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 A Beautiful Mind, 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--from Riemannian geometry and partial differential equations--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.

Customer Reviews (13)

Undiluted math
If you have an interest in John Nash AND know mathematics, this is an interesting collection. The main body of the book consists of eight papers in mathematics and his Phd Thesis in uncut form, accompanied by a small introduction. Apart from that there is a general introduction from his friend Kuhn, a short biography from his biographer Nasar, a 7-page autobiography, the statement of the Nobel-prize committee, a collection of photos of Nash in various phases of his career, and a short explanation to the game of Hex that Nash invented when he arrived in Princeton.

Being an economist I was only interested in the thesis with the existence proof of the Nash equilibrium, and I am sure I would not have understood an alpha of any of the other papers. You really need to be a mathematician to appreciate this bundle. For those who want to know about Nash the man, I would recommend his autobiography "A beautiful mind" or the film with the same title.

An essential reading !

In case you have been captivated by "A beautiful mind", and be disposed to know more about the controversial existence of John Nash, pick up this book, that surely will catch your entire attention.

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 CurtinBook Description

In this dramatic and moving biography, Sylvia Nasar re-creates the life of a mathematical genius whose brilliant career was cut short by schizophrenia and who, after three decades of devastating mental illness, miraculously recovered and was honored with a Nobel Prize.

A Beautiful Mind traces the meteoric rise of John Forbes Nash, Jr., from his lonely childhood in West Virginia to his student years at Princeton, where he encountered Albert Einstein, John von Neumann, and a host of other mathematical luminaries. At twenty-one, the handsome, ambitious, eccentric graduate student invented what would become the most influential theory of rational human behavior in modern social science. Nash's contribution to game theory would ultimately revolutionize the field of economics.

As a young professor at MIT, still in his twenties, Nash dazzled the mathematical world by solving a series of deep problems deemed "impossible" by other mathematicians. As unconventional in his private life as in his mathematics, Nash fathered a child with a woman he did not marry. At the height of the McCarthy era, he was expelled as a security risk from the supersecret RAND Corporation -- the Cold War think tank where he was a consultant.

At thirty, Nash was poised to take his dreamed-of place in the pantheon of history's greatest mathematicians. His associates included the most renowned mathematicians and economists of the era: Norbert Wiener, John Milnor, Alexandre Grothendieck, Kenneth Arrow, Robert Solow, and Paul Samuelson. He married an exotic and beautiful MIT physics student, Alicia Larde. They had a son. Then Nash suffered a catastrophic mental breakdown.

Nasar details Nash's harrowing descent into insanity -- his bizarre delusions that he was the Prince of Peace; his resignation from MIT, flight to Europe, and attempt to renounce his American citizenship; his repeated hospitalizations, from the storied McLean, where he came to know the poet Robert Lowell, to the crowded wards of a state hospital; his "enforced interludes of rationality" during which he was able to return briefly to mathematical research. Nash and his wife were divorced in 1963, but Alicia Nash continued to care for him and for their mathematically gifted son, who was diagnosed with schizophrenia as a teenager. Saved from homelessness by his loyal ex-wife and protected by a handful of mathematical friends, Nash lived quietly in Princeton for many years, a dreamy, ghostlike figure who scrawled numerological messages on blackboards, all but forgotten by the outside world.

His early achievements, however, fired the imagination of a new generation of scholars. At age sixty-six, twin miracles -- a spontaneous remission of his illness and the sudden decision of the Nobel Prize committee to honor his contributions to game theory -- restored the world to him. Nasar recounts the bitter behind-the-scenes battle in Stockholm over whether to grant the ultimate honor in science to a man thought to be "mad." She describes Nash's current ambition to pursue new mathematical breakthroughs and his efforts to be a loving father to his adult sons.

