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