A Beautiful Mind (3 page)

P.S. I LOVE your name.

— Sylvia Nasar

Prologue

Where the statue stood Of Newton with his prism and silent face, The marble index of a mind for ever Voyaging through strange seas of Thought, alone.

— W
ILLIAM
W
ORDSWORTH

J
OHN
F
ORBES
N
ASH
, J
R
. — mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine — had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll’s, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. “How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof… how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you … ?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”
¹

The young genius from Bluefield, West Virginia — handsome, arrogant, and highly eccentric — burst onto the mathematical scene in 1948. Over the next decade, a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind’s survival,
²
Nash proved himself, in the words of the eminent
geometer Mikhail Gromov, “the most remarkable mathematician of the second half of the century.”
³
Games of strategy, economic rivalry, computer architecture, the shape of the universe, the geometry of imaginary spaces, the mystery of prime numbers — all engaged his wide-ranging imagination. His ideas were of the deep and wholly unanticipated kind that pushes scientific thinking in new directions.

Geniuses, the mathematician Paul Halmos wrote, “are of two kinds: the ones who are just like all of us, but very much more so,.and the ones who, apparently, have an extra human spark. We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue.”
⁴
Nash’s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn’t merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were non-rational. Like other great mathematical intuitionists — Georg Friedrich Bernhard Riemann, Jules Henri Poincaré, Srinivasa Ramanujan — Nash saw the vision first, constructing the laborious proofs long afterward. But even after he’d try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. Donald Newman, a mathematician who knew Nash at MIT in the 1950s, used to say about 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.”
⁵

No one was more obsessed with originality, more disdainful of authority, or more jealous of his independence. As a young man he was surrounded by the high priests of twentieth-century science — Albert Einstein, John von Neumann, and Norbert Wiener — but he joined no school, became no one’s disciple, got along largely without guides or followers. In almost everything he did — from game theory to geometry — he thumbed his nose at the received wisdom, current fashions, established methods. He almost always worked alone, in his head, usually walking, often whistling Bach. Nash acquired his knowledge of mathematics not mainly from studying what other mathematicians had discovered, but by rediscovering their truths for himself. Eager to astound, he was always on the lookout for the really big problems. When he focused on some new puzzle, he saw dimensions that people who really knew the subject (he never did) initially dismissed as naive or wrongheaded. Even as a student, his indifference to others’ skepticism, doubt, and ridicule was awesome.

Nash’s faith in rationality and the power of pure thought was extreme, even for a very young mathematician and even for the new age of computers, space travel, and nuclear weapons. Einstein once chided him for wishing to amend relativity theory without studying physics.
⁶
His heroes were solitary thinkers and supermen like Newton and Nietzsche.
⁷
Computers and science fiction were his passions. He considered “thinking machines,” as he called them, superior in some ways to human beings.
⁸
At one point, he became fascinated by the possibility that drugs could heighten physical and intellectual performance.
⁹
He was beguiled by
the idea of alien races of hyper-rational beings who had taught themselves to disregard all emotion.
¹⁰
Compulsively rational, he wished to turn life’s decisions — whether to take the first elevator or wait for the next one, where to bank his money, what job to accept, whether to marry — into calculations of advantage and disadvantage, algorithms or mathematical rules divorced from emotion, convention, and tradition. Even the small act of saying an automatic hello to Nash in a hallway could elicit a furious “Why are you saying hello to me?”
¹¹

His contemporaries, on the whole, found him immensely strange. They described him as “aloof,” “haughty,” “without affect,” “detached,” “spooky,” “isolated,” and “queer.”
¹²
Nash mingled rather than mixed with his peers. Preoccupied with his own private reality, he seemed not to share their mundane concerns. His manner — slightly cold, a bit superior, somewhat secretive — suggested something “mysterious and unnatural.” His remoteness was punctuated by flights of garrulousness about outer space and geopolitical trends, childish pranks, and unpredictable eruptions of anger. But these outbursts were, more often than not, as enigmatic as his silences. “He is not one of us” was a constant refrain. A mathematician at the Institute for Advanced Study remembers meeting Nash for the first time at a crowded student party at Princeton:

I noticed him very definitely among a lot of other people who were there. He was sitting on the floor in a half-circle discussing something. He made me feel uneasy. He gave me a peculiar feeling. I had a feeling of a certain strangeness. He was different in some way. I was not aware of the extent of his talent. I had no idea he would contribute as much as he really did.
¹³

But he did contribute, in a big way. The marvelous paradox was that the ideas themselves were not obscure. In 1958,
Fortune
singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory, calling him the most brilliant of the younger generation of new ambidextrous mathematicians who worked in both pure and applied mathematics.
¹⁴
Nash’s insight into the dynamics of human rivalry — his theory of rational conflict and cooperation — was to become one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel’s ideas of genetic transmission, Darwin’s model of natural selection, and Newton’s celestial mechanics reshaped biology and physics in their day.

