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

Book Description | Reviews
Chapter 1 [HTML] or [PDF format]

TABLE OF CONTENTS:

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

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File created: 7/11/2014

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