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基本説明
Explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today.
Full Description
Henri Poincare (1854-1912) was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincare explores all the fields that Poincare touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today. Math historian Jeremy Gray shows that Poincare's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincare conjecture. And Poincare's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems.
In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincare the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincare demonstrates how one man's work revolutionized math, science, and the greater world.
Contents
List of Figures ix Preface xi Introduction 1 * Views of Poincare 3 * Poincare's Way of Thinking 6 1 The Essayist 27 * Poincare and the Three Body Problem 27 * Poincare's Popular Essays 34 * Paris Celebrates the New Century 59 * Science, Hypothesis, Value 67 * Poincare and Projective Geometry 76 * Poincare's Popular Writings on Physics 100 * The Future of Mathematics 112 * Poincare among the Logicians 123 * Poincare's Defenses of Science 144 2 Poincare's Career 153 * Childhood, Schooling 153 * The Ecole Polytechnique 157 * The Ecole des Mines 158 * Academic Life 160 * The Dreyfus Affair 165 * National Spokesman 169 * Contemporary Technology 177 * International Representative 187 * The Nobel Prize 192 *"1911", "1912" 200 * Remembering Poincare 202 3 The Prize Competition of 1880 207 * The Competition 207 * Fuchs, Schwarz, Klein, and Automorphic Functions 224 * Uniformization, 1882 to 1907 247 4 The Three Body Problem 253 * Flows on Surfaces 253 * Stability Questions 265 * Poincare's Essay and Its Supplements 266 *Les Methodes Nouvelles de la Mecanique Celeste 281 * Poincare Returns 291 5 Cosmogony 300 * Rotating Fluid Masses 300 6 Physics 318 * Theories of Electricity before Poincare: Maxwell 318 * Poincare's Electricite et Optique, 1890 329 * Larmor and Lorentz: The Electron and the Ether 338 * Poincare on Hertz and Lorentz 346 * St. Louis, 1904 356 * The Dynamics of the Electron 361 * Poincare and Einstein 367 * Early Quantum Theory 378 7 Theory of Functions and Mathematical Physics 382 * Function Theory of a Single Variable 382 * Function Theory of Several Variables 391 * Poincare's Approach to Potential Theory 402 * The Six Lectures in Gottingen, 1909 416 8 Topology 427 * Topology before Poincare 427 * Poincare's Work, 1895 to 1905 432 9 Interventions in Pure Mathematics 467 * Number Theory 467 * Lie Theory 489 * Algebraic Geometry 498 10 Poincare as a Professional Physicist 509 * Thermodynamics 513 * Probability 518 11 Poincare and the Philosophy of Science 525 * Poincare: Idealist, Skeptic, or Structural Realist? 525 12 Appendixes 543 * Elliptic and Abelian Functions 543 * Maxwell's Equations 545 * Glossary 548 References 553 * Articles and Books by Poincare 554 * Other Authors 564 Name Index 585 Subject Index 589
