A Beautiful Mind (68 page)

That fall Norton Starr, a professor of mathematics at Amherst, hired a student to do some yard work for him.
⁴¹
Afterward, Starr invited him into the house for a cold drink. As they chatted, the young man learned that Starr had done his Ph.D. at MIT. Had he known a mathematician there named John Nash? Only by sight and reputation, Starr replied. “He’s my father,” the young man said. Starr looked at him searchingly. He looked at the young man again. “My God, you do look just like him,” he said. Shortly afterward, John David drove down to Princeton to visit his father. Alicia was friendly. He met his brother, Johnny, for the first time.

•  •  •

The following Christmas, Johnny came up to Boston to stay with Eleanor and John David. Eleanor welcomed him warmly, cooked him nice meals, fussed over him. He came without a winter coat, so Eleanor bought him a down jacket. Johnny was well-behaved around his older brother, but could turn nasty when he was alone with her. At the end of the holiday, Eleanor recalled, “he didn’t want to let John go. So John took him back to school with him.”
⁴²

The reunion between Nash and John Stier did not lead to a lasting reconciliation. “It just sort of petered out,” John Stier recalled. His father was more interested in talking about his own problems than his son’s. “When I asked him for advice, he’d answer with something about Nixon,” he said.
⁴³
Nash’s confidences were unsettling. Nash had some idea that his son, having attained his majority, would play “an essential and significant personal role in my personal long-awaited ’gay liberation.’ ”
⁴⁴
He had waited a long time, as he said at the time, to “tell him about my life and problems and life history.” Eleanor Stier recalled that he did so.
⁴⁵
John David eventually stopped returning his father’s calls. The two would not meet again for seventeen years. “I haven’t always wanted to have contact with him,” John David said. “Having a mentally ill father was rather disturbing.”

More often than commonly realized, schizophrenia can be an episodic illness, especially in the years following its initial onset. Periods of acute psychosis may be interspersed with periods of relative calm in which symptoms diminish dramatically either as a result of treatment or spontaneously.
⁴⁶
This was the pattern for Johnny.

In 1979, on the first day of the fall semester at Rider College in Lawrenceville, New Jersey, Kenneth Fields, the chairman of the mathematics department, was asked to talk with a freshman who had made a pest of himself at the math orientation session, questioning everything and protesting that the presentation was not rigorous enough.
⁴⁷
“I don’t need to take calculus,” the young man said when he arrived in Fields’s office. “I’m going to major in math.” Since Rider rarely attracted students with an interest or background in mathematics, Fields was intrigued. Quizzing the student as they walked around the campus, he quickly concluded that no mathematics course at Rider was advanced enough for this young man and offered to tutor him personally. “By the way, what’s your name?” he finally asked. “John Nash,” the student replied. Seeing Fields’s look of astonishment, he added, “You may have heard of my father. He solved the embedding theorem.” For Fields, who had been an undergraduate at MIT in the 1960s and was familiar with the Nash legend, it was an amazing moment.

Fields proceeded to meet with Johnny weekly. Johnny took a while to buckle down, but he was soon plowing through difficult texts in linear algebra, advanced calculus, and differential geometry. “It was obvious that he was a real mathematician,”
said Fields. He was also bright and friendly, a fundamentalist Christian who made friends with other religious, intellectually precocious students. He talked to Fields, who has several relatives who suffer from schizophrenia, about his mental illness. Occasionally he would do a riff on extraterrestrials, and on one occasion he threatened a history professor. By and large, said Fields, Johnny’s symptoms seemed to be under control. He got straight As and won an academic prize in his sophomore year.

Fields soon concluded that Johnny was wasting his time at Rider and belonged in a Ph.D. program. In 1981, despite his lack of a high school or college diploma, Johnny was accepted at Rutgers University with a full scholarship. Once there, he breezed through his qualifying examinations. From time to time he would threaten to drop out of school and Fields would get frantic calls from Alicia begging him to talk to Johnny. When Fields did, Johnny would answer, “Why do I have to do anything? My father doesn’t have to do anything. My mother supports him. Why can’t she support me?” But he didn’t drop out. He succeeded brilliantly.

