Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010190265 | QA8.4 R83 2007 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries.
Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of "gross indecency" for a homosexual affair and died in 1954 after eating a cyanide-laced apple--his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality.
The Mathematician's Brain takes you inside the world--and heads--of mathematicians. It's a journey you won't soon forget.
Author Notes
David Ruelle, a French physicist, is one of the founders of Chaos Theory. In his book, Chance and Chaos, Ruelle explains this theory and how randomness, chance, and chaos play a role in physical systems. This work, one of his better known, is accessible for the common reader, not just the scientist.
Other works by Reulle are Chaotic Evolution and Strange Attractors: The Statistical Analysis of Time Series for Deterministic Nonlinear Systems; Meteorological Fluid Dynamics: Asymptotic Modelling, Stability and Chaotic Atmospheric Motion; (for which Reulle was one of the editors); and Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval. The latter is a more technical work of a mathematical nature.
(Bowker Author Biography)
Reviews 1
Choice Review
Ruelle (emer., mathematical physics, Institut des Hautes Etudes Scientifiques, France) offers a collection of essays, generally about mathematical topics. Most are almost free-association discourses loosely referencing a common theme, from theories and theorems to personalities and philosophies, in an effort to "present a coherent set of facts and opinions." In general, no formal mathematical knowledge is required, but at times concepts and theorems are introduced too tersely to be easily followed by the uninitiated. Thus, in no more than six pages, the author moves from prime numbers and fractions through an infinite series to Descartes and algebraic geometry, on to Bourbaki and Andre Weil's sister. The next chapter is a wonderful reminiscence of Alexander Grothendieck and his time. The chapters on the Zermelo-Fraenkel axioms and the Axiom of Choice, followed by Godel's Incompleteness Theorem and the Riemann Hypothesis, beautifully convey--too concisely perhaps for general readers--the essence of the axiomatic approach to mathematics. Other chapters include "The Erlangen Program," "The Computer and the Brain," "Turing's Apple," "The Smile of Mona Lisa," and "Mathematical Physics and Emerging Behavior." Copious endnotes. An idiosyncratic, oddly intriguing work. Summing Up: Recommended. Lower-division undergraduates through faculty. J. Mayer emeritus, Lebanon Valley College
Table of Contents
| Preface | p. vii |
| Chapter 1 Scientific Thinking | p. 1 |
| Chapter 2 What Is Mathematics? | p. 5 |
| Chapter 3 The Erlangen Program | p. 11 |
| Chapter 4 Mathematics and Ideologies | p. 17 |
| Chapter 5 The Unity of Mathematics | p. 23 |
| Chapter 6 A Glimpse into Algebraic Geometry and Arithmetic | p. 29 |
| Chapter 7 A Trip to Nancy with Alexander Grothendieck | p. 34 |
| Chapter 8 Structures | p. 41 |
| Chapter 9 The Computer and the Brain | p. 46 |
| Chapter 10 Mathematical Texts | p. 52 |
| Chapter 11 Honors | p. 57 |
| Chapter 12 Infinity: The Smoke Screen of the Gods | p. 63 |
| Chapter 13 Foundations | p. 68 |
| Chapter 14 Structures and Concept Creation | p. 73 |
| Chapter 15 Turing's Apple | p. 78 |
| Chapter 16 Mathematical Invention: Psychology and Aesthetics | p. 85 |
| Chapter 17 The Circle Theorem and an Infinite-Dimensional Labyrinth | p. 91 |
| Chapter 18 Mistake! | p. 97 |
| Chapter 19 The Smile of Mona Lisa | p. 103 |
| Chapter 20 Tinkering and the Construction of Mathematical Theories | p. 108 |
| Chapter 21 The Strategy of Mathematical Invention | p. 113 |
| Chapter 22 Mathematical Physics and Emergent Behavior | p. 119 |
| Chapter 23 The Beauty of Mathematics | p. 127 |
| Notes | p. 131 |
| Index | p. 157 |
