The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them

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August 2007



"David Ruelle has written an entertaining and thoughtful book on human theorizing in that most abstract science, mathematics. Yet its content has ramifications that extend well into other thought processes."--Stephen Smale, Toyota Technological Institute at Chicago"Fascinating and quite eclectic. Ruelle has a pragmatic approach to discussing philosophical and psychological questions. He is equally pragmatic with regard to ethical and political issues involved in the professional world of the mathematician. As Ruelle repeatedly says, mathematics is a human activity."--William Messing, University of Minnesota


Preface vii
Chapter 1: Scientific Thinking 1
Chapter 2: What Is Mathematics? 5
Chapter 3: The Erlangen Program 11
Chapter 4: Mathematics and Ideologies 17
Chapter 5: The Unity of Mathematics 23
Chapter 6: A Glimpse into Algebraic Geometry and Arithmetic 29
Chapter 7: A Trip to Nancy with Alexander Grothendieck 34
Chapter 8: Structures 41
Chapter 9: The Computer and the Brain 46
Chapter 10: Mathematical Texts 52
Chapter 11: Honors 57
Chapter 12: Infinity: The Smoke Screen of the Gods 63
Chapter 13: Foundations 68
Chapter 14: Structures and Concept Creation 73
Chapter 15: Turing's Apple 78
Chapter 16: Mathematical Invention: Psychology and Aesthetics 85
Chapter 17: The Circle Theorem and an Infinite-Dimensional Labyrinth 91
Chapter 18: Mistake! 97
Chapter 19: The Smile of Mona Lisa 103
Chapter 20: Tinkering and the Construction of Mathematical Theories 108
Chapter 21: The Strategy of Mathematical Invention 113
Chapter 22: Mathematical Physics and Emergent Behavior 119
Chapter 23: The Beauty of Mathematics 127 Notes 131 Index 157


David Ruelle is professor emeritus of mathematical physics at the Institut des Hautes Etudes Scientifiques in France and distinguished visiting professor of mathematics at Rutgers University. His books include "Chance and Chaos" (Princeton).


"The text is enlivened by many unusual mathematical examples, and by Ruelle's reflections on his own and other famous mathematicians' experiences...If mathematics is what mathematicians do, are there any psychological traits or personalities that characterize mathematics? Ruelle addresses this lightly with some illuminating insights...Mathematicians and theoretical physicists will enjoy Ruelle."--Donal O'Shea, Nature "The mathematician David Ruelle is well known for his work on nonlinear dynamics and turbulence, and his new book, The Mathematician?s Brain, is a book about mathematics and what it all means... The book?s value lies in Mr. Ruelle?s description of the curious inner life of mathematicians."--David Berlinski, New York Sun "[David Ruelle], a mathematical physicist, reflects on how the mathematician works and how mathematics sheds light on the nature of knowledge. Ruelle also examines the anatomy of mathematical texts, looks at processes by which mathematical concepts are developed, and explores ideas such as infinity, the circle theorem, and algebraic geometry."--Science News "After a lifetime of research and teaching, [Ruelle argues] that mathematical breakthroughs do not come from simply manipulating symbols according to strict rules. His chapters on individual mathematicians work very well, and allow the reader...a real sense of what it is like to work at the forefront of the discipline."--Andrew Robinson, Physics World "An idiosyncratic, oddly intriguing work."--J. Mayer, Choice "David Ruelle is a mathematical physicist who tries to explain to the general reader what mathematics is and how mathematicians go about their work... The book is well organized, clearly written and gives a fair impression of the working mathematician."--Michael Atiyah, Brain "For any reader interested as much in what being a mathematician is like as in what mathematics is, this book offers the inside scoop... It is only a very good book that stimulates discussion of foundational issues at all, and The Mathematician's Brain does that and much else beside. One finds a rich, multi-textured, human account of mathematics and mathematical life here, an account that makes one wish to spend an afternoon with the author, in pleasant conversation about whatever captures one?s fancy at the moment."--Tim Maudlin, Journal of Statistical Physics "The Mathematician's Brain takes you inside the world--and heads--of mathematicians. It is a journey you won?t soon forget."--L'Enseignement Mathematique "The Mathematician's Brain is a very readable tour through the landscape of contemporary mathematics. David Ruelle locates mathematics as a human practice, subject to social and political pressures as well as the limitations of human brains, without losing site of its status as an objective, rule-governed discipline. The book is packed with personal anecdotes and speculative comments on the nature of mathematics which display the author's clear enthusiasm for his subject... As an accessible run-through of one mathematician's love-affair with his subject, The Mathematician's Brain is an inviting presentation which introduces readers to the fascinating realm of mathematics and its philosophy."--Mary C. Leng, Mathematical Reviews "It has an intimate, personal definitions flavor, inviting the reader to get to know Ruelle himself, not only the mathematics he cares to expound. He turns out do be no dry, scholar, but a humane, opinionated, deeply thoughtful fellow human. The mathematics he chooses to present is and well explained. The philosophical and aesthetic issues he explores are important and often neglected."--Reuben Hersh, Siam Review "There is an enormous amount to admire in the book... The range of topics treated is very generous."--David Corfield, Notices
EAN: 9780691129822
ISBN: 0691129827
Untertitel: Sprache: Englisch.
Erscheinungsdatum: August 2007
Seitenanzahl: 160 Seiten
Format: gebunden
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