# Critical Essay on Proof

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...

(This entire section contains 1989 words.)

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in act 1, scene 1 that when Robert was in his early twenties he had made major contributions to three fields: game theory, algebraic geometry, and nonlinear operator theory. These are exactly the same fields, according to Nasar, in which the young Nash made his impact. Nasar also points out that in the early days of his illness, Nash seemed to have a heightened awareness of life:

He began to believe that a great many things he saw— a telephone number, a red necktie, a dog trotting along the sidewalk, a Hebrew letter, a sentence in the

New York Times—had a hidden significance, apparent only to him. . . . He believed he was on the brink of cosmic insights.

This is echoed by Robert, as he recalls his mental state soon after he became ill. He tells Catherine about the clarity with which he saw things, and he believed that his mind was even sharper than before:

If I wanted to look for information—secrets, complex and tantalizing messages—I could find them all around me. In the air. In a pile of fallen leaves some neighbor raked together. In box scores in the paper, written in the steam coming up off a cup of coffee. The whole world was talking to me.

Although the play does not mention the exact nature of Robert’s illness, the
hallucinations and delusions he suffered from make it clear that he, like the
real-life Nash, was schizophrenic. Robert was no doubt mistaken when he claimed
that his mind had become sharper, because during his illness his mental
processes no longer bore any relation to reality. As with Nash, the insights he
thought he had contained meanings known only to him and were useless for
objectively verifiable mathematical knowledge. Just as Nash believed that
powers from outer space, or foreign governments, were communicating with him
through cryptic messages in the *New York Times* that only he could
decode, so too Robert used to borrow large numbers of books from libraries
because he thought that aliens were sending him messages through the Dewey
decimal numbers on the books, and he was trying to work out the code.

Was Nash’s insanity, or that of Robert in *Proof*, somehow related to
their genius? The idea that creativity and madness are linked is an old one.
Plato wrote in his dialog Ion that the poet was inspired with a kind of divine
mania, and cultural history turns up many examples of exceptionally creative
people who have been afflicted with mental illness of one kind or another,
including the philosopher Friedrich Nietzsche, the artist Vincent van Gogh, and
the writer Virginia Woolf. In more modern times, American poets Sylvia Plath
and Robert Lowell suffered from mental illness. (In 1959, Lowell was a patient
at McLean Hospital in Belmont when Nash was admitted.)

The most common type of mental illness amongst creative artists is manic-depression, also known as bipolar disorder. This is not the same as schizophrenia. Although manic-depression can produce delusions, it is mainly characterized by extreme mood swings, ranging from great elation to deep depression. Research suggests that creative artists, poets in particular, are two to three times more likely to suffer from manic-depression than scientists. For the poet or writer, it is possible that manic-depression can enhance creativity, since the mood swings may offer more acute insight into the peaks and troughs of human experience, which in turn can lend the artist’s work a profundity that might escape those who live on a more even emotional keel. Creative people who suffer from manic depression are often able to function quite normally between episodes, which is usually not the case with schizophrenia.

It would seem that schizophrenia, far from being somehow linked with creativity, is in fact inimical to it, since the feeling of heightened awareness it may produce translates only into delusional perceptions, not deeper insights into truth. Although there does seem to be a certain unusual quality to the minds and personalities of many great scientists and philosophers, madness does not describe it. Nasar points out many examples of men of genius, including Immanuel Kant, Ludwig Wittenstein, Isaac Newton, and Albert Einstein, who had emotionally detached, eccentric, solitary, inward-looking personalities that may have been useful in promoting the kind of creativity that these disciplines require. Such people—Nash was one of them before his illness—are able to think not only more profoundly but also in different ways than less gifted individuals. Nash was used to solving problems in ways that had not occurred to others. He developed this habit of thinking ‘‘out of the box’’ at an early age. His sister reported that Nash’s mother was once told that her son, then in elementary school, was having trouble with math, because he could see ways of solving mathematical problems that were different from the methods the teachers were used to.

When Nash was a mature mathematician, his mind not only worked faster than anyone else’s, he continued to approach mathematical problems in unusual ways that would unlock new possibilities that astonished his colleagues. Nasar reports that Donald Newman, a mathematician who knew Nash at MIT in the 1950s, said of him that ‘‘everyone else would climb a peak by looking for a path somewhere on the mountain. Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak.’’ Sometimes when Nash presented his unexpected results to professional audiences, there would be some who said they could not possibly believe them, so novel was Nash’s approach to the problem.

Auburn clearly incorporated this dimension of Nash’s mind into the character
of Robert in *Proof*. When Hal says to Catherine that hard work was not
the secret of Robert’s success, she contradicts him but immediately explains
that the work went on almost unseen, and Robert’s success resulted from his
taking an unusual starting point:

He’d attack a question from the side, from some weird angle, sneak up on it, grind away at it. He was slogging. He was just so much faster than anyone else that from the outside it looked magical.

Hal’s immediate response, about the beauty and the elegance of Robert’s work, also corresponds to what mathematicians said about Nash’s work. It is quite common for mathematics to be described in this way, as if it somehow partakes in the essential beauty and order of the universe. The French mathematician Henri Poincaré wrote about the aesthetic feeling known by all mathematicians when they recognized these qualities revealed in their work, describing it as ‘‘the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance.’’

A final aspect of Nash’s life finds its way into *Proof* in Catherine’s
worries that she may inherit her father’s illness, even though the depression
she suffers from is not related to the symptoms of schizophrenia. Catherine is
right to be concerned, since expert opinion considers that although the cause
of schizophrenia is unknown, there is a genetic factor in the disease. It can
be inherited and, indeed, Nash’s own son, John Charles Nash, was diagnosed,
like his father, as a paranoid schizophrenic. Like his father also, John
Charles Nash was a mathematician, brilliant but without his father’s spark of
genius. Unlike schizophrenia, genius is not transmitted through genes, and
there are numerous examples of geniuses whose offspring have been distinguished
only by their mediocrity. So for Catherine in *Proof* to inherit both
Robert’s genius and his mental illness would be a very unlikely event in real
life, although of course, as *Proof* shows, it can be turned into
excellent drama. Nash himself discovered this when at the age of seventy-three
his biographer, Nasar, took him to see a performance of the play. An article in
the Los Angeles Times by John Clark contains Nasar’s description of how Nash
reacted:

’He loved it,’ says Nasar, who admits she was a little nervous about his response. ‘It was so much fun to see him laugh and react to

Proofbecause [the father] is clearly inspired by Nash’s story, and to witness John Nash seeing this on the stage in front him—it was adorable.’

Source: Bryan Aubrey, Critical Essay on *Proof*, in *Drama for
Students*, Thomson Gale, 2005.

# The Uncertain Nature of Human Existence

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.

# Proof Positive

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.

# Or in the Heart or in the Head

*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.