Second career begins where movie ends for John Nash
By Steven Schultz
Princeton NJ -- In its fact sheet about "A Beautiful Mind," Universal Studios categorizes the movie as a "drama." And in interviews, director Ron Howard has emphasized that it is not what the industry calls a "bio-pic." That is, it is a work of fiction, based only loosely on the life of John Nash.
For Nash, Nobel laureate and senior research mathematician in the Department of Mathematics, the film's ambiguous relation to the facts of his life is both comforting and disconcerting. "It's not me," Nash said after he and his wife Alicia recently attended a preview of the film in New York with Howard. "But on the other hand, it has a lot of things that do relate to my life history."
During the filming, Nash was not overly anxious about the prospect of being the focus of a major Hollywood film. "It's very fictional, and that makes me more relaxed in a way," he said in an interview between the film crews' several visits to campus this spring and summer. Nash cooperated and consulted with the filmmakers and was paid for the use of his story.
When he actually saw the film, Nash said he tried to separate himself from it and view it as an outsider. "It was disturbing psychologically overall, but when I could think of it with some 'apartness' it was different," he said.
"Now that it has been made, I want it to be successful," Nash said. "I think it's going to be entertaining and interesting."
What the film does show, in its broadest outline, is Nash's quick rise to the top level of mathematics and the groundbreaking work in game theory that earned him a 1950 Ph.D. at Princeton, his descent into schizophrenia and, finally, his recovery and the worldwide recognition brought by the 1994 Nobel Prize in economics.
For the film, that is where the story ends. For the real Nash, now 73, the prize marked a new beginning. Nash comes nearly every day to his office in Fine Hall, regularly delivers talks at conferences and is working on fundamental open questions in game theory. The National Science Foundation recently awarded him a grant to pursue ideas that remained undeveloped in his Princeton doctoral thesis and continue to hold significant potential for shaping economic theory.
"It's like a second career for me," he said simply. "It's good."
Continuing to contribute
Nash has presented his game theory ideas at a number of economics and mathematics meetings, including international meetings in Italy and a recent conference at the State University of New York at Stony Brook.
"He really wants to do something more, to continue to make a contribution," said Nash's longtime friend, fellow Princeton graduate student and Princeton professor emeritus of mathematics Harold Kuhn. The movie plays up the theme of Nash in pursuit of "one truly original idea" and, in that regard, "it is not far off the mark," Kuhn said.
The work that won Nash the Nobel Prize involves a theory of what are called noncooperative games interactions between players, whether in a poker game or a competitive business environment, who cannot form agreements and coalitions. He developed a universal approach to predicting the strategy players would adopt under optimum circumstances. The approach "has become a standard tool in almost all areas of economic theory," according to the Nobel citation.
In his doctoral thesis, Nash suggested that his approach could provide insight into cooperative games, which are far more complicated when extended beyond two people. His idea was to reduce cooperative games to noncooperative forms. That approach, now called "the Nash program," proved to be more difficult than he had initially imagined. It has been taken up by many other researchers over the last decades and continues to be a major goal for Nash.
Nash is approaching the problem from a number of angles, including an idea taken from evolutionary biology, which has made extensive use of game theory to study evolution and competition among species. Several years ago, Nash discussed this biological game theory in an address to students at the National Youth Science Camp in his home state of West Virginia. As he spoke, he was struck with an idea for his long-sought theory of cooperative games.
Biological systems, he reasoned, start off without cooperation. Each organism fends for itself. From ants to humans, however, sophisticated forms of cooperation have emerged. In a sense, nature already solved the Nash program; any cooperative situation that arises can ultimately be explained by nothing more than the noncooperative rules of natural selection. "In a biological context, you can escape from (noncooperation)," Nash said. "Cooperative behavior can evolve as a pattern of behavior." He is now developing the mathematics to capture this idea.
"This project depends a lot on computation," he said. "It wouldn't actually have been possible without the computing resources that exist now. I use some of the latest facilities." With the support of the National Science Foundation grant, Nash is looking for a graduate student in mathematics, economics or computer science to help him with the time-consuming preparation and execution of the calculations.
But there is more than the "one truly original idea." Even in graduate school at Princeton, Nash had other work in the area of "algebraic manifolds" that could have earned him a dissertation, said Kuhn. Nash continues to have some ideas "in reserve" including work in logic theory and a theory of "ideal money," which he recently presented as a keynote talk at an economics conference in Florida.
In addition to a reproduction of Nash's original typed copy of his Ph.D. thesis and other mathematical papers, the book includes a memo from his time at the Rand Corp. in which he outlined an idea for developing the parallel computer. "It was far ahead of its time," said Kuhn.
Kuhn said he and others close to Nash are very pleased to see him working again.
"It's very hard for anyone who didn't know John at the depth of his illness to understand," Kuhn said, searching for words. "It's just a very different John. It was like night into day, and it's very good."
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