It’s December, about three-and-a-half years earlier. On the porch, Robert is wearing a t-shirt and writing in a notebook. Catherine steps outside wearing a winter coat and asks what he’s doing. He says it’s too hot in the house and that the heaters make it hard to concentrate. Catherine then asks why he didn’t answer the phone—she’s been calling, and she had to miss class to come check on him. As Catherine hands him a coat, he says that the phone distracts him.
Like the opening scenes of both Act One and Act Two, this scene also begins with Robert and Catherine on the porch. At this point, the audience is still unsure whether Catherine did or did not write the proof. With this scene beginning in a similar way to two other scenes—one where both Catherine and Robert seem stable, and the other where Catherine appears to be suffering from delusions—the sense of uncertainty builds: will this be the scene where the audience discovers if Catherine really wrote the proof? Or will this scene prove that she’s delusional? The audience needs more evidence to be sure. Robert is writing furiously in a notebook, which may mean that he’s experiencing a stroke of genius and is writing the proof, or it may mean that his mental health has now deteriorated, and he’s writing compulsively. It’s hard to tell, and this ambiguity highlights how genius and madness may look similar.
Robert then announces that “The machinery is […] on full-blast”—his mind is working creatively, like it did when he was 21. Surprised, Catherine asks if she can look at what he’s been working on. Robert asks if she is actually interested, but it’s clear she’s excited. He tells her tenderly that it makes him very happy that she is following in his footsteps by becoming a mathematician.
According to Robert, he’s experiencing a burst of creative energy. But the audience, who knows that Robert compulsively wrote nonsense in his later years, doesn’t know whether to believe him. The audience needs actual evidence to support Robert’s claim. If Robert is actually experiencing a relapse of his mental instability, then it is important to note that even Robert confuses his moments of genius with his periods of mental illness—both would feel as though his brain is “on full-blast,” perceiving things that others cannot. Catherine’s excitement over Robert’s work suggests that she has inherited his passion for math, which makes Robert very happy—he wants her to be like him in this way.
Robert confesses that he had been terrified that he would never be able to work like he used to. But it comforted him to know that Catherine would be able to finish the work he started. In fact, this is one of the main reasons people have children: a person’s kids can achieve what the parent couldn’t.
To Robert, it’s reassuring to know that his daughter will carry on his legacy. Family is one way in which people live on after death—their children carry on their genes and (hopefully) achieve what they couldn’t.
Now that his mind is working again, Robert tells Catherine that the two of them can work together. He selects one of the notebooks and gives it to Catherine. She reads a bit of it before telling Robert that they should go inside.
Robert clearly has confidence in Catherine’s abilities—he, a genius by all accounts, wants her help and input on his work, which suggests that she has indeed inherited his abilities. But when Catherine reads the notebook that he gives her, she doesn’t respond positively; instead, she simply tries to persuade Robert to go inside. Her reaction suggests that there may be something wrong.
Robert refuses to go inside until they talk through the proof, so Catherine begins to read the notebook aloud. It’s just gibberish, a string of thoughts about temperature, months, bookstores, and the occasional number. Robert begins to shiver. Catherine closes the book and leads him into the house. Robert begs her not to leave, and Catherine promises she won’t.
Robert’s “proof” turns out to be evidence that he has slipped back into a state of mental delusion. Curiously, in his writing, he makes a series of incoherent connections. During this state of mental instability, Robert perceives patterns and meanings that others cannot see, just like during his periods of genius. At the same time, Robert’s gibberish “proof” suggests that he wasn’t the one who wrote the proof Catherine claimed to have written. Given that Robert wasn’t mentally sound enough to have written the proof, Catherine’s claim seems a lot more believable. Catherine also demonstrates her selflessness and dedication when he begs her not to leave him. Having already cared for him for years, Catherine knows that taking care of Robert will mean giving up her social and academic life. Yet knowing that he wants her to care for him at home, she respects his wishes.