In researching Proof, Auburn consulted with a number of mathematicians and also read the biographies of prominent mathematicians, aspects of whose lives find their way into the play. When Hal tells Catherine that some of the older mathematicians he encounters at conferences are addicted to amphetamines, which they take to make their minds feel sharp, he is amplifying the well-known story of mathematician Paul Erdös who began taking amphetamines so he could keep up the fast pace of his mathematical work. When friends persuaded him to stop taking the amphetimines for a month, Erdös complained that he had not been able to do any creative work during that time and promptly resumed taking the drugs.

Andrew Wiles is another mathematician whose story finds an echo in Proof. Wiles, a professor of mathematics at Princeton University, worked for many years to prove Fermat’s Last Theorem when the conventional wisdom was that such a proof was impossible. In 1993, Wiles announced at a conference that he had proved the theorem. It transpired that he had been working on it in solitude, in an office in his attic, for seven years, telling no one of what he was doing. This surely inspired the picture Drawing of a geometric calculation by presented in Proof of Catherine, who also works in solitude and in secret, and then suddenly, out of the blue, unveils a ground-breaking mathematical proof.

But the mathematician whose life story is most closely linked to Proof is John Forbes Nash, Jr, who is the subject of A Beautiful Mind (1998), a biography by Sylvia Nasar which was made into a popular movie in 2001. Nash was a mathematical genius. In 1949, when he was twenty-one years old and a graduate student at Princeton University, he wrote a slim, twenty-seven-page doctoral thesis on game theory (a theory of how people behave when they expect their actions to influence the behavior of others) that revolutionized the field of economics. Nash became a professor at the Massachusetts Institute of Technology (MIT) when he was only twentythree and quickly went on to solve a series of mathematical problems that other mathematicians had deemed impossible. He seemed destined to become one of the greatest mathematicians in the history of the discipline. Then, in 1959, when Nash was thirty years old, his behavior, which had always been eccentric, became bizarre and irrational. He heard strange voices and became obsessed with the idea of world government. He accused a colleague of entering his office to steal his ideas. He turned down the offer of a chair at the University of Chicago with the explanation that he was going to become Emperor of Antarctica. Nash was admitted to McLean Hospital in Belmont, Massachusetts, where he was diagnosed as a paranoid schizophrenic.

Schizophrenia is a severe mental disorder that distorts thinking and perception. It leads to a loss of contact with reality and bizarre, sometimes antisocial behavior as the sufferer withdraws into his own inner world. Schizophrenia is difficult to treat and there is no cure. Nash spent the next thirty years afflicted with the disease, which would occasionally go into temporary partial remission before returning. His career was destroyed although he made a surprise recovery during the 1990s. He resumed living a normal life and studying mathematics and was awarded the Nobel Prize in 1994.

The parallels between the real life of Nash and the fictional life of Robert in Proof are many, and they prompt questions of whether genius and insanity are linked and whether both are inherited. Robert is clearly a Nash-like figure. Hal reminds Catherine...

In his Puliter Prize–winning play Proof, Auburn brings into high relief the uncertain nature of life by contrasting it with the world of mathematics, where the truth or falsity of an idea can be proved with absolute certainty. In the world of numbers, two plus two always equals four; there is no doubt involved. But in matters of flesh and blood, especially in the way people relate to the world around them, there is no formula for absolute knowledge.

The tenuous nature of reality as perceived through human eyes is vividly depicted in the play’s very first scene. Catherine, the troubled daughter of Robert, a brilliant mathematician of world renown, is having a revealing conversation with her father early in the morning of her twenty-fifth birthday. During the conversation, it is revealed that Robert suffers from mental illness. By its very nature, mental illness radically distorts a person’s perceptions of the world. It is also the nature of such an illness that the person afflicted with it is deluded into thinking that his perceptions are completely grounded in reality. As Robert tells Catherine, ‘‘Crazy people don’t sit around wondering if they’re nuts.’’ As their conversation continues, he reinforces the point by saying, ‘‘Take it from me. A very good sign that you’re crazy is an inability to ask the question, ‘Am I crazy?’’’

