Summary
Act 2, Scene 1. Four years prior. Robert is dozing on the porch, when Catherine comes out and tells him she's going to the store to get some dinner. He complains that he doesn't want pasta again, and Catherine reveals to him that she's going to Northwestern to go back to school—that they have agreed to give her a free ride and that Claire has agreed to pay her expenses.
Robert is not so keen on Catherine moving to Evanston and leaving him all alone. They argue about the fact that Robert has not been well, when Hal interrupts them, delivering his thesis. Robert tells him he interrupted an argument, then offers him a drink, which he accepts. Robert tells Hal that Catherine is starting up her undergraduate degree at Northwestern soon. Hal comments on the fact that starting up at a new place is always exciting.
"Maybe I want to have the place to myself for a while, did that ever occur to you? It's awful the way children sentimentalize their parents," Robert says. He then delivers a monologue about how he loves to see young people at the bookstore browsing. He turns to Catherine and tells her, "Maybe you'll pick up where I left off...Don't underestimate yourself." Suddenly, in the midst of planning for Hal to come back the next week, Robert realizes it's Catherine's birthday; "I am sorry. I used to have a pretty good memory for numbers," he says.
Robert tells Catherine he's going to take her out, and she tells him she wants to eat steak, potatoes and creamed spinach, and drink "that Chicago beer that's watery with no flavor and you can just drink gallons of it." They invite Hal along, but he doesn't want to come. When Hal leaves and Catherine goes to change, Robert writes in his notebook, "September 4th. A good day."
Scene 2. Back in the present, Hal asks Catherine about the proof she wrote. "I started after I quit school. I finished a few months before Dad died," Catherine says. Claire asks to see the notebook, skeptical that Catherine did the work. Catherine tries to explain: "After I dropped out of school I had nothing to do. I was depressed, really depressed, but at a certain point I decided, Fuck it, I don't need them. It's just math, I can do it on my own...It was hard but I did it." Claire still doesn't believe, and Hal does not know either.
Claire asks Catherine to walk them through the proof to prove that she did it, but insists that Catherine cannot look at the proof while she explains it. "I didn't MEMORIZE it. It's not a muffin recipe," Catherine says, indignant. Claire gives her back the book, but Hal is skeptical, insisting that perhaps Robert wrote the proof and explained it to her. "I'm just saying there's no proof that you wrote this," Hal says.
When Hal offers to bring the proof to some guys in his department, Claire refuses to let him take it, accusing him of trying to steal her work. Suddenly, he alleges that the handwriting is her father's. She tells him that she has similar handwriting to him, but this isn't enough, as he thinks that Robert could have dictated it to her. "I'm a mathematician too," Catherine says, but Hal is unconvinced. "You could not have done this work," Hal says.
"It would be a real disaster for you, wouldn't it? And for the other geeks who barely finished their Ph.Ds, who are marking time doing lame research, bragging about the conferences they go to—WOW—playing in an awful band, and whining that they're intellectually past it at twenty-eight, BECAUSE THEY ARE." Hal leaves, dejected, and Catherine tries to rip the book apart, but Claire wrestles it out of her hands.
Analysis
At the top of the second act, we get a window into Robert and Catherine's actual dynamic when they were living together. We see a scene in a time of remission for Robert, but there is a great deal of tension between them, and a codependent dynamic that we see has formed as a result of their cohabitation. When Catherine tells Robert she plans to return to school, he is skeptical of how she will be able to manage. We see that he was a discouraging force in her development as an individual and a mathematician, and while they share a great deal, he is a tough critic.
As the scene progresses, we see that, as much as Robert likes to be tough on Catherine, he also believes in her tremendously. When Hal shows up with his thesis, Robert brags to him that Catherine will be attending Northwestern soon. When she says, "I think I can do it," Robert tells her, "Of course you can." For all his roughness and prickly attitude, in his heart of hearts, he believes in his daughter, and the reason he is tough on her is because he wants to see her flourish.
In this section, we get a window into Robert's perspective, at a time when he realized that his authority as a mathematician was dwindling in his later years, and that nothing pleased him more than seeing young people discover for the first time. He delivers an affectionate monologue about seeing young people just browsing at a bookstore, and the pleasure that he takes in seeing young people inherit the work that he began. His connection to the world is a vicarious one, a sense that people younger than him will inherit the world he began to create.
Back in the present, Catherine must contend with the fact that people are skeptical that the proof is her work. Claire, who doubts that Catherine is completely mentally well, sees Catherine's claims to authorship as just more evidence of her insanity, and Hal does not come to her defense either. What seemed like it might be a moment of triumph and revelation for Catherine turns into a moment in which people only doubt her more. From this climax, a new conflict emerges, and Catherine must prove to the people around her that the work is hers.
The title "Proof" takes on a double meaning here. Not only does it signify the document that showed up in the bottom drawer of her father's desk, but it also describes the conflict that Catherine finds herself in—the fact that she must prove that she is the author of this work. Not only is the proof mathematical, but it is a matter of proving her own brilliance and identity. The skepticism around Catherine's authorship is pointed and particularly gendered, as Hal and Claire do not believe that Catherine, a young woman, could possibly have churned out such impressive work.
