Summary
Scene 3. Nighttime. Out on the porch, Catherine is sitting. Inside, Hal's band is playing for a post-funeral party. He comes out with two beers and joins her, inviting her to come inside. She reluctantly takes the beer and asks him how many people are still there. "It's down to about 40," he says, and adds that it is not Claire's friends, but mathematicians.
In spite of herself, Catherine concedes that "the performance of 'Imaginary Number' was...sort of...moving." They talk about how many people came to the funeral, and Hal comments on the fact that the mathematicians will likely stay at the house for a long time, since they like to party so much. Catherine is surprised to learn that mathematicians are party animals, and that many of them are hooked on amphetamines to make them feel sharp. Catherine and Hal discuss the fact that most prominent mathematicians are young men and Hal cannot think of any examples to counter this stereotype.
Catherine brings up Sophie Germain, a mathematician born in Paris in 1776, who posed as a man in letters and wrote to Gauss, a famous mathematician, sending him revolutionary work in the field. When Catherine seems to know more about the principle that Sophie Germain discovered, Germain Primes, Hal is impressed. He kisses her suddenly.
He apologizes and tells her he is drunk. Catherine doesn't seem to mind and tells him he can keep looking in her father's study for as long as he wants. After asking him about his own work, Catherine moves closer to Hal and kisses him. Hal tells Catherine that he liked her even before he met her, when he saw her visit her dad at the college. Catherine remembers him coming over to drop off a draft of his thesis four years prior. "I remember you," she says, "I thought you seemed...not boring."
Scene 4. Catherine is on the porch in a robe the next morning. Hal comes out and asks if she wants to go out for breakfast. She tells him she should wait until Claire leaves in a few hours, and he tells her he wants to spend the day with her. Suddenly, Catherine takes a key from around her neck and gives it to Hal, telling him to look in the bottom drawer of her father's desk.
As Hal goes to investigate, Claire comes in, hungover. She tells Catherine she couldn't keep up with the physicists and Catherine thanks her for the dress. Claire again invites Catherine to come live in New York and sort through the next step in her life. Catherine replies, "It's been a pretty weird couple of years. I think I'd like to take some time to figure things out."
Claire then reveals that she's planning to sell the house to the university. "I LIVE HERE," Catherine yells, suddenly angry. The sisters fight about the fact that Claire was not around to care for their father, but Claire insists that she paid off the mortgage on the house while living in a studio in Brooklyn. Claire alleges that their father should have been institutionalized, before insinuating that she thinks Catherine inherited some of his instability.
When Catherine realizes that Claire has been scouting out some mental health resources in New York for her, she becomes infuriated. "I HATE YOU," she yells at her sister, just as Hal comes out onto the porch with a notebook. He has found a "very important proof" in a notebook in the drawer that Catherine tipped him off to.
Hal reveals that the proof "means that during a time when everyone thought your dad was crazy...or barely functioning...he was doing some of the most important mathematics in the world." Catherine then reveals that she wrote the proof herself.
Analysis
Tonally, the play has two contrasting sides. At times, it can be comedic and wry, with darkly humorous jokes about insanity, mental illness, and death that lend levity to the action. At other moments, the stakes of the action feel distressingly high, and we see that the characters are wrestling with some serious demons. David Auburn's writing seamlessly interweaves the comedic with the devastating.
The question of gender is raised when Hal and Catherine start to talk about famous mathematicians. First they talk about age, and the fact that many mathematicians fear that they will lose relevance after a certain age. In telling Catherine that many mathematicians believe that "young guys" are the most creative of the bunch, she questions the fact that it's all guys. The only important woman in mathematics they can come up with is someone long dead.
As they become a little closer and learn more about one another, Hal and Catherine begin to fall in love. When Catherine demonstrates her understanding of math and of the history of math, Hal cannot help but kiss her. Even though he is immediately self-conscious about having come on to her, she demonstrates that she hardly minded when she comes on to him, kissing him abruptly. For the first moment in the play, we see Catherine beginning to blossom and open up to someone, after the trauma of caring for and losing her father.
Claire and Catherine's relationship becomes all the more complicated when we learn that Claire is apparently selling the house from under Catherine, and also apparently believed their father should have been put in an institution. This is a double slap for Catherine, who believes that she has done only what is best for their father, and that she is entitled to make her own decisions. Things only get worse when Claire insinuates that she believes Catherine has inherited some of their father's instability. Not only are Claire and Catherine different, but Claire demonstrates a chilly disregard for Claire's struggles.
In a climactic moment, just as it seems that everything is crumbling for Catherine, Hal emerges with a proof of her father's that could change everything. The discovery of the proof could completely change things for Catherine, as the person who found the proof. Then, just after this happens, things become even more climactic when Catherine reveals that not only did she find the proof, but she wrote it herself. Just before the end of the act, everything that we thought we knew about Catherine's circumstances changes dramatically.