Robert is, in fact, an expert on the subject. After displaying mathematical genius in his early twenties, his career had been cut short by a debilitating mental illness. This is a man who, after rocking the math world with his proofs, began attempting to decipher the Dewey decimal codes of library books because he was convinced that they held hidden secret messages. Consequently, Catherine is wary of accepting the insights of a certified crazy person. It is not until midway through this first scene that the audience discovers that Richard is actually dead and that the action playing out in front of them is only a figment of Catherine’s imagination, calling into question her sanity. As a result, from the outset, the audience itself is forced to ask the question: What is true and what is not—and how do you prove the conclusions arrived at?

This theme is carried throughout the play as Auburn compels the audience to keep wondering what the truth is. There is a particularly poignant scene near the end of act 2 when Robert makes another appearance, this time in a flashback. After suffering through years of mental illness, he has experienced months of clarity. His recovery has been so significant that Catherine, who had given up pursuit of her own career in mathematics in order to care for him, was able to return to school. She pays a visit to her dad and finds him sitting outside in the freezing cold, working. He tells her that his ‘‘machinery,’’ meaning his brain, is once again firing on all cylinders. He is exhilarated to the point of being overheated and has gone out into the December day in order to cool off. Trying to describe for his incredulous daughter the incredible feeling that he is experiencing, Robert tells her that it is not as if a light has suddenly turned on in his mind, but rather the whole ‘‘power grid’’ that has been activated after years of dormancy. ‘‘I’m back!’ he tells her. ‘‘I’m back in touch with the source—the font, the— whatever the source of my creativity was all those years ago. I’m in contact with it again.’’ She reads what he has been scribbling in his notebook and in an instant it becomes painfully clear that what has returned is not the spark of genius but insanity.

The play’s most significant questions are raised about Catherine, who is the main focus of uncertainty. Has she inherited her father’s genius? Does she suffer from the same mental illness that afflicted him? Have both the incandescent brilliance and the dark demons been passed from father to daughter? Again, unlike the world of mathematics, the answers to those questions are anything but clear-cut. It is part of Auburn’s genius that he constructed a play guaranteed to hold the audience’s interest by inserting the compelling elements of a mystery into what is, at its heart, the story of complex human relations. In an interview with Mel Gussow of the New York Times, Auburn notes that the genesis of this play can be traced to two ideas. One involved writing about two sisters ‘‘quarreling over the legacy of something left behind by their father.’’ The other had to do with someone whose parent suffered from mental illness and began to wonder whether she, too, might be starting to succumb to madness. To pull the audience along, Auburn tells Gussow that he wanted to use what Alfred Hitchcock referred to as a ‘‘Maguffin,’’ or plot device involving an object of mysterious origin. In this case, Auburn chose to insert the discovery of a mathematical proof into the story. That proof, whose existence is revealed at the end of act 1, provokes two essential questions: Is it indeed a brilliant breakthrough and, if so, who produced it—Robert or, as she herself claims, Catherine?

The character asking those questions is Hal, a former student of Robert’s who has gone on to become a mathematics professor. He also has had a romantic eye on Catherine for many years. The question of the proof’s validity is relatively easy to solve. Writing about this play in The Chronicle of Higher Education, David Rockmore explains that this is fundamental to the concept of a proof. ‘‘Assuming that a person knows the language and has the background,’’ writes Rockmore, ‘‘anyone could, in theory, check all of the steps and decide on the correctness of a proof, and any two persons would make the same judgment.’’ Determining whether Catherine is the source of this brilliant piece of work, or is instead merely suffering from the same sort of insane delusions that afflicted her father, is a much more difficult task. As Rockmore, a professor of mathematics at Dartmouth College, observes, ‘‘In statements about life, proofs of similarly absolute certainty are difficult, if not impossible, to derive.’’

