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| Foreword | |
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| Acknowledgments | |
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| Introduction | |
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| The Foundations | |
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| The 1920s: Sets | |
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| The 1940s: Structures | |
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| The 1960s: Categories | |
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| The 1980s: Functions | |
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| Pure Mathematics | |
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| Mathematical Analysis: Lebesgue Measure (1902) | |
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| Algebra: Steinitz Classification of Fields (1910) | |
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| Topology: Brouwer's Fixed-Point Theorem (1910) | |
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| Number Theory: Gelfand Transcendental Numbers (1929) | |
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| Logic: Gouml;del's Incompleteness Theorem (1931) | |
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| The Calculus of Variations: Douglas's Minimal Surfaces (1931) | |
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| Mathematical Analysis: Schwartz's Theory of Distributions (1945) | |
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| Differential Topology: Milnor's Exotic Structures (1956) | |
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| Model Theory: Robinson's Hyperreal Numbers (1961) | |
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| Set Theory: Cohen's Independence Theorem (1963) | |
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| Singularity Theory: Thom's Classification of Catastrophes (1964) | |
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| Algebra: Gorenstein's Classification of Finite Groups (1972) | |
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| Topology: Thurston's Classification of 3-Dimensional Surfaces (1982) | |
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| Number Theory: Wiles's Proof of Fermat's Last Theorem (1995) | |
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| Discrete Geometry: Hales's Solution of Kepler's Problem (1998) | |
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| Applied Mathematics | |
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| Crystallography: Bieberbach's Symmetry Groups (1910) | |
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| Tensor Calculus: Einstein's General Theory of Relativity (1915) | |
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| Game Theory: Von Neumann's Minimax Theorem (1928) | |
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| Functional Analysis: Von Neumann's Axiomatization of Quantum Mechanics (1932) | |
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| Probability Theory: Kolmogorov's Axiomatization (1933) | |
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| Optimization Theory: Dantzig's Simplex Method (1947) | |
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| General Equilibrium Theory: The Arrow-Debreu Existence Theorem (1954) | |
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| The Theory of Formal Languages: Chomsky's Classification (1957) | |
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| Dynamical Systems Theory: The KAM Theorem (1962) | |
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| Knot Theory: Jones Invariants (1984) | |
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| Mathematics and the Computer | |
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| The Theory of Algorithms: Turing's Characterization (1936) | |
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| Artificial Intelligence: Shannon's Analysis of the Game of Chess (1950) | |
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| Chaos Theory: Lorenz's Strange Attractor (1963) | |
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| Computer-Assisted Proofs: The Four-Color Theorem of Appel and Haken (1976) | |
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| Fractals: The Mandelbrot Set (1980) | |
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| Open Problems | |
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| Arithmetic: The Perfect Numbers Problem (300 BC) | |
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| Complex Analysis: The Riemann Hypothesis (1859) | |
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| Algebraic Topology: The Poincare Conjecture (1904) | |
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| Complexity Theory: The P=NP Problem (1972) | |
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| Conclusion | |
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| References and Further Reading | |
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| Index | |