It’s the day after the party, right after Catherine announced that she wrote the proof. Hal is baffled, asking multiple times if she really wrote it. Claire asks Hal how and where he found the notebook, cutting off Catherine whenever she offers answers. Claire eventually asks Catherine directly if she wrote the proof, and Catherine says yes—she started it when she got depressed after she had to drop out of school to take care of Robert.
Neither Hal nor Claire appears to believe that Catherine wrote the proof. Although the characters haven’t explained why they doubt Catherine, the audience may also feel hesitant to believe Catherine—from her imagined conversation with Robert to her paranoid assumption that Hal was stealing notebooks, the audience has good reason to doubt Catherine’s word. They need more evidence to believe her statement. If Catherine did write the proof, it is important to note that she did so during a period of depression. It would seem that mental illness and genius are inextricable from each other. If the proof is hers, it would mean that she inherited both Robert’s mental instability and his genius, both of which come into play when she writes this proof.
Claire doesn’t believe Catherine, because it’s written in Robert’s handwriting. Catherine asks Hal to confirm that it is actually her handwriting and not her father’s, but Hal isn’t sure. Claire then asks Catherine to explain the proof without using the book, which Catherine angrily says is impossible—it’s extremely long, and she didn’t memorize it.
Claire’s immediate refusal to believe Catherine is in-line with her behavior so far—she never respects what Catherine says. Therefore, it’s not a surprise that she doesn’t believe that Catherine wrote the proof, particularly because Claire believes that Catherine is succumbing to the same mental illness that Robert suffered from. As a result, Claire interprets information to match her theory, as opposed to objectively gathering evidence to make a claim. But with Catherine’s history of delusions, it does make sense to be skeptical of her claim. In order to get Claire, Hal, and the audience to believe her, Catherine needs to provide proof.
Claire relents and tells Catherine to go over the proof with Hal. But Hal raises the possibility that Robert went over it with Catherine before he died. He suggests that he take it to some “guys” in the math department, and Claire agrees.
Hal, like Claire, doesn’t believe that Catherine wrote the proof. He’s so certain that Robert wrote it that he refuses to compare Catherine’s handwriting to the handwriting in the proof. In this way, Hal is also so set on proving his own theory that he passes up evidence that could be important to finding out who is the author of the proof. All the same, Hal is intent on rigorously analyzing the proof, which he wants to do with some of his colleagues. Given that Hal refers to his colleagues as “guys,” either all his colleagues are men, or all the colleagues he would trust with this project are men. The former suggests systematic sexism (women are not being encouraged to study and research math at high levels) while the former suggests Hal’s internalized sexism—he only trusts men to be smart enough for this project.
But Catherine refuses, exclaiming that Hal wants to claim the discovery as his own. Hal denies this; he just wants to know more about the proof. When Catherine says that she can explain it to him now, Hal tells her that “[she] [doesn’t] know.” She claims again that she wrote it, but he says that it’s written in Robert’s handwriting. Catherine quietly insists that her handwriting looks similar to her father’s.
Now that Hal has broken Catherine’s trust in him by not believing that she wrote the proof, she feels that she can’t trust him with anything. Trust is easily broken. Catherine is even certain that he is going to try to take her discovery as his own. Given that Hal is a man, it is likely that he would be believed over Catherine who, as a woman, would likely be dismissed as incapable of discovering something so innovative. In this way, Catherine’s chance at being recognized for her work lies in Hal’s hands.
Catherine laments that she trusted Hal with her work; she chose him to be the first person that she told. When she asks if he wants to test her handwriting, he replies that Robert could have dictated it to her. As a mathematician, he “know[s] how hard it would be” to make this kind of discovery. When Catherine reminds Hal that she, too, is a mathematician, he dismisses her, saying that she only took a couple college classes and that this kind of math could only be accomplished by someone like Robert when he was “at the peak of his powers.”
Catherine is really upset that Hal doesn’t believe her. She had waited to show off the proof until she found someone that she could trust. Up until this moment, Hal and Catherine’s budding relationship was steadily building. But by not believing her, Hal destroys their relationship. While Hal may have good reason to suspect that Catherine didn’t write the proof—the handwriting looks like Robert’s and Catherine has only a little formal education—his skepticism also appears to be motivated by sexist thinking. It’s suggested that one of the reasons that Hal doesn’t believe that Catherine wrote the proof is that he doesn’t think that she, a woman, could write something so innovative. He condescends to her, dismissing her abilities and implying that she isn’t really a mathematician like he is. The only person that Hal thinks could write the proof is Robert, a man. If Catherine did indeed write the proof, then Hal’s sexist stereotyping threatens her chance of being recognized for her work. Additionally, if Catherine is the author, then she and her father are even more similar than the audience knew—her ingenious work looks like his.
Furious, Catherine tells Hal that just because the work is “too advanced” for him doesn’t mean that she didn’t write it. People like Hal just don’t want to believe that she—someone who never got a Ph.D.—could accomplish such ground-breaking work. Without a word, Hal leaves the porch.
With their relationship now in tatters, Catherine insults Hal. While she doesn’t call out Hal’s sexism, she does call out his elitism—he seems unwilling to accept that someone who hasn’t undergone his training could discover something so beyond his comprehension. This elitism is similar to Hal’s sexism in that, in both cases, Hal is resistant to believe that someone who isn’t him—an educated male—could accomplish something that he can’t.
Catherine is distraught. After a moment, she tries to destroy the notebook in her hands, but Claire grabs the book away from her. When Catherine manages to wrestle it back, she simply throws it to the ground and walks away.
Catherine is devasted that neither Hal nor Claire—but particularly Hal—believes her. Their skepticism appears to be taking a toll on her already fragile emotional state. She almost tries to destroy the proof, which, if hers, is extremely valuable to her (it could jumpstart her career and make her famous). Her attempt to destroy it suggests that she is despairing, no longer interested in her future now that the one thing that was giving her joy—her budding relationship with Hal—is destroyed.