Melvyn Nathanson, then a professor of mathematics at Rutgers, liked to assign what he called simple versions of unsolved classical problems in his graduate course on number theory.
⁴⁸
“I gave one the first week,” he recalled. “Johnny came back with the solution the following week. I gave another one that week and a week later he had that solution too. It was extraordinary.” Johnny wrote a joint paper with Nathanson that became the first chapter of his dissertation.
⁴⁹
He then wrote a second paper on his own, which Nathanson called “beautiful” and which also became part of the thesis.
⁵⁰
His third paper was an important generalization of a theorem proved by Paul Erdos in the 1930s for a special case of so-called B sequences.
⁵¹
Neither Erdos nor anyone else had succeeded in proving that the theorem held for other sequences, and Johnny’s successful attack on the problem would generate a flurry of papers by other number theorists.

When Johnny got his Ph.D. from Rutgers in 1985, said Nathanson, he seemed poised for a long and productive career as a first-rate research mathematician. An offer of a one-year instructorship at Marshall University in West Virginia seemed like the first of the usual steps that eventually carry new mathematics Ph.D.’s to tenured positions somewhere in academia. While Johnny was in graduate school, Alicia Larde returned to El Salvador for good and Alicia Nash moved to a job as a computer programmer at New Jersey Transit in Newark.
⁵²
Things seemed rather hopeful.

47
Remission

As you know, he has had his illness, but right now he’s fine. It’s not attributable to one or several things. It’s just a question of living a quiet life.

— A
LICIA
N
ASH
, 1994

P
ETER
S
ARNAK,
a brash thirty-five-year-old number theorist whose primary interest is the Riemann Hypothesis, joined the Princeton faculty in the fall of 1990. He had just given a seminar. The tall, thin, white-haired man who had been sitting in the back asked for a copy of Sarnak’s paper after the crowd had dispersed.

Sarnak, who had been a student of Paul Cohen’s at Stanford, knew Nash by reputation as well as by sight, naturally. Having been told many times Nash was completely mad, he wanted to be kind. He promised to send Nash the paper. A few days later, at teatime, Nash approached him again. He had a few questions, he said, avoiding looking Sarnak in the face. At first, Sarnak just listened politely. But within a few minutes, Sarnak found himself having to concentrate quite hard. Later, as he turned the conversation over in his mind, he felt rather astonished. Nash had spotted a real problem in one of Sarnak’s arguments. What’s more, he also suggested a way around it. “The way he views things is very different from other people,” Sarnak said later. “He comes up with instant insights I don’t know I’d ever get to. Very, very outstanding insights. Very unusual insights.”
¹

They talked from time to time. After each conversation, Nash would disappear for a few days and then return with a sheaf of computer printouts. Nash was obviously very, very good with the computer. He would think up some miniature problem, usually very ingeniously, and then play with it. If something worked on a small scale, in his head, Sarnak realized, Nash would go to the computer to try to find out if it was “also true the next few hundred thousand times.”

What really bowled Sarnak over, though, was that Nash seemed perfectly rational, a far cry from the supposedly demented man he had heard other mathematicians describe. Sarnak was more than a little outraged. Here was this giant and he had been all but forgotten by the mathematics profession. And the justification for the neglect was obviously no longer valid, if it had ever been.

