## Essays and Criticism

## 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 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...

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