Consequently, Auburn does not wrap his play up into a neat and tidy package. In that sense, it mirrors life. As the play approaches the final curtain, Hal comes to believe that it was indeed Catherine who produced the proof. It is Catherine herself who keeps the mystery alive, telling Hal:

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.

That is the way life is. Very few things are completely provable beyond a shadow of doubt. But absent proof, there is always possibility. And so, it is entirely appropriate that this play ends on an optimistic note. There is the promise that Catherine is indeed every bit as brilliant a mathematician as her father. There is also the very real possibility that she will not be overtaken by madness and will instead be able to keep a firm grasp on reality. As the curtain falls with her and Hal sitting side by side, there is no proof positive that the two will find happiness and build a life together. There is, however, hope.

Source: Curt Guyette, Critical Essay on Proof, in Drama for Students, Thomson Gale, 2005.

Manhattan theater club does it again! David Auburn’s Proof is what Copenhagen ought to be: a play about scientists whose science matters less than their humanity. Here, those of us who want their dramatic characters to be real people need not feel excluded. Robert, a world-famous mathematician who went crazy; Catherine, his mathematically brilliant but too-depressed-to-work daughter; Hal, a young math teacher going through Robert’s hundred-plus confused notebooks: and Claire, Robert’s older daughter and a successful actuary, are above all fascinating individuals. Robert isn’t any less human even for being, through most of the play, dead. All four—whether loving, hating, encouraging or impeding one another—are intensely alive, complex, funny, human.

The very first scene in Proof is masterly: a birthday dialogue between father and daughter, in which Catherine, alive, is barely living, and her celebrated father is sparklingly trying to rouse her into action although he is (I hate to give it away but must) dead—Catherine’s fantasy. Yet this mysterious, droll, and electrifying scene is really exposition in disguise: something generally a bore, but here so splendidly reconceived as to fascinate—as indeed all of Proof does.

So here we have Robert, the near-genius mathematician who went mad and eventually died, and Catherine, who gave up a potentially great mathematical career to look after him and, in the process, let herself run down, perhaps irreversibly. Here, too, is Claire, the narrowly practical daughter, who wants to save Catherine from what may be incipient madness by dragging her from Chicago to New York and supervising her life—benignly as she sees it, but horribly as Catherine does. And here is Hal, revering Robert’s work and secretly in love with Catherine, bumbling and bungling everything. Out of this curious quartet, Auburn creates emotionally and intellectually enveloping music.

The performances are perfect: Larry Bryggman’s lovable but exasperating Robert; Johanna Day’s officious yet well-meaning Claire: Ben Shenkman’s clumsy but gradually maturing Hal. As for Mary- Louise Parker, her Catherine is a performance of genius. Is there another young actress as manifold, incisive, sexy, and effortlessly overpowering? Add to this Daniel Sullivan’s superb direction and the classy production values (by John Lee Beatty, Jess Goldstein, and Pat Collins), and it all spells J-O-Y. Instead of taking up more time reading, you are urged to run and get your tickets immediately.

Source: John Simon, ‘‘Proof Positive,’’ in New York, June 5, 2000, p. 106.

Proof, which recently re-opened at the Walter Kerr Theatre after a run at the Manhattan Theatre Club, is the latest in a string of plays with one-word titles that represent the theater’s belated tribute to the conceptual mind. Tom Stoppard probably started the whole fashion with Arcadia, a period comedy that features, among other things, dialogues on English gardening and Newtonian physics. But the trend has exploded in the last few years to include Yasmina Reza’s Art, an argument provoked by a post-modern painting, Margaret Edson’s Wit, an infirmity play surrounded by a frame of metaphysical poetry, and Michael Frayn’s Copenhagen, a scientific discourse on the subject of quantum theory, indeterminacy, and atomic fission. These are the major examples of a genre with terse titles and prolix personae that has now managed to occupy the middle (or the middlebrow) ground of the Western stage.

