Proof

by

David Auburn

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Hal is one of Robert’s former PhD students at the University of Chicago. After Robert’s death, it’s Hal who goes through Robert’s 103 notebooks, searching through delusional scribblings to see if there’s anything with mathematical value. This means that Hal is a frequent visitor at Robert’s (now Catherine’s) house, which leads him and Catherine to socialize. While they initially have an antagonistic rapport (Catherine even calls the police on him once), she grows to trust Hal due to his kindness towards her, and they eventually develop a romantic relationship. Despite this, Hal maintains a somewhat sexist and patronizing attitude throughout the play, reflecting the exclusionary atmosphere of the male-dominated field of math. Catherine is a mathematical genius, but Hal seems to believe that because she’s a woman and because she’s not formally educated in math, she couldn’t possibly have much knowledge or ability, and he often explains concepts to her that she already understands. Catherine proves him wrong multiple times throughout the play, but Hal still doesn’t believe her when she claims to have written a groundbreaking proof—he assumes that the work must be Robert’s, since Catherine couldn’t possibly be such an innovative mathematician. This betrayal devastates Catherine, and she hardly gets out of bed for a week. But despite Hal’s sexism, he’s not inflexible—he goes over the proof with several colleagues and realizes that Catherine actually is the author, which leads him to try earnestly to make amends. In order to rebuild their relationship, Hal has to re-earn Catherine’s trust, which he does by expressing confidence in both her sanity and her genius.

Hal Quotes in Proof

The Proof quotes below are all either spoken by Hal or refer to Hal. For each quote, you can also see the other characters and themes related to it (each theme is indicated by its own dot and icon, like this one:
Genius and Mental Instability Theme Icon
). Note: all page numbers and citation info for the quotes below refer to the Farrar, Straus and Giroux edition of Proof published in 2001.
Act One, Scene 1 Quotes

HAL: […] When your dad was younger than both of us, he made major contributions to three fields: game theory, algebraic geometry, and nonlinear operator theory. Most of us never get our heads around one. He basically invented the mathematical techniques for studying rational behavior, and he gave the astrophysicists plenty to work over too. Okay?

CATHERINE: Don’t lecture me.

Related Characters: Hal (speaker), Catherine (speaker), Robert
Page Number: 17
Explanation and Analysis:

HAL: […] “Talking with students helps. So does being outside, eating meals in restaurants, riding buses, all the activities of ‘normal’ life. Most of all Cathy. The years she has lost caring for me […] her refusal to let me be institutionalized—her keeping me at home, caring for me herself, has certainly saved my life. Made writing this possible. Made it possible to imagine doing math again […] I can never repay her.”

Related Characters: Hal (speaker), Robert (speaker), Catherine
Page Number: 23
Explanation and Analysis:
Act Two, Scene 1 Quotes

ROBERT: […] I’m not doing much right now. It does get harder. It’s a stereotype that happens to be true, unfortunately for me—unfortunately for you, for all of us.

CATHERINE: Maybe you’ll get lucky.

ROBERT: Maybe I will. Maybe you’ll pick up where I left off.

CATHERINE: Don’t hold your breath.

ROBERT: Don’t underestimate yourself.

Related Characters: Robert (speaker), Catherine (speaker), Hal
Page Number: 57
Explanation and Analysis:
Act Two, Scene 2 Quotes

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.

Related Characters: Hal (speaker), Catherine (speaker)
Related Symbols: Proof
Page Number: 63
Explanation and Analysis:

HAL: I’m a mathematician […] I know how hard it would be to come up with something like this. I mean it’s impossible. You’d have to be…you’d have to be your dad, basically. Your dad at the peak of his powers.

CATHERINE: I’m a mathematician too.

HAL: Not like your dad.

CATHERINE: Oh, he’s the only one who could have done this?

HAL: The only one I know.

Related Characters: Hal (speaker), Catherine (speaker), Robert
Related Symbols: Proof
Page Number: 64
Explanation and Analysis:
Act Two, Scene 5 Quotes

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.

Related Characters: Hal (speaker), Catherine (speaker), Robert
Related Symbols: Proof
Page Number: 80
Explanation and Analysis:

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?

CATHERINE: Nothing.

You should have trusted me.

Related Characters: Hal (speaker), Catherine (speaker)
Related Symbols: Proof
Page Number: 80-81
Explanation and Analysis:

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.

