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Summary
Summary
A comprehensive look at the mathematics, physics, and philosophy of Henri Poincaré
Henri Poincaré (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 Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today.
Math historian Jeremy Gray shows that Poincaré'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 Poincaré conjecture. And Poincaré'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. Poincaré 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 Poincaré demonstrates how one man's work revolutionized math, science, and the greater world.
Author Notes
Jeremy Gray is professor of the history of mathematics at the Open University, and an honorary professor at the University of Warwick. His most recent book is Plato's Ghost: The Modernist Transformation of Mathematics (Princeton).
Reviews (3)
Publisher's Weekly Review
The great French mathematician Poincare's (1854-1912) rigorous research and quest for understanding influenced fields as diverse as algebra, geometry, astronomy, and physics. Drawing on Poincare's voluminous notebooks, essays, and other writings, Gray, a math historian at Britain's Open University, chronicles Poincare's remarkable achievements in language that is by turns sparkling and dense. The biography of a mind, Gray's narrative doesn't linger over the details of Poincare's life but concentrates on mathematician's wide-ranging and penetrating insights into celestial mechanics, topology, number theory, and algebraic geometry. Gray reveals Poincare's work pattern: when reflecting on a topic, he liked to walk about; he took few notes when preparing to work and often approached a problem without any idea of a solution. One of his most celebrated achievements was cracking the three-body problem, which asserted the impossibility of predicting the relationships among three bodies moving under mutual gravitational attraction. Chock full of the equations and formulas that Poincare developed to support and prove his groundbreaking work, Gray's intellectual biography deftly illuminates the workings of a fertile mind but the volume will be most appreciated by the devoted math and science reader. 13 b&w photos. (Dec.) (c) Copyright PWxyz, LLC. All rights reserved.
Choice Review
Gray (Open Univ., UK), a mathematics historian and scholar on the life and work of Henry Poincare, has with the support of a Leverhulme Research Fellowship produced this comprehensive and definitive "scientific biography." Gray offers abundant rich information on Poincare's ideas and scientific process, the evolution and maturity of his mathematics including his missteps, the dexterity of his reasoning, and the influences that shaped his thought. Absent are particulars concerning his domestic, personal, and emotional life. Poincare was prolific and his interests diverse. He made important contributions to non-Euclidean geometry, the three-body problem in celestial mechanics, and the motion of rotating fluid masses, important for understanding Saturn's rings. He also made significant advances in electromagnetic theory and electron dynamics; complex function theory and differential equations; topology, number theory, and algebraic geometry; and the philosophy of science and the practice of science as a profession. Appendixes and a glossary provide concise mathematical background for uncommon topics. The volume includes comprehensive bibliographies of Poincare's publications as well as related published research by his colleagues and important secondary sources. Mathematicians and historians of mathematics will most benefit from Gray's scholarship. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and researchers/faculty. M. Mounts Dartmouth College
Library Journal Review
In the first full-length English-language book to cover Henri Poincare's (1854-1912) contributions to mathematics, physics, and philosophy, Gray (history of mathematics, Open Univ.; Plato's Ghost: The Modernist Transformation of Mathematics) illuminates how the French polymath tackled so many different problems with such success. Poincare is best known for his work in mathematics, including Newton's n-body problem on the movement of celestial objects; his famous Millennium Prize-problem conjecture, which dealt with algebraic topology; and his general influence in that field. Gray uses Poincare's manuscripts and supplementary archival sources to document his influence in divergent fields of interest, including celestial mechanics, Lorentz's transformations, and the philosophy of mathematics and science. Although he includes traditional biographical elements, Gray spends considerable time describing Poincare's ways of thinking during a transitional period of French and scientific history. VERDICT This book is lengthy, written for a general audience, and devoid of mathematical proofs, though it also includes pictures, figures, and references. An interesting history that will be of special interest to students and scholars.-Ian D. Gordon, Brock Univ. Lib., St. Catharines, Ont. (c) Copyright 2012. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
Table of Contents
| List of Figures | p. ix |
| Preface | p. xi |
| Introduction | p. 1 |
| Views of Poincaré | p. 3 |
| Poincaré's Way of Thinking | p. 6 |
| 1 The Essayist | p. 27 |
| Poincaré's and the Three Body Problem | p. 27 |
| Poincaré's Popular Essays | p. 34 |
| Paris Celebrates the New Century | p. 59 |
| Science, Hypothesis, Value | p. 67 |
| Poincaré and Projective Geometry | p. 76 |
| