Book Description

When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well. Since then, Sylvia Nasar's celebrated biography, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics, in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.

From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.

In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.

The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from. ... Read more

Reviews (12)

Fascinating Reading
Even without the Nobel Prize for Economics, the outstanding movie by Ron Howard ("A Beautiful Mind"), or the exceptional biography by Sylvia Nasar (also "A Beautiful Mind"), Professor John Nash would a legend. While cursed with severe mental illness, Dr. Nash was and is an extraordinary man. His contributions to game theory were so ahead of their time it took over 30 years for economists and business leaders to apply them fully. When they were applied, they advanced everything from international trade talks and arms control treaties, to radio frequency auctions and the study of evolutionary biology. Dr. Nash's work has had a profound, highly practical impact on negotiation and decision making throughout business and government. He created a path toward win-win solutions to complex, multi-party agreements.

This book is largely a collection of Dr. Nash's own writings, each a significant contribution to mathematics or economics. Nash's papers are thoughtfully introduced and explained - thankfully so given the complexity of Nash's writings. Also included is Nash's own touching and revealing autobiography.

The result is a compelling glimpse inside the thought processes of a genius - a beautiful mind indeed. Thanks to Harold Kuhn and Sylvia Nasar for pulling this wonderful collection together.

An excellent compilation
Having written about the life of the mathematician John Nash in the excellent biography "A Beautiful Mind", Sylvia Nasar teams up with the mathematician Harold W. Kuhn to produce a book that introduces the mathematical contributions of Nash, something that was done only from a "popular" point of view in Nasar's biography. For those who have the background, this book is a fine overview of just what won Nash acclaim in the mathematical community, and won him a Nobel Prize in economics.

It is always easy to dismiss ideas as trivial after they have been discovered and have been put into print. This is apparently what John von Neumann did after discussing with Nash his ideas on noncooperative games, dismissing his ideas as a mere "fixed point theorem". At the time of course, the only game-theoretic ideas that had any influence were those of von Neumann and his collaborator, the Princeton economist Oskar Morgenstern. The rejection of ideas by those whose who hold different ones is not uncommon in science and mathematics, and, from von Neumann's point of view at the time, he did not have the advantage that we do of examining the impact that Nash's ideas would have on economics and many other fields of endeavor. Therefore, von Neumann was somewhat justified, although not by a large measure, in dismissing what Nash was proposing. Nash's thesis was relatively short compared to the size on the average of Phd theses, but it has been applied to many areas, a lot of these listed in this book, and others that are not, such as QoS provisioning in telecommunication and packet networks. The thesis is very readable, and employs a few ideas from algebraic topology, such as the Brouwer fixed point theorem.

The paper on real algebraic manifolds though is more formidable, and will require a solid background in differential geometry and algebraic geometry. However, from a modern point of view the paper is very readable, and is far from the sheaf and scheme-theoretic points of view that now dominate algebraic geometry. It is interesting that Nash was able to prove what he did with the concepts he used. The result could be characterized loosely as a representation theory employing algebraic analytic functions. These functions are defined on a closed analytic manifold and serve as well-behaved imbedding functions for the manifold, which is itself analytic and closed. These manifolds have been called 'Nash manifolds' in the literature, and have been studied extensively by a number of mathematicians.

I first heard about John Nash by taking a course in algebraic topology and characteristic classes in graduate school. The instructor was discussing the imbedding problem for Riemannian manifolds, and mentioned that Nash was responsible for one of the major results in this area. His contribution is included in this book, and is the longest chapter therein. Here again, the language and flow of Nash's proof is very understandable. This is another example of the difference in the way mathematicians wrote back then versus the way they do now. Nash and other mathematicians of his time were more 'wordy' in their presentations, and this makes the reading of their works much more palatable. This is to be contrasted with the concisness and economy of thought expressed in modern papers on mathematics. These papers frequently employ a considerable amount of technical machinery, and thus the underlying conceptual foundations are masked. Nash explains what he is going to do before he does it, and this serves to motivate the constructions that he employs. His presentation is so good that one can read it and not have to ask anyone for assistance in the understanding of it. This is the way all mathematical papers should be written, so as to alleviate any dependence on an 'oral tradition' in mathematical developments.

Nash's proof illuminates nicely just what happens to the derivatives of a function when the smoothing operation is applied. The smoothing operator consists of essentially of extending a function to Euclidean n-space, applying a convolution operator to the extended function, and then restricting the result to the given manifold. Nash gives an intuitive picture of this smoothing operator as a frequency filter, passing without attenuation all frequencies below a certain parameter, omitting all frequencies above twice this parameter, and acting as a variable attenuator between these two, resulting in infinitely smooth function of frequency.

The next stage of the proof of the imbedding theorem is more tedious, and consists of using the smoothing operator and what Nash calls 'feed-back' to construct a 'perturbation device' in order to study the rate of change of the metric induced by the imbedding. Nash's description of the perturbation process is excellent, again for its clarity in motivating what he is going to do. The feed-back mechanism allows him to get a handle of the error term in the infinitesimal perturbation, isolating the smoother parts first, and handling the more difficult parts later. Nash reduces the perturbation process to a collection of integral equations, and then proves the existence of solutions to these equations. A covariant symmetric tensor results from these endeavors, which is CK-smooth for k greater than or equal to 3, and which represents the change in the metric induced by the imbedding of the manifold. The imbedding problem is then solved for compact manifolds by proving that only infinitesimal changes in the metric are needed. The non-compact case is treated by reducing it to the compact case. The price paid for this strategy is a weakening of the bound on the required dimension of the Eucliden imbedding space.

The last chapter concerns Nash's contribution to nonlinear partial differential equations. I did not read this chapter, so I will omit its review.

Good Collection of Nash Writings!
I only rate books that I really enjoy reading. While this one has some techy chapters, readers without a strong math background can still enjoy it.

Professor Nash's story was brought to life by the movie, this book shows why. One day his manifold theory will rule! ;)

excellent
Personally, I found this book to be very interestring. The proofs and ideas are presented in clear and non-rigomorphic fashion. One is able to read the works of Nash in the way he himself presented them, and hopefully appropriate some mental strategies used by this genius. There is much that goes on behind the scene of creation of proofs. I think mathematicians of today would greatly benefit from availability of larger number of books which would contain the mathematical works in the way they were originally presented. This is certainly a major step in that direction.

A Most Welcome Mathematical Banquet
I can't begin to express how deeply satisfying it was to peruse these papers by John Nash. You almost felt you were right there at his side, as he penned them.

There is even something in the book for non-mathematical types: Sylvia Nasar's Introduction and the autobiographical essay (Chapter Two). But for me the greatest interest resided in the remaining chapters: 4-11.

Of these, I particularly enjoyed reading the original presentation of Nash's Thesis on 'Non-Cooperative Games' (Chapter 6), and was fascinated not only with the air-tight logic of his proofs, but the use of hand written-in symbols.

Of course, Chapter 7 is just the re-hashing of Ch. 6, but in proper type-set form, rather than Nash's original script. But - give me the former any day! Reading the original form and format almost made me feel like Nash's Thesis aupervisor, including the same excitement of a new discovery!

Chapter 8 'Two person Cooperative Games' nicely extends the mathematical basis to cover this species of interaction.(And in many ways, people will find the cooperative game model easier to understand than the non-cooperative).

Chapter 9 is important because it delves into the issue of parallel control, and logical functions such as used in high speed digital computers. This chapter was of much interest to me since particular aspects of parallel control figured in my own model of consciousness - recently presented in Chapter Five of my book, 'The Atheist's Handbook to Modern Materialism'. Astute readers who read both books will quickly see the analog between the Schematic of Logical Unit Function (p. 122) and my own Figure 5-13 ('Development of Neural Assemblies', p. 156).

I enjoyed Chapter 10, 'Real Algebraic Manifolds' because of my ongoing interest in Algebraic Topology, and especially homology and homotopy theory. In his chapter, Nash presents a cornucopia of methods for representation, which I am still playing with for different manifolds.

Chapter 11, 'The Imbedding Problem for Riemannian Manifolds', is a delight for anyone familiar with Einstein's General Relativity, or even differential geometry. When you read through this chapter, you also will understand why Nash is still very interested (and involved) in research to do with general relativity and cosmology. Particularly fun for me was his section on 'Smoothing of Tensors' (p. 163) and 'Derivative Size Concept for Tensors' (p. 164).

Chapter 12, 'Continuity of Solutions of Parabolic and Elliptic Equations' is like 'dessert' for anyone who is intensely interested (as I am) in modular functions, which themselves are related intimately to elliptic equations.

In short, I think this book has something for both mathematicians and non-math types alike. Obviously, the former are likely to get more out of it, so the question the latter group must ask is whether the purchase is worth satiating their curiosity about Nash.

I know how I would answer, even if I couldn't tell a derivative from a differential. However, this book can be read on all kinds of levels, and that's the beauty of it. ... Read more

Amazon.com

Stories of famously eccentric Princetonians abound--such as that of chemist Hubert Alyea, the model for The Absent-Minded Professor, or Ralph Nader, said to have had his own key to the library as an undergraduate. Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up--only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.

Economist and journalist Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees). This highly recommended book is indeed "a story about the mystery of the human mind, in three acts: genius, madness, reawakening." --Mary Ellen Curtin ... Read more

Reviews (253)

An ambitious biography
Now that the Ron Howard film has been released, it is difficult to review the book on its own merits. Yet this biography is so strong, it can stand on its own. Nasar is an excellent writer who can create excellent pen pictures of life at RAND, MIT and Princeton. She shows great style in creating the environment of the late 1940s and the 1950s. Nash emerges as a complex, demanding and flawed person - an individual. Nash has since refuted the claims of anti-semitism and homosexuality in the book, but it is good to see that Nasar does not side step the issues at all. It is probably prudent to read Nash's comments on the book before making a judgement.

Where Nash is weak is in her descriptions of mathematical formulae. She does not appear to have any real understanding of the mathematics and I would have thought a plain English explanation of his work would have strengthened the biography. I got a little frustrated that she did not tackle this task. Yet it is perhaps a measure of Nash's genius that the ideas are so complex they cannot be easily reduced to a paragraph. Still she could have tried harded in this area. Nasar tends to get around this problem, by getting another expert to describe the brilliance of the idea, rather than the mathemtical idea itself.

Based on my own experiences with people with schizophrenia, Nash's recovery is remarkable and this is the section is probably the most interesting, perhaps because it is so startling. Even after reading the biogrpahy, I still find it hard to believe that someone could recover given the severity of the illness, so it gives some hope to people who suffer this disability and those close to them.

An absorbing biography and close to a great one.

Beautiful...and Intriguing
John Forbes Nash, Jr. was a genius who suffered from paranoid schizophrenia and was in and out of mental institutions for most of his life. Nasar's book, as she states so succinctly in her prologue, is Nash's story, "in three acts: genius, madness, reawakening."

Naturally introverted, even at a young age, Nash was described as being "bookish and slightly odd." His mother had him reading by the time he was four and instead of coloring books, his father gave him science books to read. But despite his parents' efforts, the young Nash was prone to daydreaming in school, which led his teachers to describe him as an underachiever. A loner and the ultimate nerd, his best friends were books, his bedroom resembled a science lab, he was always the last to be chosen for baseball, and at a school dance, he danced with chairs rather than girls.

Although his elementary school math teachers complained he couldn't do the work, his mother noticed he wasn't following the teachers' instructions because he had devised a simpler way of solving the problems. By high school, he was deciphering problems his chemistry teacher wrote on the blackboard, without using pencil or paper. In college, his math professors would call on Nash when they themselves ran into problems solving complex equations they were presenting to their classes.

But together with his brilliance were eccentricities that became more evident as Nash aged. Those close to him characterized him as "disconnected" and "deeply unknowable."

He had little use for textbooks and was known for solving difficult (and often previously unsolvable) problems using "no references but his own mind." His peers called the results he was able to obtain "beautiful" and "striking", perhaps his greatest achievement being his work on game theory, which led to a Nobel Prize for economics in 1994. He possessed a true love of discovery - while swimming with a friend in California, the two were dragged out to sea by an undercurrent and nearly drowned. Finally reaching shore exhausted, the friend was grateful for surviving while Nash, after briefly catching his breath, re-entered the surf exclaiming, "I wonder if that was an accident. I think I'll go back in and see."

