catherine that just because he “went bughouse” (11) doesn’t mean that Catherine will inherit the same problems. He tells her that “crazy people don’t sit around wondering if they’re nuts” (12). Robert suggests that Catherine go to sleep, but Catherine realizes that Robert has disproven his own theory that crazy people don’t know they’re crazy by describing himself as having gone “bughouse.” Robert reminds her that he’s also dead. He died of heart failure a week ago, and the funeral is the next day. Robert admits that the fact that Catherine is sitting and talking to him is possibly “a bad sign” (13).

Hal enters onto the porch from the house. He is 28 and carrying a backpack. The door slams behind him, surprising Catherine. Hal apologizes and asks why she’s drinking champagne. Catherine says that she just likes champagne and offers him the rest of the bottle. Hal declines, asking if he can come back the next day to finish going through Robert’s papers. Catherine reminds him that the funeral is the next day, and Hal apologizes again and tells her that he is planning to go to the service.

Catherine points out that Hal has been rummaging through Robert’s study for three days, and Hal says that he needs at least another week. He suggests that he could take some of Robert’s notebooks home to read and then return them, but Catherine adamantly opposes this idea. She tells Hal that there’s nothing of value in the notebooks, as her father had graphomania, causing him to write compulsively. Hal asserts that he is willing to look through everything to make sure that there isn’t something to find. Hal excuses himself to go and see his friends from the math department who are playing in a band. He admits that he is also in the band.

Before he leaves, Hal presses Catherine, asking if he can come back on Monday, saying, “I loved your dad. I don’t believe a mind like his can just shut down. He had lucid moments. He had a lucid year, a whole year four years ago” (16). Hal goes on to praise the major contributions Robert made to the field, adding, “If I came up with one-tenth of the shit your dad produced, I could write my own ticket to any math department in the country” (17). Suddenly, Catherine demands to look in Hal’s backpack. Hal accuses her of paranoia and reminds Catherine that she claimed there was nothing in Robert’s notes worth stealing. Catherine replies that if that’s true, there’s no reason for Hal to come back.

Catherine tells Hal about caring for Robert, even having to remind him to bathe. After her mother died, Catherine became Robert’s sole caretaker. Robert would take books out of the library because he believed that “aliens were sending him messages through the Dewey decimal numbers on the library books” (19). Caretaking for her father was a heavy burden for young Catherine, and she adds, “I dropped out of school. I’m glad he’s dead” (19).

Catherine wants to be alone, but Hal tells her that there will be more people who want to read Robert’s notebooks. Catherine says that she will do it herself, but Hal doubts her math abilities. He says, “I know your dad taught you some basic stuff, but come on” (20). Suddenly, Catherine seizes Hal’s bag. There’s nothing in there but Hal’s belongings. She tells him that he can come back tomorrow. Hal suggests that she speak to someone at the university health service. After his mother died, talking to a therapist there helped.

As Hal is leaving, Catherine stops him to hand him his coat. She discovers a notebook. Irate, she orders him to leave. She picks up the phone to call the police, and he insists that she look at something. It’s a note in which Robert expressed gratitude for Catherine’s caretaking and noted the date of her birthday. Hal tells her that he was planning to wrap it and give it to her. He wishes her a happy birthday and leaves. Catherine begins to cry, and police sirens sound in the distance.

In Scene 2, Catherine’s sister, Claire, sits on the porch drinking coffee. She is 29 and “stylish, attractive” (23). Catherine emerges from the house, her hair wet from the shower. Claire offers coffee and food, as she’s restocked the empty house with groceries. Claire has brought Catherine a dress to wear to the funeral, and she offers to take Catherine shopping. Claire is not an academic like her sister and father.

Claire wants to have people over after the funeral. She tells Catherine that she and her boyfriend, Mitch, have decided to get married. Catherine congratulates Claire and tells her that she will be at the wedding. Claire asks Catherine how she feels about their father’s death and what she plans to do now, but Catherine deflects. Claire reveals that, while Catherine was in the shower, police officers came by to follow up on the call Catherine made the night before.

Catherine explains what happened, but Claire is dubious, questioning Catherine as if Hal does not really exist. According to Claire, the police told her that Catherine was “abusive” and “lucky they didn’t haul [her] in” (30). The officers attempted to search the house, but Catherine became belligerent because she didn’t want to let them in. Claire offers for Catherine to stay with her in New York. She suggests that Catherine “could use some downtime” as she has “had a very hard time” (31). Catherine insists that she is fine in Chicago. They argue, and Hal interrupts, calling Catherine’s name from offstage. With an exaggerated gesture, Catherine introduces Hal, showing that he does exist. Again, Catherine insists that she is fine and does not need her sister to look after her. To Catherine’s exasperation, Claire notes that Hal is “cute” (32). Claire adds, “We need to make some decisions. But I shouldn’t have tried to start first thing in the morning” (32).

Scene 3 begins with Catherine alone on the porch, still dressed in black from Robert’s funeral. A party has gathered in the house, and a “not-very-good but enthusiastic band” (33) plays loudly. Hal enters from the house, “sweaty and revved up from playing” (33) with two beers. Catherine points out that the band might be a little much for a funeral reception. Hal tells her that they’ve finished playing and offers her a beer. She hesitates and then accepts it. There are about 40 people still at the party, all mathematicians. It was Claire’s idea for Hal’s band to play. The funeral was very well-attended. Hal compliments Catherine’s dress.