Related Characters: Hal (speaker), Catherine (speaker), Robert
Page Number: 82
Explanation and Analysis:
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Hal Character Timeline in Proof

The timeline below shows where the character Hal appears in Proof. The colored dots and icons indicate which themes are associated with that appearance.
Act One, Scene 1
Genius and Mental Instability Theme Icon
Hal enters the room, startling Catherine. As he apologizes for staying so late, Robert disappears. Noticing... (full context)
Proof, Trust, and Credibility Theme Icon
Incredulous, Catherine asks how much more time Hal needs; he has already had three days. But Hal says he’ll need at least another... (full context)
Genius and Mental Instability Theme Icon
Hal tells Catherine that he has to go see some friends from the math department play... (full context)
Proof, Trust, and Credibility Theme Icon
When Hal invites Catherine to come with him, she refuses. He suggests another day, but she rudely... (full context)
Proof, Trust, and Credibility Theme Icon
Catherine abruptly demands to see Hal’s backpack, but Hal insists that he wouldn’t take anything out of the house like Catherine... (full context)
Sexism Theme Icon
Proof, Trust, and Credibility Theme Icon
Hal tells Catherine to calm down, that she’s being paranoid—after all, she herself just said that... (full context)
Genius and Mental Instability Theme Icon
Caretaking and Sacrifice Theme Icon
...writing dozens of hours a day, Catherine had to drop out of school. She tells Hal that she is glad that her father is dead. (full context)
Proof, Trust, and Credibility Theme Icon
Hal tries to empathize, but Catherine curses at him and insists that he doesn’t know her.... (full context)
Sexism Theme Icon
...be the one to look through the books; Robert was her father, after all. But Hal says she doesn’t have the skills required to determine what isn’t nonsense. When Catherine insists... (full context)
Genius and Mental Instability Theme Icon
Proof, Trust, and Credibility Theme Icon
Catherine suddenly snatches Hal’s backpack and rifles through it. But there’s no notebook there, only various personal items. Embarrassed,... (full context)
Genius and Mental Instability Theme Icon
Proof, Trust, and Credibility Theme Icon
As Hal gets up to leave, Catherine realizes that he has forgotten his jacket. But when she... (full context)
Sexism Theme Icon
Proof, Trust, and Credibility Theme Icon
Robert wrote that it was “a good day,” since Catherine had some good news—Hal doesn’t know what this refers to, but he thought Catherine might. Catherine asks when Robert... (full context)
Caretaking and Sacrifice Theme Icon
...at home. Robert plans to take Catherine out to dinner that night for her birthday. Hal remarks that the entry is dated September 4, which is the same day as today. (full context)
Genius and Mental Instability Theme Icon
Family and Heredity Theme Icon
Proof, Trust, and Credibility Theme Icon
Hal hands Catherine the notebook, acknowledging that he shouldn’t have tried to “sneak it out,” even... (full context)
Act One, Scene 2
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
...of questions to which Catherine responds tersely, but eventually Claire pieces together the story about Hal and the notebook. She gently asks Catherine if she is dating or sleeping with Hal,... (full context)
Proof, Trust, and Credibility Theme Icon
...or was she partying with her boyfriend? When Claire asks if she was drinking with Hal, Catherine says no. But Claire points to the empty champagne bottle on the table and... (full context)
Genius and Mental Instability Theme Icon
Proof, Trust, and Credibility Theme Icon
As they argue, Hal calls out Catherine’s name and then steps onto the porch. Catherine victoriously announces who he... (full context)
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
After an awkward silence, Claire calmly introduces herself to Hal, who asks if he can get some work in before the afternoon. Claire invites him... (full context)
Act One, Scene 3
Proof, Trust, and Credibility Theme Icon
...out onto the porch. As a band finishes a song, there’s cheering—a few moments later, Hal steps out onto the porch, sweaty from playing. Catherine looks at him and says that... (full context)
Proof, Trust, and Credibility Theme Icon
When Hal encourages Catherine to join the party, she declines. But she does accept one of the... (full context)
Proof, Trust, and Credibility Theme Icon
...admits that one of the band’s songs—the one called “Imaginary Number”—was a pretty nice tribute. Hal agrees; he thinks that the funeral was lovely, and that Robert probably would have enjoyed... (full context)
Proof, Trust, and Credibility Theme Icon
Hal compliments Catherine on her dress, and she replies that Claire gave it to her, but... (full context)
Sexism Theme Icon
Proof, Trust, and Credibility Theme Icon
According to Hal, quite a few older mathematicians are addicted to amphetamines, since they think “math is a... (full context)
Sexism Theme Icon
Awkwardly, Hal acknowledges that he was wrong. Catherine explains that Sophie Germain taught herself math during the... (full context)
Sexism Theme Icon
Hal realizes who Catherine is talking about—Sophie Germain is the person behind Germain Primes. He gives... (full context)
Sexism Theme Icon
When Hal asks whether Gauss ever discovered Germain’s real identity, Catherine says that he did. He then... (full context)
Sexism Theme Icon
Proof, Trust, and Credibility Theme Icon
Hal is stunned for a moment, then he kisses Catherine before pulling abruptly away. He’s embarrassed... (full context)
Family and Heredity Theme Icon
Proof, Trust, and Credibility Theme Icon
Catherine isn’t surprised, and when Hal says he’ll probably quit reading the notebooks soon, she asks him about his research. His... (full context)
Proof, Trust, and Credibility Theme Icon
