In the play’s opening scene, Catherine and Robert are debating whether Catherine is crazy, and Robert insists that crazy people don’t ask if they’re crazy, so she must be sane. This reasoning seems compelling—until the audience learns that Catherine is currently drinking alone and talking to her dead father, either because she’s drunk or hallucinating. This undermines the audience’s ability to trust their own eyes: Robert initially seemed to be a flesh-and-blood person, but he’s not. It also undercuts Catherine’s credibility, since she’s seeing things that aren’t there. Catherine’s credibility later becomes the core issue of the play when she claims to have written the proof, and the audience—alongside other characters—must evaluate whether to believe her. Their skepticism is reasonable but damaging, particularly to Catherine’s relationship with Hal. Hal doubts Catherine, which makes Catherine doubt Hal, and this wounds them both—but they have to get to a place where they can trust each other again, both for their professional success (getting this proof out into the world) and for their happiness (rescuing their relationship). In the end, just as there’s no easy way to write a mathematical proof, there’s no shortcut to building credibility with others—people must prove themselves, often over and over, to earn trust.
The play immediately creates an environment of uncertainty, making the audience skeptical—particularly of Catherine. This is most apparent in the opening scene, when a conversation that initially seems like proof of Catherine’s sanity—her father reassuring her that “Crazy people don’t sit around wondering if they’re nuts”—instead makes her seem unstable. Robert turns out to be dead, and Catherine may be hallucinating. In this moment, the audience realizes that they can’t trust what they see, and that Catherine’s perceptions must be taken with a grain of salt. Catherine’s credibility is further diminished when she accuses Hal of stealing one of Robert’s notebooks, believing that he plans to publish Robert’s work under his own name. This accusation makes Catherine seem unjustifiably paranoid. And even when Catherine does find Hal with a notebook, his motives aren’t the sinister ones she imagined: he wanted to show Catherine a journal entry that was about her. This exchange deflates Catherine’s credibility, but it also shows a human tendency that isn’t unique to her: it’s easy to misinterpret evidence to support what one already believes.
The play’s major crisis of credibility comes when Catherine claims to have written a complex and groundbreaking proof—a claim the other characters doubt. Their skepticism is well-founded. For one, Catherine has very little formal education in math (she took only a few college classes before dropping out to care for her father), but the proof relies on math so complex that only a few people—ones at the top of their field—can parse it. This leads Hal to conclude that Robert probably wrote the proof, not Catherine. Furthermore, Catherine hasn’t been the most reliable narrator; by this point in the play, her tendency towards mental illness is well-established, so it seems reasonable to suspect that her claiming authorship of the proof is a grandiose delusion. And one devastating piece of evidence is the handwriting in the proof, which looks like Robert’s. This could be a coincidence, but when Hal and Claire weigh all of the evidence, it doesn’t make sense to trust Catherine. Importantly, Hal remains skeptical of his initial conclusion, and when he and his colleagues investigate the proof, he re-evaluates Catherine’s claim. The proof turns out to use mathematical ideas that were developed so recently that Robert wouldn’t have understood them, which points to Catherine being its author. Furthermore, Robert dated everything he wrote, but there are no dates in this proof. After weighing this new evidence, Hal is convinced that Catherine is the proof’s author. While his initial doubt was painful for everyone involved, the process of rigorously weighing the evidence has led him to the right conclusion, vindicating the role of skepticism and evidence.
