A Beautiful Mind


By Sylvia Nasar (Simon & Schuster, 1998)


(This commentary was first published in the September 19, 2002 ArtVoice of Buffalo.)


Much of my professional life was spent either in university mathematics departments or in a kind of never-never-land association with them as a mathematics educator. And one part of that life was even spent in the mathematics graduate school of Princeton University. Thus I found myself reliving a part of my own experience as I read Sylvia Nasar's A Beautiful Mind.


For the non-movie goers among you, this is the true story behind the Academy Award winning film with the same title. It is about a remarkably creative mathematician who descends into the delusional world of schizophrenia and who climbs far enough back out of that world to be awarded a Nobel Prize for his earlier work.


It is to be noted that there is no Nobel mathematics category. The subject of this story, John Nash, received his joint award in economics in 1994. The only other Nobel mathematician I know of is Buffalo's own Herbert Hauptman who shared the chemistry prize in 1985.


I am amazed at how well Ms. Nasar captures the ambience of university life and in particular the politics of high level mathematics. John Nash fit perfectly in that life -- I am tempted to say, even when he was at his craziest. Life in a math department like that of Princeton -- or at the University at Buffalo for that matter -- is not all wine parties in Fine Hall. There is very much a cut-throat one-upmanship and even anti-student aspect of such a department. And it was in this competitive world that Nash thrived until his illness became too serious.


"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. 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 drugs could heighten physical and intellectual performance. He was beguiled by the idea of alien races of hyper‑rational beings who had taught themselves to disregard all emotion. 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?'


"His contemporaries, on the whole, found him immensely strange. They described him as 'aloof,' 'haughty,' 'without affect,' 'detached,' 'spooky,' 'isolated,' and 'queer.' 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.'"


But the wonderful thing about academic accomplishment is that it has a life of its own: "While Nash the man remained frozen in a dreamlike state, a phantom who haunted Princeton in the 1970s and 1980s scribbling on blackboards and studying religious texts, his name began to surface everywhere -- in economics textbooks, articles on evolutionary biology, political science treatises, mathematics journals. It appeared less often in explicit citations of the papers he had written in the 1950s than as an adjective for concepts too universally accepted, too familiar a part of the foundation of many subjects to require a particular reference: 'Nash equilibrium,' 'Nash bargaining solution,' 'Nash program,' 'De Giorgi‑Nash result,' 'Nash embedding,' 'Nash‑Moser theorem,' 'Nash blowing‑up.'  When a massive new encyclopedia of economics, The New Palgrave, appeared in 1987, its editors noted that the game theory revolution that had swept through economics 'was effected with apparently no new fundamental mathematical theorems beyond those of von Neumann and Nash.'


"Even as Nash's ideas became more influential ‑ in fields so disparate that almost no one connected the Nash of game theory with Nash the geometer or Nash the analyst -- the man himself remained shrouded in obscurity. Most of the young mathematicians and economists who made use of his ideas simply assumed, given the dates of his published articles, that he was dead. Members of the profession who knew otherwise, but were aware of his tragic illness, sometimes treated him as if he were. A 1989 proposal to place Nash on the ballot of the Econometric Society as a potential fellow of the society was treated by society officials as a highly romantic but essentially frivolous gesture -- and rejected. No biographical sketch of Nash appeared in The New Palgrave alongside sketches of half a dozen other pioneers of game theory."


Most doctors agree that you do not recover from schizophrenia. They are troubled by Nash's case and some believe that he did not suffer from this affliction. But the evidence is otherwise: "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. He has spoken of being preoccupied by delusions, of being unable to work, and of withdrawing from the people around him. Mostly, however, he has defined it as an inability to reason. Indeed, he has told Harold Kuhn and others that he is still plagued by paranoid thoughts, even voices, although, in comparison to the past, the noise level has been turned way down. Nash has compared rationality to dieting, implying a constant, conscious struggle. It is a matter of policing one's thoughts, he has said, trying to recognize paranoid ideas and rejecting them, just the way somebody who wants to lose weight has to decide consciously to avoid fats or sweets."


I very much enjoyed the motion picture A Beautiful Mind, but this book is far and away a fuller and better story.-- Gerry Rising