Nash was in California during the Cold War working for the internationally famous think tank known as the RAND Corporation. Funded by the U.S. Air Force, RAND was populated by "the best minds in mathematics, physics, political science, and economics." Their principle focus was developing strategies to deter - or if that failed, to win - a nuclear war against Russia. Suddenly, the game theory Nash had been intrigued by at Princeton had a practical application, for war is the ultimate game of conflict. Years later, a more profitable application would be the FCC's $7-billion sale of cell phone air space to competing communications conglomerates.

Possibly the oddest in an odd bunch of ducks, Nash's math colleagues over the years included a professor who used a mathematical formula to select his suits; the manic-depressive Norbert Wiener (the founder of cybernetics), who was known to say such things as "When we met, was I walking to the faculty club or away from it? For in the latter case I've already had my lunch"; and others who were "beset by shyness, awkwardness, strange mannerisms, and all kinds of physical and psychological tics.'"

By the age of 30 it became apparent Nash was more than just eccentric as he started to display symptoms of paranoid schizophrenia; behaving suspiciously, becoming suspect of others, and finally announcing that "abstract powers from outer space" were communicating with him through encrypted messages printed in the New York Times and broadcast by radio stations. He developed "an obsession with the stock and bond markets," investing his mother's savings, convinced he could outsmart the markets and earn a profit. Instead, the results were "disastrous, to say the least." He was offered a prestigious chair in the mathematics department at the University of Chicago - something he had long strived for - but in response the chairman of the department received a strange letter from Nash declining the offer since he had decided to become the "Emperor of Antarctica" instead.

Eventually, his illness required long periods of hospitalization while he endured drug and insulin shock therapy, with the result being the loss of a considerable portion of his memory. When an associate came to visit during one of his hospital stays, Nash mused, "What if they don't let me out until I'm NORMAL?" Although Nash shared some exquisite company, at one point being hospitalized with the poet Robert Lowell, on the whole he was slightly atypical of the average mental patient. Most don't work on a paper on fluid dynamics while institutionalized, and he took some ribbing for this. Nasar notes an instance when another patient remarked, "Professor, let me show you how one uses a broom."

Despite his illness, the math community rallied around Nash. A colleague remembers, "Everybody wanted to help [him]. His was a mind too good to waste."

By 1990, his illness had gone into remission and he was able to stop taking antipsychotic drugs, while learning to separate rational thinking from delusional thinking. In spite of his amazing recovery, awarding him with the Nobel Prize was a contentious issue due to his history of schizophrenia. But once awarded, there was resolve that the right decision had been made about a very worthy individual. One committee member recalls, "We resurrected him in a way. It was emotionally satisfying." Soon after it was announced he had won, Nash half-joked "he hoped that getting the Nobel would improve his credit rating because he really wanted a credit card."

Nasar's engaging account of Nash's life and work is both comprehensive and well-written. It is highly recommended reading if you're looking for the full story.

A Beautiful Mind
John Nash's story is truly inspirational. I could not stop the audio until I got to the end!

John Nash, a mathematical genius, had many ups and downs in his life, including a diagnosed mental illness and various social problems that made his life painful and complicated. His Nobel-prize winning work occurred while he was writing his dissertation at Princeton. He was not recognized until later in his life for his ground-breaking contribution to "game theory".

His story is one not only of his incredible gift, mental illness and remission, but really one of personal victory. In the end, he learns to live in harmony with those around him doing what he enjoyed most.

One of my most recent favorites!

An amazing piece of detective work
As I have said in the title, this book is an amazing piece of detective work about the life of Great John Nash. This is by far the work that beats the movie. If you have seen it, do not stop there - read the book, because it is TRUE! If you are interested into mathematics, into the Game theory - read it, not to learn the science, but to appreciate the scientist! However, I still give it 4 stars since the level of writing drops a little after exhilarating first few chapters. Nevertheless this is a great read!!!

a not-really-that-beautiful mathematician
(hey everyone else is making a pun with their titles so why not me?)

well this book has been well commented on so i'll try to keep this brief.

first, it is fact that many great mathematicians develop some sort of mental illness (it happened to kurt godel, georg cantor, and even issac newton). nash, then, is not really an unusual case.

what does make him interesting, then, is the fact that he had "reawakened" from his illness and continued to do math in his old age. such among mathematic circles is very rare.

and his math is indeed great. nash's ability to solve problems concerning manifolds and other topological spaces is still making waves in math today. the layman unfortunately, like nasar, doesn't appreciate this fully, which is a shame. i would have liked to get a mathematician's view on johnny's life.

