*Proof*).

David Auburn’s play Proof illustrates that there’s a fine line between genius and mental illness. The play focuses on Catherine, a young woman who may have inherited both her father’s mathematical genius and his mental instability. When her father, Robert, was alive, his delusion and genius were sometimes hard to differentiate—throughout his life, he was obsessed with math, but sometimes his work was groundbreaking and other times, in his periods of mental illness, his work was gibberish. Like Robert, Catherine is a talented mathematician who is prone to bouts of erratic behavior and depression. The tension between genius and illness comes to a head for Catherine when she reveals that she has written a ground-breaking mathematical proof during one of her periods of depression, and neither her sister, Claire, nor her father’s former student, Hal, believe her. Rather than seeing this proof as evidence of her genius, they see it as a symptom of madness: she may be imagining that she is the author, or the proof could be gibberish (just like her father’s later work), or she might have just claimed her father’s work as her own. Of course, in the end, Catherine did write the proof, and she seems to be both a genius and somewhat unstable. This connection between genius and illness points out something that genius and madness have in common: the tendency to see what others can’t.

In Catherine’s family, genius and madness seem inextricably linked—one doesn’t exist without the other. Robert, for example, was a mathematical genius who also suffered from mental illness, and it seems that Catherine is following in his footsteps when she writes an innovative proof during a bad depressive spell. By contrast, Catherine’s sister Claire has inherited neither genius nor madness; her math skills are above average but not noteworthy, and she is levelheaded and emotionally stable. The implication is that, at least in their family, genius doesn’t come without madness—they’re two sides of the same coin.

Genius and madness are also linked because they can be tough to differentiate; madness often looks like genius and vice versa. Robert was a ground-breaking mathematician whose revolutionary contributions to the field made him famous, and his genius lay in his ability to see patterns that others couldn’t. But Robert’s madness also came in the form of seeing patterns that others don’t. For instance, Robert would sometimes suspect that “aliens were sending him messages through the Dewey decimal numbers on library books.” Claiming to have invented new mathematical concepts and claiming to have been contacted by aliens are both unlikely and outlandish claims, which shows how genius and madness can resemble one another.

The play exploits this ambiguity between genius and madness to produce its central tension: whether Catherine really wrote a genius mathematical proof, or whether she’s simply delusional. Like her father, Catherine’s defining trait is her unique perception of the world, which can sometimes seem delusional and at other times brilliant. For instance, Catherine seems bizarrely paranoid when she interprets Hal’s excitement over Robert’s notebooks as evidence that Hal is trying to steal them and publish her father’s work under his own name. She’s partially right (he is trying to sneak a notebook out of the house), but she’s dead wrong about his motives, which makes her seem like she’s inventing facts that aren’t there. But her most outlandish claim—that she wrote the proof tucked away in her father’s desk drawer—turns out to be absolutely true, even if nobody believes her. It’s worth noting that the play ties her ability to write the proof to her unique perception of things: she describes writing it as “just connecting the dots,” even though those “dots” were not obvious to any mathematician but her. Prime numbers are notoriously tricky numbers in math—although the numbers are a sequence, there is no known pattern to them. For Catherine to find a pattern in prime numbers is to see something that others cannot. This is the crux of both her instability and her genius.

Both Claire and Hal make the mistake of thinking of mental illness and brilliance as being mutually exclusive. Claire sees the proof as “proof” that Catherine is delusional (as she suspects that Robert, not Catherine, wrote it). Hal sees the proof as “proof” that Robert was actually experiencing a period of genius when “everyone thought [he] was crazy.” But the proof isn’t so straightforward—it doesn’t show that Catherine is crazy or that Robert was sane. Instead, it’s evidence that Catherine is both genius and unstable: she wrote the groundbreaking proof while in a period of intense depression, making her mental illness inextricable from her brilliant discovery. In this way, the play suggests that people who experience mental instability are able to experience and interpret the world in a different way, which can help them discover brilliant things.

## Genius and Mental Instability ThemeTracker

*Proof*. Click or tap on any chapter to read its Summary & Analysis.

*Proof*LitChart as a printable PDF.

## Genius and Mental Instability Quotes in *Proof*

*Proof*related to the theme of Genius and Mental Instability.

**Act One, Scene 1 Quotes**

ROBERT: You see? Even your depression is mathematical. Stop moping and get to work. The kind of potential you have—

CATHERINE: I haven’t done anything good.

ROBERT: You’re young. You’ve got time.

CATHERINE: I do?

ROBERT: Yes.

CATHERINE: By the time you were my age you were famous.

CATHERINE: You died a week ago […] You’re sitting here. You’re giving me advice. You brought me champagne.

ROBERT: Yes.

CATHERINE: Which means…

ROBERT: For you?

CATHERINE: Yes.

ROBERT: For you, Catherine, my daughter, who I love very much…It could be a bad sign.

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**Explanation and Analysis:**

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.

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**Act One, Scene 4 Quotes**

CLAIRE: Living here with him didn’t do you any good. You said that yourself.

You had so much talent…

CATHERINE: You think I’m like Dad.

CLAIRE: I think you have some of his talent and some of his tendency toward…instability.

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**Act Two, Scene 2 Quotes**

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.

**Act Two, Scene 3 Quotes**

CLAIRE: […] I probably inherited about one one-thousandth of my father’s ability. It’s enough.

Catherine got more, I’m not sure how much.

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**Act Two, Scene 4 Quotes**

CATHERINE: “[…] In September the students come back and the bookstores are full. Let X equal the month of full bookstores. The number of books approaches infinity as the number of months of cold approaches four. I will never be as cold now as I will in the future. The future of cold is infinite. The future of heat is the future of cold. The bookstores are infinite and so are never full except in September…” […] It’s all right. We’ll go inside.

ROBERT: I’m cold.

CATHERINE: We’ll warm you up.

ROBERT: Don’t leave. Please.

CATHERINE: I won’t. Let’s go inside.

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