JOHN FORBES NASH, JR. — 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 wrong-headed. 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:

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...