Based on hundreds of interviews with Nash's family, friends, and colleagues and scores of letters and documents, A Beautiful Mind is a heartbreaking but inspiring story about the most remarkable mathematician of our time and his triumph over a tragic illness. ... Read more

Customer Reviews (1)

A beautiful read
This man's story is facinating. I read this after seeing the movie and it was wonderful.The book gives some deeper insight into his marriage and life as well that you'll enjoy. ... Read more

Book Description
This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer.New to the Second Edition · Presents program steps as Turbo Pascal code · Includes more algorithmic examples · Contains an extended bibliographyThe accompanying software (available by coupon at no charge) includes not only the algorithm source codes, but also driver programs, example data, and several utility codes to help in the software engineering of end-user programs. The codes are designed for rapid implementation and reliable use in a wide variety of computing environments. Scientists, statisticians, engineers, and economists who prepare/modify programs for use in their work will find this resource invaluable. Moreover, since little previous training in numerical analysis is required, the book can also be used as a supplementary text for courses on numerical methods and mathematical software. ... Read more

Book Description
The brothersPaul and John Nash, in their very different ways, were a major influence on twentieth century British design. Paul Nash (1889-1946) is now recognised as the most significant war artist of the last century; John Nash (1893-1977) as a plantsman artist.Both worked as designers and as tutors at the Royal College of Art, Paul encouraging a generation of designer artists that included Eric Ravilious, Edward Bawden and Enid Marx. As a committee member of the Design and Industries Association and President of the newly formed Society of Industrial Artists (now the Chartered Society of Designers) Paul promoted design as no less an art form than the fine arts of painting and sculpture. His clients included London Transport, Shell and Curwen Press and publishers the Nonesuch and Golden Cockerel Presses. John became well known for his Edward Lear influenced humorous illustrations and his superb plant drawings and wood engravings that illustrate innumerable books and publications.Paul Nash and ... Read more

Book Description
Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics invented by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics.

John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained relatively obscure until the 1970s, when evolutionary biologists began to find it useful. In the 1980s economists began to embrace game theory.Since then game theory math has found an ever expanding repertoire of applications among a wide range of scientific disciplines.

Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks.

A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or "a Code of Nature," in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences and physical sciences in a way that may bring Asimov's dream closer to reality. ... Read more

Customer Reviews (7)

Journalistic hypes and some patently false claims
I am an academic economist who knows something about game theory, so when I bought this book I did not hope to learn anything new but just to be entertained by an "illuminating" author during my leisure hours. I was disappointed to the point of anger.

This book is basically a journalist's report based on interviews with a few (probably half a dozen) individuals as the pages are filled with quotes from several academics in good standing.I think it would have been better to simply present many illuminating quotes from these individuals without inserting additional insights that the author gleaned from them, because many of the author's insertions were at best misleading and at worst patently false.

Just for an example, the author keeps insisting that payoff numbers in games are "money" as economists are interested in monetary matters. It might probably be true that von Neumann preferred interpreting payoffs of a game as money, but most practicing economists and game theorists certaintly do not do that.

An annoying repeated phrase is that "xxx told me (in an exclusive interview) that..." where xxx is one of the half dozen individuals mentioned above.Most of what xxx told the author must be correct, relevant and have some meaning but these are simply taken out of context by bits and spread throughout the text.

Also the basic hype about game theory's possibility to be a Theory of Everything seems to come out of (as the author admits) one person's recent writings at Bell Labs. The idea itself presented as such sounds simply outrageous (even to an academic economist like myself) but rather a surpring fact is that game theory's origins are in fact related to such an outrageous idea from physicists, mathematicians and "cyberneticians", one story of which is told in Mirowski, Machine Dreams. Mirowski's book has its own faults, and is a lot more heavy going (with some 500 + pages with small fonts and requiring a lot of knowledge), but at least it shows seriousness and a lot of research the author took to it.

