Summary
Scene 3. The next day, Hal comes to the house and knocks on the door, calling for Catherine. Claire comes out and tells him that she delayed her flight. She then tells Hal that Catherine has been in bed for a whole day, and will not eat or talk.
"Why did you sleep with her?" Claire suddenly asks, accusing Hal of taking advantage of Catherine in a fragile state. When he asks to speak with her, Claire tells him he cannot and that she's going to take her to New York. Hal won't take no for an answer, but Claire says, "You fucking mathematicians: You don't think. You don't know what you're doing. You stagger around creating these catastrophes and it's people like me who end up flying in to clean them up." She tells Hal that she'll give him Catherine's number once they've settled in New York.
Hal doesn't leave, and Claire correctly guesses that he wants the notebook. He is surprised that she gives it to him so readily, but she puts his trust in him to do what is right. She tells him her card is in the notebook and instructs him to call her when he has a plan. "Can you tell me about it? The proof. I'm just curious," Claire says, telling him she's a currency analyst and that she has some math knowledge, though Catherine has more.
Scene 4. Three and a half years earlier, in the winter, Robert is on the porch. Catherine comes out and is alarmed that he's not wearing a jacket. When she beckons him inside, he tells her that the radiators dry out the air and he cannot concentrate with all the clanking. She tells him that she was calling all day and that she had to skip class to come down and make sure he was okay.
When Robert tells her that "the machinery"—his name for his mathematical brain—is working, Catherine can hardly believe it. He tells her that he feels inspired in a way that he hasn't in years. Suddenly he becomes self-conscious that he hasn't asked Catherine about her life and asks about school. She doesn't care, and wants to see his work.
Robert confides to Catherine that even though his life is comfortable, he was getting terrified that he would never work again. "Then I remembered something and a part of the terror went away. I remembered you. Your creative years were just beginning. You'd get your degree, do your own work. You were just getting started." Robert invites Catherine to work on the proof with him and hands her a notebook, asking her to collaborate. When he yells at her to read his work to him, she opens the book and reads what he's written. It's nonsense, all about the nature of cold and heat. She brings him inside.
Scene 5. In the present, a week after the events in Scene 3, Catherine and Claire drink coffee on the porch, preparing to go to New York. Claire tells Catherine that there's no rush and she can spend some time alone at the house before they go. "I want to do everything I can to make this a smooth transition for you. So does Mitch," Claire says. Catherine begins to speak sarcastically about all the amazing things she can do in New York, angry that Claire wants to put her in an institution. "I would like to see a doctor called Doctor Von Heimlich: Please find one. And I would like him to wear a monocle. And I'd like him to have a very soft, very well-upholstered couch, so that I'll be perfectly comfortable while I'm blaming everything on you," Catherine says.
Claire realizes that Catherine is being sarcastic about wanting to come with her, and becomes upset, pulling Catherine's plane ticket out of her bag and storming off.
Hal enters, out of breath and bedraggled, and tells Catherine that the proof is right. "I already knew," Catherine says. She is dismissive, and tells Hal that he can do whatever he wants with the proof. Suddenly, he says, "I don't think your father wrote it." He tells her the proof is very hip, that her father wouldn't have been able to do it. "You blew it," she tells him, bluntly, telling him that he should have trusted her, and that his belated approval doesn't prove anything about his belief in her.
Hal asks if she's going to New York, saying she should stay in Chicago. Catherine says she doesn't mind the idea of being taken care of. "I don't think I should spend another winter here," Catherine says, but Hal says, "There is nothing wrong with you."
He hands her the book, and she tells him that she usually worked on it after midnight and that parts of it feel unfinished or sloppy. She says that her father's work was more elegant, and Hal asks her to walk him through it, insisting that if they go slowly, they could discover something elegant.
Analysis
At the beginning of this section, a giant betrayal occurs, about which Catherine has no knowledge. While Catherine is bedridden, Claire blocks her from speaking to her boyfriend, Hal, and passes over the proof to Hal to do with it what he thinks is best. Catherine gets no say in what happens to the proof or what happens to her, as Claire effectively plans to take her to New York and give the work away without her consent. A devastating dramatic irony comes into play, as the audience becomes aware of this betrayal before Catherine has even been able to emerge from her bed.
In this section, it becomes clear that Robert, Catherine's father, was always the person who believed in her the most. In the flashback scene, he tells her that the thought of her and the fact that she is just beginning her career as a mathematician brings him intellectual inspiration and hope for the future. "I'm proud of you," he says, before inviting her to work on the proof with him, and we see that, while most other people have doubted Catherine, her grip on reality, her abilities, Robert had tremendous faith in her powers as a thinker.
The play takes many sharp emotional turns. Nearly every scene features a moment that goes in a different direction than the audience might have expected. For instance, the scene between Catherine and Robert, which seems so heartwarming at first, becomes completely tragic when Catherine actually reads what he's been writing. Then, the scene between Claire and Catherine before their departure seems like an uncharacteristically tender and sisterly moment, but soon turns sour as Catherine becomes more and more sarcastic and biting about the move. David Auburn specializes in the quick turn, in setting up a scene that goes in a completely unexpected direction.
Part of these quick turns has to do with the fact that Catherine is, above all, a contrarian. When it seems like she is going along with Claire's plan, she cruelly shows Claire that she has no desire for her help. When Hal finally comes to the realization that the proof is Claire's work, she doesn't care anymore. Part of the curse of Catherine's brilliance is the fact that she feels so out of step with the people around her, often because she is five steps ahead of them. In a moment when there should be some kind of resolution, when Hal admits that he believes what she's always known, Catherine is left cold, disappointed that it's taken him so long to believe her.
In the end, mathematics, and the proof that Catherine wrote, become a metaphor for her life and her sense of self. She complains to Hal that the proof is "stitched together" and notes that her father's work was always more elegant. To this, Hal replies, "Talk me through it? Whatever's bothering you. Maybe you'll improve it...Maybe you'll discover something elegant." In this moment, he is clearly talking about the proof, but he also seems to be talking about Catherine herself, the fact that if she works with him, and is patient, she can "improve" her life, and maybe "discover something elegant." The play ends on an ambiguous but hopeful note, with the implication that Catherine will work with Hal and begin to rebuild her life.