After a moment, Catherine asks Hal about his sex life, referencing the wild conferences he had mentioned before. Hal can’t tell... (full context)
Proof, Trust, and Credibility Theme Icon
After the second kiss, Hal says that he has always liked Catherine, even just from glimpsing her at a distance... (full context)
Act One, Scene 4
Proof, Trust, and Credibility Theme Icon
The next morning, Catherine is sitting on the porch when Hal, who is partially dressed, steps out to join her. Claire is still sleeping, having drunk... (full context)
Proof, Trust, and Credibility Theme Icon
As they break apart, Hal tells Catherine that last night was incredible. Catherine pauses and, after thinking it through, pulls... (full context)
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
...to move. Enraged, Catherine begins to tell her sister that she hates her, but then Hal enters carrying a notebook. (full context)
Proof, Trust, and Credibility Theme Icon
Hal asks Catherine how long she has known about the notebook. She says “a while,” and... (full context)
Genius and Mental Instability Theme Icon
Hal announces that the notebook contains a very important proof, although he admits that he hasn’t... (full context)
Act Two, Scene 1
Proof, Trust, and Credibility Theme Icon
...front door. Catherine leaves the porch to answer it. She returns to the porch with Hal, who is carrying an envelope. Robert informs Hal that he came at a terrible time,... (full context)
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
Hal awkwardly suggests that he come back at a different time, but Robert tells him to... (full context)
Family and Heredity Theme Icon
Caretaking and Sacrifice Theme Icon
Hal gives Robert the envelope, which he says is only a draft. Robert congratulates him and... (full context)
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
Hal assures Catherine that she’ll have a great time at school, adding that it’s always nice... (full context)
Family and Heredity Theme Icon
When Hal asks Robert if he’s working on anything, Robert says no and adds that he’s glad... (full context)
Family and Heredity Theme Icon
...replies that perhaps she will “pick up where [he] left off.” After a quiet moment, Hal announces that he has to leave. Robert suggests a time to meet about the draft... (full context)
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
...that evening, and the two of them joke about what they will order. Remembering that Hal is still with them, Robert invites him along. Catherine also urges Hal to come, and... (full context)
Act Two, Scene 2
Genius and Mental Instability Theme Icon
Family and Heredity Theme Icon
Proof, Trust, and Credibility Theme Icon
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... (full context)
Genius and Mental Instability Theme Icon
Proof, Trust, and Credibility Theme Icon
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... (full context)
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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.... (full context)
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But Catherine refuses, exclaiming that Hal wants to claim the discovery as his own. Hal denies this; he just wants to... (full context)
Family and Heredity Theme Icon
Sexism Theme Icon
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Catherine laments that she trusted Hal with her work; she chose him to be the first person that she told. When... (full context)
Sexism Theme Icon
Furious, Catherine tells Hal that just because the work is “too advanced” for him doesn’t mean that she didn’t... (full context)
Act Two, Scene 3
Genius and Mental Instability Theme Icon
Proof, Trust, and Credibility Theme Icon
The next day, Hal knocks on the door and calls for Catherine. Claire steps onto the porch and explains... (full context)
Caretaking and Sacrifice Theme Icon
Claire asks why Hal slept with Catherine, suggesting he took advantage of her. But Hal insists that it was... (full context)
Proof, Trust, and Credibility Theme Icon
Hal agrees, but he doesn’t move, since he has another reason for coming. To his surprise,... (full context)
Genius and Mental Instability Theme Icon
Family and Heredity Theme Icon
Proof, Trust, and Credibility Theme Icon
...with the notebook, adding that he should call her when he has more information. As Hal begins to leave, Claire asks him to explain the proof to her. Hal asks how... (full context)
Act Two, Scene 5
Proof, Trust, and Credibility Theme Icon
Caretaking and Sacrifice Theme Icon
It’s a week after Claire gave Hal the notebook. Claire is on the porch, where she grasps a plane ticket and checks... (full context)
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Catherine remains on the porch and Hal suddenly appears, sweaty and out of breath from running. He’s relieved that Catherine is still... (full context)
Sexism Theme Icon
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When Catherine tells Hal that she’s leaving, he asks her to wait. Apathetic, she tells him to publish the... (full context)
Family and Heredity Theme Icon
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Catherine replies that Robert could have read about the newer techniques. Hal admits that it’s possible, but that the proof—unlike Robert’s other notebooks—is undated. As for the... (full context)
Proof, Trust, and Credibility Theme Icon
Hal says he would love to at least hear Catherine talk about writing the proof, but... (full context)
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After a moment, Hal asks Catherine if she’s really going to New York City. She says she is, and... (full context)
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As she traces her fingers over the book, Catherine tells Hal that writing the proof was like “connecting the dots.” She never worked on it with... (full context)