Lesson Three A Beautiful Mind
Sylvia Nasar
1. John Forbes Nash, Jr. –mathematical genius, inventor of a theory of rationed 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,
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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 message? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”
2. 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.” 3.
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
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human rationality as for its dark anxieties about mankind’s survival, Nash proved himself, in the words of the eminent geometer Mikhail Gromov, “the most remarkable mathematician of the second half of the century”. 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.
4. 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”. 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.
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The flashes of intuition were nonrational. Like other great mathematical intuitionist — Georg Friedrich Bernhard Riemann, Jules Henri Poincare, Srinivasa Rammanujan — 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
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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 na?ve or wrong-headed. Even as a student, his indifference to others’ skepticism, doubt, and ridicule was awesome. 6. 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. His heroes were solitary thinkers and supermen like Newton and Nietzsche. Computers and science fiction were his passions. He considered “thinking machines”, as he called them, superior in some ways to human beings. At one point, he became fascinated by the possibility that
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