Indeholder "Preface", "Acknowledgments", "Introduction", "Overture", "1. The Mathematical Landscape", " What is Mathematics?", " Where is Mathematics?", " The Mathematical Community", " The Tools of the Trade", " How Much Mathematics is Now Known?", " Ulam's Dilemma", " How Much Mathematics Can There Be?", " Appendix A - Brief Chronological Table to 1910", " Appendix B - The Classification of Mathematics. 1868 and 1979 Compared ", "2. Varieties of Mathematical Experience", " The Current Individual and Collective Consciousness", " The Ideal Mathematician", " A Physicist Looks at Mathematics", " I.R. Shafarevitch and the New Neoplatonism", " Unorthodoxies", " The Individual and the Culture ", "3. Outer Issues", " Why Mathematics Works: A Conventionalist Answer", " Mathematical Models", " Utility", " 1. Varieties of Mathematical Uses", " 2. On the Utility of Mathematics to Mathematics", " 3. On the Utility of Mathematics to Other Scientific or Technological Fields", " 4. Pure vs. Applied Mathematics", " 5. From Hardyism to Mathematical Maoism ", " Underneath the Fig Leaf", " 1. Mathematics in the Marketplace", " 2. Mathematics and War", " 3. Number Mysticism", " 4. Hermetic Geometry", " 5. Astrology", " 6. Religion ", " Abstraction and Scholastic Theology ", "4. Inner Issues", " Symbols", " Abstraction", " Generalization", " Formalization", " Mathematical Objects and Structures; Existence", " Proof", " Infinity, or the Miraculous Jar of Mathematics", " The Stretched String", " The Coin of Tyche", " The Aesthetic Component", " Pattern, Order, and Chaos", " Algorithmic vs. Dialectic Mathematics", " The Drive to Generality and Abstraction", " The Chinese Remainder Theorem: A Case Study", " Mathematics as Enigma", " Unity within Diversity ", "5. Selected Topics in Mathematics", " Group Theory and the Classification of Finite Simple Groups", " The Prime Number Theorem", " Non-Euclidean Geometry", " Non-Cantorian Set Theory", " Appendix A", " Nonstandard Analysis", " Fourier Analysis ", "6. Teaching and Learning", " Confessions of a Prep School Math Teacher", " The Classic Classroom Crisis of Understanding and Pedagogy", " Polya's Craft of Discovery", " The Creation of New Mathematics: An Application of the Lakatos Heuristic", " Comparative Aesthetics", " Nonanalytic Aspects of Mathematics ", "7. From Certainty to Fallibility", " Platonism, Formalism, Constructivism", " The Philosophical Plight of the Working Mathematician", " The Euclid Myth", " Foundations, Found and Lost", " The Formalist Philosophy of Mathematics", " Lakatos and the Philosophy of Dubitability ", "8. Mathematical Reality", " The Riemann Hypothesis", " Pi and Pi Hat", " Mathematical Models, Computers, and Platonism", " Why Should I Believe a Computer?", " Classification of Finite Simple Groups", " Intuition", " Four-Dimensional Intuition", " True Facts About Imaginary Objects ", "Glossary", "Bibliography", "Index".

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