It was the great Hungarian-born polymath John von Neumann who first recognized that social behavior could be analyzed as games. Von Neumann’s 1928 article on parlor games was the first successful attempt to derive logical and mathematical rules about rivalries.
¹⁵
Just as Blake saw the universe in a grain of sand, great scientists have often looked for clues to vast and complex problems in the small, familiar phenomena of daily life. Isaac Newton reached insights about the heavens by juggling wooden balls. Einstein contemplated a boat paddling upriver. Von Neumann pondered the game of poker.

A seemingly trivial and playful pursuit like poker, von Neumann argued,
might hold the key to more serious human affairs for two reasons. Both poker and economic competition require a certain type of reasoning, namely the rational calculation of advantage and disadvantage based on some internally consistent system of values (“more is better than less”). And in both, the outcome for any individual actor depends not only on his own actions, but on the independent actions of others.

More than a century earlier, the French economist Antoine-Augustin Cournot had pointed out that problems of economic choice were greatly simplified when either none or a large number of other agents were present.
¹⁶
Alone on his island, Robinson Crusoe doesn’t have to worry about others whose actions might affect him. Neither, though, do Adam Smith’s butchers and bakers. They live in a world with so many actors that their actions, in effect, cancel each other out. But when there is more than one agent but not so many that their influence may be safely ignored, strategic behavior raises a seemingly insoluble problem: “I think that he thinks that I think that he thinks,” and so forth.

Von Neumann was able to give a convincing solution to this problem of circular reasoning for games that are two-person, zero-sum games, games in which one player’s gain is another’s loss. But zero-sum games are the ones least applicable to economics (as one writer put it, the zero-sum game is to game theory “what the twelve-bar blues is to jazz; a polar case, and a point of historical departure”). For situations with many actors and the possibility of mutual gain — the standard economic scenario — von Neumann’s superlative instincts failed him. He was convinced that players would have to form coalitions, make explicit agreements, and submit to some higher, centralized authority to enforce those agreements.
¹⁷
Quite possibly his conviction reflected his generation’s distrust, in the wake of the Depression and in the midst of a world war, of unfettered individualism. Though von Neumann hardly shared the liberal views of Einstein, Bertrand Russell, and the British economist John Maynard Keynes, he shared something of their belief that actions that might be reasonable from the point of view of the individual could produce social chaos. Like them he embraced the then-popular solution to political conflict in the age of nuclear weapons: world government.
¹⁸

The young Nash had wholly different instincts. Where von Neumann’s focus was the group, Nash zeroed in on the individual, and by doing so, made game theory relevant to modern economics. In his slender twenty-seven-page doctoral thesis, written when he was twenty-one, Nash created a theory for games in which there was a possibility of mutual gain, inventing a concept that let one cut through the endless chain of reasoning, “I think that you think that I think… .”
¹⁹
His insight was that the game would be solved when every player independently chose his best response to the other players’ best strategies.

Thus, a young man seemingly so out of touch with other people’s emotions, not to mention his own, could see clearly that the most human of motives and behavior is as much of a mystery as mathematics itself, that world of ideal platonic forms invented by the human species seemingly by pure introspection (and yet somehow linked to the grossest and most mundane aspects of nature). But Nash
had grown up in a boom town in the Appalachian foothills where fortunes were made from the roaring, raw businesses of rails, coal, scrap metal, and electric power. Individual rationality and self-interest, not common agreement on some collective good, seemed sufficient to create a tolerable order. The leap was a short one, from his observations of his hometown to his focus on the logical strategy necessary for the individual to maximize his own advantage and minimize his disadvantages. The Nash equilibrium, once it is explained, sounds obvious, but by formulating the problem of economic competition in the way that he did, Nash showed that a decentralized decision-making process could, in fact, be coherent — giving economics an updated, far more sophisticated version of Adam Smith’s great metaphor of the Invisible Hand.

By his late twenties, Nash’s insights and discoveries had won him recognition, respect, and autonomy. He had carved out a brilliant career at the apex of the mathematics profession, traveled, lectured, taught, met the most famous mathematicians of his day, and become famous himself. His genius also won him love. He had married a beautiful young physics student who adored him, and fathered a child. It was a brilliant strategy, this genius, this life. A seemingly perfect adaptation.

Many great scientists and philosophers, among them René Descartes, Ludwig Wittgenstein, Immanuel Kant, Thorstein Veblen, Isaac Newton, and Albert Einstein, have had similarly strange and solitary personalities.
²⁰
An emotionally detached, inward-looking temperament can be especially conducive to scientific creativity, psychiatrists and biographers have long observed, just as fiery fluctuations in mood may sometimes be linked to artistic expression. In
The Dynamics of Creation,
Anthony Storr, the British psychiatrist, contends that an individual who “fears love almost as much as he fears hatred” may turn to creative activity not only out of an impulse to experience aesthetic pleasure, or the delight of exercising an active mind, but also to defend himself against anxiety stimulated by conflicting demands for detachment and human contact.
²¹
In the same vein, Jean-Paul Sartre, the French philosopher and writer, called genius “the brilliant invention of someone who is looking for a way out.” Posing the question of why people often are willing to endure frustration and misery in order to create something, even in the absence of large rewards, Storr speculates: