July 26, 1998|By Laura Demanski | Laura Demanski,Special to the sun

"A Beautiful Mind," by Sylvia Nasar. Simon & Schuster. 440 pages. $25. At age 21, John Forbes Nash unleashed a theory of rational behavior that would change the face of economics and win a Nobel Prize. Nine years later, he was confined to a mental hospital with a full-blown case of schizophrenia.

Now 70, Nash has inspired the biography "A Beautiful Mind," by New York Times economics reporter Sylvia Nasar. Was Nash's mental illness the dark underside of his stunning numerical brilliance? Is it the case that "a predisposition to schizophrenia was integral to Nash's exotic style of thought as a mathematician?" After all, as Nasar points out, the same mixed blessing has bedeviled great mathematical thinkers throughout history, including Isaac Newton.

Storming the Princeton math department as a graduate student in the 1940s, John Nash seized on some of math's classic unsolved problems. His 1950 dissertation helped pioneer the field of game theory, now a vital tool for economists. Instead of laboriously building a proof from the ground up, like most of his colleagues, Nash would usually glimpse the solution in a flash of insight and then work backward to the proof.

It was about a decade later that the visionary gleam began to yield delusions instead of insights. Nash had joined the faculty at the Mass achusetts Institute of Technology, where he boldly sought to make good on the Riemann Hypothesis. Still undiscovered today, the Riemann proof is considered "the holy grail of pure mathematics."

Nasar speculates that tackling this recalcitrant but tantalizing problem in the mathematics of prime numbers may have helped push Nash over the edge of mental health. The level of abstraction one must inhabit to work at such a problem forces a nTC removal from the workaday world. Also, the visionary quality of Nash's genius had led him to place tremendous faith in his intuitions, so that when they ran wild he may have been unable to tell the difference.

In 1959, a few months after a disastrous, incoherent lecture on his Riemann work, Nash was committed to the world-famous McLean Hospital in a state of acute paranoia. Through the 1960s, he would move in and out of institutions, unable to work.

Eventually Nash's illness went into unexpected remission. In 1994, he was brought back out of obscurity by winning the Nobel Prize. But his son inherited both his mathematical gift and his schizophrenia. Despite the belated accolade, and a recovery deemed miraculous by experts on mental illness, this story's dominant note remains tragic.

As a portrait of a troubled man and great mathematician, "A Beautiful Mind" is limited only by Nash's ultimate inscrutability. As a history of the culture in which mathematicians theorize and practice, the book is colorful and informative.

However, Nasar's biography falls short as an illumination of the supposed overlap between keen mathematical insight and dementia. To realize this, the most intriguing of its ambitions, it would have needed to reveal more of the substance of Nash's work. Only then could we have grasped for ourselves the beauty as well as the blight of his legendarily beautiful mind.

Laura Demanski is writing a doctoral dissertation on Victorian literature. She previously worked for Simon & Schuster and the University of Chicago Press.

Pub Date: 7/26/98