I am still trying to figure out why this development leaves me somewhat less ecstatic than it does my critical colleagues. Obviously we should encourage anything that raises the intellectual level of our benighted theater; and it is also true that some of these plays (notably Wit) have a lot more going for them than mental pyrotechnics. Yet the danger of this kind of Cliffs Notes approach to playwriting is that the dramatist, simply by dropping names or equations, will feel relieved of the obligation to investigate the emotional and spiritual aspects of the material, and the spectator will leave the theater feeling a lot more intelligent than he actually is. ‘‘Tell me where is fancy bred,’’ Shakespeare wrote, ‘‘Or in the heart or in the head.’’ There is no doubt that this playwright, at least, located the seat of the imagination (which he called ‘‘fancy’’) in the noncerebral parts of the human body.

Proof is David Auburn’s first major production; and if it is not exactly the brilliant debut that some have been claiming, it certainly represents the work of a writer with a fairly decent grasp on his not terribly fanciful material. The ‘‘proof’’ of the title is a breakthrough mathematical equation regarding prime numbers, the authorship of which is a subject of dispute. Catherine (Mary-Louise Parker) is the daughter of an intermittently psychotic and recently deceased professor at the University of Chicago (Larry Bryggman), whose ghost comes to visit her from time to time. She has a fling with one of her father’s graduate students (Ben Shenkman) after she finds him rifling through her father’s notebooks. She is in conflict with her rather unimaginative sister (Johanna Day), who has come to sell the family house and move Catherine to New York. And when this relatively under-educated woman claims to be the author of the theorem in question (I am ruining what is intended to be a stunning first act revelation), there is some debate as to whether she is really treading in her father’s demented footsteps.

We never learn the actual nature of the discovery, or why it constitutes such a great contribution to human knowledge. By his own admission, Auburn does not know or care much about mathematical theory. But what makes this play problematic is not its author’s ignorance regarding prime numbers. It is the thinness of his plot. He runs out of material so quickly that, by the middle of the second act, the play jerks to a halt and starts running in place. Proof sometimes looks like a rather austere stage version of Good Will Hunting, insofar as it features a whiz kid central character who is also an idiot savant. But if Good Will Hunting was concerned with questions of class, Proof focuses on questions of gender— how ‘‘Shakespeare’s sister’’ could have written all his plays if she hadn’t been forced to shine unappreciated on the ocean floor, and so on.

David Auburn’s writing may not be terribly electric or dynamic. But Daniel Sullivan’s direction muffs the few opportunities that the playwright Mary-Louise Parker with her Tony award for Proof offers to hoist the action out of the quotidian. With its spectral visitations from the heroine’s father and its non-linear treatment of time, Proof is, after all, something of a ghost story. But the production remains mired in domesticity. It is relentlessly realistic, with John Lee Beatty contributing another in his gallery of Edward Hopper brick structures, and Neil A. Mazzela’s lighting failing to distinguish between the gritty present and the ethereal past.

Where the evening does prosper is in the acting, especially in Mary-Louise Parker’s Catherine. I first saw this fine actress in 1988 playing Emily to Eric Stolz’s George in the Lincoln Center production of Our Town. Young as she was at the time, she made it instantly clear that she was born for the stage, a promise that she confirmed nine years later playing L’il Bit in How I Learned to Drive. Here she turns the twenty-eight-year-old Catherine into a restless, angry ragdoll of a woman with a frazzled slouch, who manages to accomplish one of the speediest costume changes in recorded history. (She goes up a whole flight of stairs, then appears seconds later on stage in a completely new set of rumpled clothes.) That she can also create such texture out of her underwritten role is an even more impressive feat of stage magic.

Source: Robert Brustein, ‘‘Or in the Heart or in the Head,’’ in New Republic, September 13, 2000, pp. 28–29.