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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