Catherine wonders when everyone will leave, and Hal replies, “No way to know. Mathematicians are insane” (34). Hal tells Catherine that a lot of the older mathematicians he meets at conferences are on amphetamines because “they think they need it. […] They think math’s a young man’s game” (34). Catherine concurs that her father thought the same thing. Hal concedes that most of the innovative work is done by young men. Catherine tells Hal about Sophie Germain, an 18th century mathematician who hid in her father’s study during the French Revolution and sent proofs to German mathematician Carl Friedrich Gauss under a man’s name.

Once reminded, Hal knows all about Germain’s contribution to the field. He is surprised to discover that Catherine understands Germain’s work in depth. Hal asks if Gauss ever discovered Germain’s identity, and Catherine tells him that he did, reciting the letter of praise Gauss wrote to Germain when he learned she was a woman. Suddenly, Hal kisses her. He immediately apologizes, but Catherine tells him that it’s ok. She apologizes for her behavior the previous night. Hal tells her that he was “pushy” and admits that there probably isn’t anything of value in the notebooks. Hal tells her that the notebook he tried to steal seems to be the only lucid one and it doesn’t even contain any math.

Hal tells Catherine that his own research is “not exactly setting the world on fire” (37). Catherine replies, “It’s not about big ideas. It’s work. You’ve got to chip away at a problem” (37). Hal describes Robert’s work as “beautiful,” “streamlined,” and “elegant” (37). He says, “It’s okay. At a certain point you realize it’s not going to happen, you readjust your expectations. I enjoy teaching” (37). Catherine suggests that there is still time, and Hal jokes, “I’m twenty-eight, remember? On the downhill slope” (38). Catherine quips back, “Have you tried speed? I’ve heard it helps” (38). After a moment, Catherine asks, “What do you do for sex? […] At your conferences?” (38) Hal demurs, laughing awkwardly, unsure whether she is flirting. He replies, “Well we are scientists. […] So there’s a lot of experimentation” (38). Catherine kisses him. Hal tells her that he would see her with her father and always liked her, but he didn’t want to flirt with his advisers daughter. Catherine remembers seeing him at the house four years ago when Hal stopped by to drop off a draft of his thesis. Catherine remembers Hal as well and tells him he seemed “not boring.” They continue to kiss.

Scene 4 starts the next morning. Catherine is on the porch, and Hal enters, not fully dressed. They make awkward conversation. Claire is still asleep, and Catherine wonders if she ought to wake her up because Claire has a flight to catch. Hal suggests that Catherine let her sleep, since Claire drank a lot the previous night. Hal tells Catherine that he usually goes out for breakfast on Sunday mornings, and he invites Catherine to join him. She declines, saying that she should be there when Claire gets up. He asks if he should stay, and she agrees but adds that Hal can continue his work in her father’s office. Hal emphasizes that he’s staying to spend time with her, not her father’s work. He then realizes that he is “coming on way too strong” (40). Catherine laughs, relieved, and they kiss. After a moment, Catherine gives him a key to a locked desk drawer in her father’s office. Hal kisses her again and goes inside.

Claire enters with a hangover. She complains that Catherine left her alone with a physicists and that all of her friends had to leave early to “pay their babysitters or bake bread or something” (41). Claire comments that the band was “terrible” and Catherine counters that the band was decent and seemed to be having fun. Claire comments that the dress she brought Catherine seemed to work out, and Catherine thanks her and says that she loves the dress.

Claire notes that Catherine seems to be in a good mood. She reminds Catherine that she will be flying out in a few hours and tells her not to try to clean the house, messy from the party, by herself. Claire promises to hire someone. Again, Claire invites Catherine to move to New York. Catherine tells her that she needs some time to figure out what she is going to do next. Claire thinks Catherine can do that in New York, and Catherine responds that she plans to remain in the house in Chicago. Claire states, “We’re selling the house” (43). Claire goes on to explain that she is planning to sell the house to the university, which has “wanted the block for years” (43). Catherine is shocked and tells Claire that the house is her home, but Claire points out that the house is “in bad shape. It costs a fortune to heat. It’s time to let it go” (43). Catherine is furious.

Claire expresses regret for having left Catherine to take care of their father alone, adding, “Now I’m trying to help” (43). Catherine tells her that it is too late to help, now that their father is dead. Claire reminds her that she has been working and living in Brooklyn while paying the bills for the house in Chicago. Catherine points out that Claire was able to finish school, unlike Catherine, who dropped out to care for their father. Claire suggests that it would have been better to have Robert committed to a facility, but Catherine disagrees, asserting, “He needed to be here. In his own house, near the university, near his students, near everything that made him happy” (44). Claire notes that Robert never produced any work again, and that Catherine had wasted her potential caring for him.

Catherine accuses Claire of thinking that Catherine is mentally frail, like their father. She wonders if Claire has not only looked for apartments but also a “living facility for your bughouse little sister” (45). Claire denies it at first, but then admits that she had looked into doctors and resources to help Catherine. Catherine is furious. Claire attempts to backtrack, claiming that they would only utilize those resources if Catherine wants them, but Catherine tells her that she hates her.  

Hal enters, surprising Claire who didn’t know he was in the house. Hal is ecstatic, holding a notebook. The notebook from the locked desk drawer contains a proof, one that “proves a theorem… a mathematical theorem about prime numbers, something mathematicians have been trying to prove… since there were mathematicians, basically” (24). Hal adds, “Most people thought it couldn’t be done” (47). Excited, Hal tells Catherine that “newspapers all over the world are going to want to talk to the person who found this notebook” (47). Catherine responds that she didn’t find the proof, she wrote it.