Brilliantly understood and explained, questionably authored.
The book jacket tells us that Seigfried won an award "for interpreting [science] for the public."I'm sure that that award was well deserved, for he has a knack for taking complex ideas and presenting them to a less-educated crowd.His two or three page explanations of concepts that took me weeks (and loads of homework/study) to grasp are nothing short of amazing.He often uses examples or analogies rooted in works of fiction to illustrate his points.The way these works are summarized to include only relevant information, and yet still capture the essence of those stories, is marvelous.Also, unlike many books of this genre, after reading it I did not feel like I needed to re-take any classes or brush up on my math.In fact, the most in-depth math involved (calculating a Nash equilibrium) should be crystal clear to a tenth-grader, and it is conveniently relocated to an appendix so that it doesn't bother any take-your-word-for-it readers.

Why only three stars then? Because this is a book review, and explanatory prowess isn't the only thing that it takes to write a book.

The humor in the book is very hit-and-miss.I wouldn't remove it, because when it hits... it's wonderful, but perhaps he should've gotten a humor-editor, someone to help him decide what to include and what to leave out.For example, Seigfried goes about explaining the mathematical differences between what he calls a "Robinson Crusoe economy" (one in which a single person makes decisions about fixed values) and a "Gilligan's island economy" (one in which each person makes decisions based upon other people, who make decisions based on other people, who...).Seigfried states that,

"Mathematically, that meant that no longer could you simply compute ... for Robinson Crusoe.Your calculationshad to accommodate ... for Gilligan, the Skipper too, the millionaire, and his wife, the movie star, the Professor, and Mary Ann."

How cool! But then there are other instances.While using a game between fictional characters Alice and Bob to demonstrate some simple game theory, he inserts parenthetically: "(As I said, Alice would probably tell him to shove it)," directly between two rules of the game.We had already been told that this game was not in Alice's favor, and that it was simplified for the purpose of example.The text is peppered about equally with good, relevant, non-interrupting humor, as it is with not-so-good humor.

Furthermore, while he can explain very-high-level science to a high-school-graduate (and two thumbs up for that) his narration seems to be directed at an audience with a damaged memory.I say this because we are told at least four times that Colin Camerer is into Behavioral Game Theory, and that Neuroeconomics is a fledgling hybrid field.
The organization of the book favors the understanding of game theory over the understanding of its history.One is presented with concepts fundamental to game theory, some uses of it, some game theory developments, some views into advanced game theory; it works very well to foster understanding.With each chunk of theory work, Seigfried includes the history (which I was pleasantly surprised at--it's fascinating) that contributed to that chunk of theory.The problem here is that the first section takes place mostly in the eighteenth century, the second-to-last section in the twenty-first, and the last section in the seventeenth and also the twentieth.The jumping around in time was confusing.I can't say what the best organisational method is, but I don't think this is it.

Lastly, and most importantly, is the hype that he gives game theory.I am interested in it, that's why I picked up the book, and the occasional renewal of that interest was nice, but he takes it a step too far.The reader is told time and time again how freakin' amazing game theory is, it's all true.The problem is that after pages of this game theory hype, and a mid-book discrediting of some evolutionary psychologists who dared disagree, I begin to question how strongly his bias is affecting his writing. It doesn't come across too strongly until the final few pages (which, in my mind, bumped it down from a four-star) in which he compares game theory to a unified field theory, or physics' golden "theory of everything."He says game theory is the theory concerned with everything else (i.e. the social/biological/economic half of everything).I agree that it could be a framework to hold "everything else" together, but that's like saying that all baked goods can be divided between pie, and things-with-frosting.It doesn't include the whole picture, and it does so in a deceptive way.

I should, however, admit that I am subject to the same type of biases as the author.When I read, in that last few pages, that:

"Game theory is not, however, the same as the popular 'Theory of Everything' that theoretical physicists have long sought.That quest is mearly for the equations describing all of nature's basic particles and forces, the math describing the building blocks."

I became quite upset: MEARLY?! that theory is only one of the most important goals of science, ever!Well, you can see that my bias clouds my judgement too, interperet as you will...