•  •  •

That was 1990. In retrospect, it is impossible to say exactly when Nash’s miraculous remission, which began to be noted by mathematicians around Princeton roughly at the beginning of this decade, really began. But, in contrast to the onset of his illness, which became full-blown in a matter of months, the remission took place over a period of years. It was, by his own account, a slow evolution, “a gradual tapering off in the 1970s and 1980s.”
²

Hale Trotter, who saw Nash nearly every day in the computer center during those years, confirms this: “My impression was of a very gradual sort of improvement. In the early stages he was making up numbers out of names and being worried by what he found. Gradually, that went away. Then it was more mathematical numerology. Playing with formulas and factoring. It wasn’t coherent math research, but it had lost its bizarre quality. Later it was real research.”
³

As early as 1983, Nash was beginning to come out of his shell and making friends with students. Marc Dudey, a graduate student in economics, sought Nash out in 1983. “I felt bold enough at the time to want to meet this legend.”
⁴
He discovered that he and Nash shared an interest in the stock market. “We’d be walking along Nassau Street and we’d be talking about the market,” Dudey recalled. Nash struck Dudey as a “stock picker” and on occasion Dudey followed his advice (with less than stellar results, it must be said). The following year, when Dudey was working on his thesis and was unable to solve the model he wanted to use, Nash helped to bail him out. “The calculation of an infinite product was involved,” Dudey recalled. “I was unable to do it, so I showed it to Nash. He suggested I use Stirling’s formula to compute the product and then he wrote down a few lines of equations to indicate how this should be done.” All during this time, Nash struck Dudey as no odder than other mathematicians he had encountered.

By 1985, Daniel Feenberg, who had helped Nash factor a number derived from Rockefeller’s name a decade earlier and was now a visiting professor at Princeton, had lunch with Nash. He was deeply struck by the change he saw in Nash. “He seemed so much better. He described his work in the theory of prime numbers. I’m not competent to judge it, but it seemed like real mathematics, like real research. That was very gratifying.”
⁵

The changes were for the most part visible only to a few. Edward G. Nilges, a programmer who worked in Princeton University’s computer center from 1987 to 1992, recalled that Nash “acted frightened and silent” at first.
⁶
In Nilges’s last year or two in Princeton, however, Nash was asking him questions about the Internet and about programs he was working on. Nilges was impressed: “Nash’s computer programs were startlingly elegant.”

And in 1992, when Shapley visited Princeton, he and Nash had lunch and were able, for the first time in many, many years, to have quite an enjoyable conversation. “Nash was quite sharp then,” Shapley recalled. “He was free of this distraction. He’d learned how to use the computer. He was working on the Big Bang. I was very pleased.”
⁷

•  •  •

That Nash, after so many years of severe illness, was now “within the normal range for the ‘mathematical personality’” raises a great many questions. Had Nash really recovered? How rare is such a recovery? Did the “recovery” indicate he had never really had schizophrenia, which, as everyone knows, is incurable? Were his psychotic episodes in the late 1950s through the 1970s really symptoms of bipolar illness, which is generally less debilitating and carries better odds of recovery?

Absent a re-diagnosis based on Nash’s psychiatric records, no absolutely definitive answer is possible. Psychotic symptoms alone, psychiatrists now agree, “do not a schizophrenic make,” and distinguishing between schizophrenia and bipolar illness when symptoms first appear remains difficult even with today’s more precise diagnostic criteria.
⁸
Nonetheless, there are strong reasons for believing that Nash’s initial diagnosis was, in fact, correct and that he is one of a very small number of individuals who suffered a long and severe course of schizophrenia to experience a dramatic remission.

The fact that Nash’s younger son has also been diagnosed with paranoid schizophrenia and schizoaffective disorder is strong evidence that Nash himself had schizophrenia.
⁹
In contrast to the Freudian theories popular in the 1950s, when Nash was first diagnosed, schizophrenia is now thought to have a strong genetic component.
¹⁰

The duration and severity of Nash’s symptoms — his inability to do work that was, prior to and since his illness, the principal passion of his life, and his withdrawal from most human contact — is also powerful evidence. Moreover, Nash has described his illness not in terms of highs and lows, bouts of mania followed by disabling depression, but rather in terms of a persistent dreamlike state and bizarre beliefs in terms not dissimilar to those used by other people with schizophrenia.
¹¹