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===Act II=== Four years earlier, Robert sits in the backyard. Catherine tells him she thinks he is getting better and he agrees. She blurts out that she has decided to go to college in a couple months, funded by Claire, but promises she will be only a short drive away if he were to need her again. Robert protests and demands to know why she waited so long to tell him. When she points out that he hadn't been well until recently and was, at one point, trying to decode [[Extraterrestrial life|extraterrestrial]] messages in library books, he becomes upset. Hal interrupts, much to his embarrassment, to present his final dissertation to Robert. Robert assures him they will eventually work out the problem points together, then suddenly realizes he has forgotten Catherine's birthday. He apologizes and offers to take her out to dinner. Catherine invites Hal along but he says he can't go. Catherine shows Hal out and Robert sits down to write a notebook entry, declaring it to be the aforementioned "good day". Resuming the end of the first act, Catherine declares she was the one who wrote the proof and is met with incredulity by both Hal and her sister. The handwriting is very much like Robert's and Hal questions Catherine's mathematical abilities given that she only had a few months' education at Northwestern. Catherine tells him that her real education was living with Robert. When Hal offers to show it to other math experts to confirm the authenticity of the proof, Catherine refuses. She tells Hal she trusted him and then accuses him of having no talent and being past his prime. Hal storms off and Catherine begins to rip the notebook apart. Claire gets it away from her and Catherine runs into the house. The next morning, Hal attempts to visit Catherine and apologize for his behavior. Claire stops him to say Catherine won't talk to her, let alone Hal. Claire accuses him of sleeping with Catherine despite her being unstable. Hal argues that he had no bad intentions and insists Catherine is stronger than Claire thinks. He requests to have the notebook to verify its authenticity with fellow mathematicians. Claire gives it to him and tells him she is taking Catherine with her to New York the next day. She expresses concern for Catherine's future mental stability. Almost four years earlier, Robert sits in the backyard, in the cold and writing furiously. Catherine enters and reprimands him for sitting in the cold with no jacket. Robert tells her it is too hot in the house and that the cold is better for helping him work. Catherine is shocked that he is working again and he assures her that he is sharper than ever. She is ecstatic that his previous mental instability has passed and asks to see his work. He says he would love for her to take a look and asks if she'd like to take time off school to work with him. Before she decides, Robert insists she look at his latest idea and thrusts a notebook into her hands. Catherine glances at it and becomes quiet. She tells him they need to go inside and Robert explodes with fury. He yells at her to read what he has written. She reads aloud, a nonsensical, rambling paragraph mathematically equating winter, books, and the cold. It is obvious that Robert's mind is deteriorating as it had been before. Catherine realizes Robert is descending into confusion and shivering uncontrollably. She tries to take him inside when he asks her not to leave. She promises she won't. Four years later, Claire is in the backyard. Catherine enters with her suitcase. She asks Claire about life in New York. Claire mentions potential schools or jobs for Catherine, who is quick to mock her by making ridiculous demands for a Freudian psychiatrist who will listen as she blames all her problems on Claire. Claire leaves Catherine's plane ticket before storming off. Hal enters and tells Catherine that the proof checks out and apologizes for not believing her. Catherine tells him there is no proving that she wrote it and he can claim it as his own if he wants. Hal tells her he believes she is the one who wrote it and offers to read through it with her. Catherine admits she knows she is like her father but is terrified of becoming like her father. Hal reassures her that maybe she will be better. Catherine opens the proof and begins to talk through it with Hal.
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