So buy this book, I can't stress enough how great the explanations within are, but take it with a grain of salt (and perhaps some of your own research).

for the beginner and rather misleading
This is a 215 page book.If you are familiar with the Prisoner's Dilemma there just isn't a whole lot here for you.The discussionof statistical mechanics pales in comparison (and is rather similar to the outline of) Philip Ball's vastly superior "Critical Mass".Go there first. I know that is a different subject but a good chunk of this book discusses it.The author creates a ridiculous and unrealistic strawman of evolutionary pyschology and then repeatedly belittles it because human societies are variable (what a novel and unexpected concept!).Usuaully the author presents one example of work within each field he discusses - I suppose this keeps it readable but disappointing light fare.Go read "Critical Mass", don't waste your time with this.

I think I get it know
I first picked up this book because I thought it would be more of a biography of John Nash.The book is more a discussion of how game theory can be used to help understand nature.

The book was very readable and even gave me a historic perspective about where this trend is going.Although there is some very limited math in the book, it is very clearly explained.The books is very readable and engaging.

After reading this book, I know want to know more about game theory and its predictive capabilities.I would highly recommend this book.

Far-Reaching Theory Now Accessible
The movie "A Beautiful Mind" was inspiring and touching.But, it really did not explain Nash's contributions to the world in the form of game theory.Now readers have a chance to understand the theory and practice behind this Nobel Prize winning discovery in Tom Siegfried's book, "A Beautiful Math."
This thorough, historical, mathematical, and metaphorical description of game theory really helps me to see the implications of Nash's discovery.This work influences psychology, evolutionary biology, sociology, anthropology,statistical physics, quantum physics and more. Its far-reaching implications are brought to life within an eloquent explanation that touches on all branches of science. ... Read more

Book Description
John Nash (1752-1835) was the most successful and fashionable architect of his time. Architect, town-planner, landscape designer, bridge-builder, engineer and entrepreneur, Nash outlived his principal patron, George IV, by five years. After a disheartening start, when his first speculative buildings in Bloomsbury failed and left him bankrupt, Nash moved to Wales to rebuild his career, eventually returning to London in 1796. He had made a remarkable recovery and went on to become the most successful and fashionable architect of the period. His buildings reflect a variety of styles, including neo-classical, Tudor and Gothic, with a strong emphasis on the Picturesque. His Metropolitan Improvements - Regent's Park, Regent Street, Trafalgar Square - were the most comprehensive developments ever carried out in London, even until recent times.This fully illustrated comprehensive survey of Nash's works includes all of his known and attributed works. Michael Mansbridge's superb photographs of Nash's extant buildings show Nash's architecture as never before and are complemented by contemporary views and old photographs of demolished buildings, as well as original sketches of designs never executed. The illustrations are accompanied by catalogue entries giving general information about the buildings, their settings and their original owners. In all, nearly 300 projects are discussed. Each entry has its own bibliography and many have plans.The lively introduction, written by the distinguished architectural historian Sir John Summerson (1904-92), gives a perspective portrait of this imaginative and influential architect. The book includes a gazetteer, a list of clients and patrons, a glossary of architectural terms, and two maps - one of Great Britain and Ireland and one of London - giving the locations of Nash's buildings. ... Read more

Book Description
Brilliant physicist Alex Moor has created a device that will revolutionise the world - technology that can observe and study any point in space and time. This is a machine that can look into history and the future. Man can now explore the universe without leaving the earth. It is the greatest tool of learning man has ever known.Alex Moor is a humanitarian and pacifist. He isn't prepared for the treachery and greed that his brainchild causes. When politicians and the military become involved the stakes are high. An act of betrayal changes the course of history and plunges civilisation towards oblivion. Alex Moor must survive an incredible journey and conquer his own demons if humankind is to survive. ... Read more

Customer Reviews (1)

To Find a Crooked Line
Time travel and alternative histories are well travelled territories for SF writers but this work manages to pull a few new punches. The story is cleverly plotted and the parallel stories woven by the author come together effectively and dramatically at the climax. The action sequences are written at great pace and the author manages to deal with a lot of modern day issues in a short space of time, the primary message I think being the unhealthy corporate control of society. The alternative second world war is certainly thought provoking.Worth a read. ... Read more