but, as a pop bio, it's not too bad. i agree with other reviews that it contained too much minute detail, and her references to nash looking like a golden god were overstated and a bit offputting. i wouldn't be surprised if nasar was really in love with nash. (she might have dedicated her book to alicia to subdue any suspicions of that sort.)

in the end, though, we see the life of one of the greatest modern mathematicians, through triumph and tribulation, which was the ultimate goal of the book. i would recommend this book to some and not to others. ... Read more

Reviews (1)

Hoover: Running the Country
This was the most introspective book I have read. If you think that you know alot about scandals you do not. This is one big conspiracy theory supported by compelling evidence. You ask yourself is this story true. Hoover was one of the most corrupt figures in American history. The deeds that transpired in his years of running the FBI are incomprehensible. It needs to be information to the general public. A must read. ... Read more

Book Description

This digital document is an article from Sarasota Herald Tribune, published by Sarasota Herald-Tribune on February 3, 2002. The length of the article is 1134 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Mind games; Schizophrenia and genius are the subjects of Sylvia Nasar's biography of Nobel Laureate John Forbes Nash Jr.(FLORIDA WEST) (book review)
Publication: Sarasota Herald Tribune (Newspaper)
Date: February 3, 2002
Publisher: Sarasota Herald-Tribune
Page: E6

Article Type: Book Review

Distributed by Thomson Gale ... Read more

Reviews (3)

This Book's a Joke!
Shoddy speculative fiction from one of America's worst crime writers.

Ridiculous Retread
This book is largely a reprint of Nash's wildly implausible 1970 book, Dillinger: Dead or Alive?, though coauthor Ron Offen is left out of the credits this time. The "evidence" for Dillinger's survival as presented in Nash's first book was based mainly on erroneous notations in Dillinger's long missing autopsy report and has been largely rebutted by more serious Dillinger researchers, notably Girardin and Helmer in Dillinger: The Untold Story. New "evidence" introduced by Nash in The Dillinger Dossier consists mostly of the revelations of "Blackie" Audett, an obscure ex-con and author of a volume of tall tales entitled Rap Sheet. Audett, now deceased, claimed to have known every major outlaw of the 30s, to have been involved in nearly every crime of the period, and to have aided John Dillinger in his permanent escape from justice. This alleged eyewitness to the Kansas City Massacre, who was in Leavenworth at the time, seems to have found a willing dupe in Nash but Audett's word doesn't hold a candle to the three known sets of postmortem fingerprints taken from the dead man by the FBI. While scarred by acid, the prints remained easily identifiable as Dillinger's. This book originally came with a mail order offer of Nash's taped interviews of Audett. It seems that few, if any, who ordered the tape ever received it and at least some got a refund check, with no further explanation. The late Joe Pinkston, author of Dillinger, A Short and Violent Life, owner of the John Dillinger Historical Museum and himself a trained lie detector examiner, once suggested to this reviewer that possibly Nash, or his publisher, realized that the tape could be tested with a PSE (Psychological Stress Evaluator) which would indicate Audett was lying, and removed the tape offer for this reason. At any rate, The Dillinger Dossier, like most of Nash's books, is one best avoided by serious historians but perfect for conspiracy freaks and anyone who appreciates a good joke.

A Great Chunk of Americana
This book (an expanded and updated version of Nash's earlier "Dillinger: Dead or Alive") tells a fascinating tale and (as is always the case with Nash) tells it well. Was John Dillinger really gunned down at the Biograph Theatre in July, 1934, or was the dead man a double set up to take the fall? At first, the idea that Dillinger might have survived the Biograph shooting for several decades seems right up there with alien abductions, but Nash makes an excellent case. And with what we now know about Hoover's FBI, the idea that the Bureau would have covered up the debacle for decades to avoid criticism is hardly shocking -- in fact, it's pretty hard to believe that Hoover would *not* have covered it up.

Even if you don't buy Nash's central hypothesis, the book is a great read, full of colorful period detail. If you have any interest in Dillinger or the early history of the FBI, buy it. ... Read more

Book Description

This digital document, covering the life and work of (John) (Nash) Douglas Bush, is an entry from Contemporary Authors, a reference volume published by Thomson Gale. The length of the entry is 759 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author