But even as the play shows the importance of searching for proof, it doesn’t overlook the human cost of doubt. Catherine has been miserable throughout the play—her father has just died, her sister is treating her horribly, and she’s worried that her life is going nowhere. The only thing that seems to bring her joy is her budding relationship with Hal. But Hal’s refusal to take her at her word that she wrote the proof wrecks their relationship and her fragile emotional state. She retreats to her bedroom for a week and, feeling defeated, she agrees to move to New York with her sister. In this, Catherine seems to have lost her spirit—all because she trusted Hal and he broke her trust. And this trust is difficult to rebuild. When Hal returns to her house confident that she has written the proof, it doesn’t matter to Catherine—she no longer trusts him, so his belief in her is meaningless. Just as Hal needed to see lots of evidence before he could trust that Catherine wrote the proof, Catherine needs to see lots of evidence in order to trust Hal again. But Hal—a skeptic himself—seems to understand this. In the play’s final conversation, Hal apologizes and accepts Catherine’s anger. Slowly, the antagonism drains from their conversation and Catherine agrees to walk Hal through her proof. Catherine is still skeptical of him, but he seems prepared to prove himself worthy of her trust.
This process of building trust resembles, in some ways, the process of writing a mathematical proof. In mathematics, one cannot simply claim that something is true—instead, one must rigorously demonstrate it, showing through evidence and logic that the initial claim is correct. In her proof, Catherine lays out 40 pages of mathematical argument to prove an elusive idea that many mathematicians believed to be unprovable. And it’s standard procedure in math for others to doubt a proof; in order for it to be accepted in the community, many mathematicians must vet a proof, testing it for illogic or inaccuracy. The play suggests that this process of providing evidence and overcoming skepticism is a natural way to build credibility, even outside of the field of math. Trust is earned in human relationships, and doubt—however painful it may be—must be slowly overcome.
Proof, Trust, and Credibility ThemeTracker
Proof, Trust, and Credibility Quotes in Proof
CATHERINE: You died a week ago […] You’re sitting here. You’re giving me advice. You brought me champagne.
CATHERINE: Which means…
ROBERT: For you?
ROBERT: For you, Catherine, my daughter, who I love very much…It could be a bad sign.
CATHERINE: I know you mean well. I’m just not sure what I want to do. I mean to be honest you were right yesterday. I do feel a little confused. I’m tired. It’s been a pretty weird couple of years. I think I’d like to take some time to figure things out.
CLAIRE: You could do that in New York.
CATHERINE: And I could do it here.
CLAIRE: But it would be much easier for me to get you set up in an apartment in New York, and—
CATHERINE: I don’t need an apartment, I’ll stay in the house.
CLAIRE: We’re selling the house.
CLAIRE: […] You wrote this incredible thing and you didn’t tell anyone?
CATHERINE: I’m telling you both now. 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. So I kept working here. I worked at night, after Dad had gone to sleep. It was hard but I did it. […]
CLAIRE: Catherine, I’m sorry but I just find this very hard to believe.
HAL: I’ll tell them we’ve found something, something potentially major, we’re not sure about the authorship; I’ll sit done with them. We’ll go through the thing carefully […] and figure out exactly what we’ve got. It would only take a couple of days, probably, and then we’d have a lot more information. […]
CATHERINE: You can’t take it …] You don’t waste any time, do you? No hesitation. You can’t wait to show them your brilliant discovery.
HAL: I’m trying to determine what this is.
CATHERINE: I’m telling you what it is.
HAL: You don’t know!
CATHERINE: I wrote it.
HAL: […] Your dad dated everything. Even his most incoherent entries he dated. There are no dates in this.
CATHERINE: The handwriting—
HAL: —looks like your dad’s. Parents and children sometimes have similar handwriting, especially if they’ve spent a lot of time together.
HAL: Come on, Catherine. I’m trying to correct things.
CATHERINE: You can’t. Do you hear me?
You think you’ve figured something out? You run over here so pleased with yourself because you changed your mind. Now you’re certain. You’re so…sloppy. You don’t know anything. The book, the math, the dates, the writing, all that stuff you decided with your buddies, it’s just evidence. It doesn’t finish the job. It doesn’t prove anything.
HAL: Okay, what would?
You should have trusted me.
HAL: There is nothing wrong with you.
CATHERINE: I think I’m like my dad.
HAL: I think you are too.
CATHERINE: I’m…afraid I’m like my dad.
HAL: You’re not him.
CATHERINE: Maybe I will be.
HAL: Maybe. Maybe you’ll be better.