Title: The Essential John Nash
	Editor: Harold W. Kuhn and Sylvia Nasar
	Reviewer: Ariel Rubinstien
	Publisher: Princeton University Press
	ISBN: 0 691 09527 2
	Pages: 224
	Price: £19.95

For those who study game theory and economics, the essence of Nash is found in the so-called Nash equilibrium, a concept that jumps out at any student of game theory from almost any article in the field and from every single textbook.

Nash won the prize for his fundamental contributions to game theory, a collection of formal models serving as tools to discuss the interaction of rational players; a theory that has moved in the past 20 years from the fringe of economics to its central strand.

The photo of the handsome, smiling Nash that appears on the jacket of this book was taken in the 1950s, the period during which he wrote the seminal contributions that eventually won him the Nobel prize in 1994. The cracks on the picture provide a hint of an essential period in Nash's life. For more than 20 years, he appeared as a mysterious figure at Princeton University, sloppily dressed, hunched over a cafeteria table with piles of computer printouts with strange calculations, reading newspapers others had left on the tables. This was the period Nash describes as the "time of my change from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as 'schizophrenic'".

I believe that Nash would most appreciate it if we identified "the essential John Nash" with the collection of all his works, from the first to the last letter he will one day write. Thus, the book that contains reprints of Nash's eight most important papers, both in game theory and mathematics, fits his own spirit.

What further makes the book "the essential John Nash" is the inclusion of two documents in which he talks about himself: the autobiography he was asked to prepare for the Nobel proceedings and a 45-line afterword that concludes the book. Nash's papers in economics are all extremely short, elegant and beautiful. So are these two documents, which convey his introspective personality better than anything else. Princeton University Press enriches us with one of the most beautifully designed economics book I have ever seen and at a low price.

The book's editors are two key players in the "Nash game". Harold Kuhn is a prominent Princeton mathematics professor. His name is widely familiar in economics and mathematics in the context of the Kuhn-Tucker theorem that launched the theory of non-linear programming in 1950. Kuhn was not only one of Nash's fellow graduate students and a member of the circle of brilliant minds surrounding Nash during his Princeton graduate days, he was also a constant member of the network of friends and colleagues who gave both professional and emotional support to Nash in the decades in which he was sick.

Kuhn was also a key figure in the process that led the Nobel committee to granting the prize to a person suspected of being someone who might "embarrass the king". Kuhn's comments on Nash, and some of the articles, are written in his special personal style: short words that convey a message of care and depth.

The second editor, Sylvia Nasar, adds to the book an introduction consisting of a wonderful summary of Nash's life. Her encounter with the life of Nash started from the Nobel announcement, when dozens of other journalists trumpeted game theory and tried to explain it. Nasar was the only journalist who recognised that the announcement was not merely a proclamation of the victory for game theory within economics but, more important, a human event. She published a long article in The New York Times in which she described Nash as a young and handsome genius, as a sick person who roams Princeton's idyllic campus like a ghost, and as a recovered man who wins the Nobel prize and returns to research. The moving article paved the way for her book A Beautiful Mind .

Nasar is a masterly writer who ran to the far corners of the world to chase down bits of missing information in her efforts to get to the bottom of Nash's mind. A Beautiful Mind was a bestseller and contained the material that inspired the Oscar-winning film. Both the book and the film encouraged mentally ill people and fascinated millions all over the world.

Why are we so intrigued by the story of John Nash? We are curious to understand a person who proves theorems we are unable to fathom. We imagine the voices from another world he has heard. We ask where he was for 30 years during which he walked among us but wasn't here. We are frightened and we are attracted by this combination of "crazy" and "genius", an invitation for visiting the edge of our own minds.

The movie has a cliched, happy ending. I would opt for a sadder one. This is probably the reason that I am moved so much by The Essential John Nash , which I see as the missing, true end of the movie. Not tragic, not happy. A mixture of scholarly brilliance and autumnal sadness that is summarised so well by Nash himself in the book's afterword.

He writes: "The point of view of the person whose work and history become the subject matter of a book is different than that of the readers of the book. In a person's total life experience there is really no "inessential" and no "essential". The big thing is that a human has the opportunity and the experience of existence and life, and he or she may hope for reincarnation or to go to heaven when the life is indeed over and history."

Ariel Rubinstein is professor of economics, Tel Aviv University, Israel, and Princeton University, New Jersey, US.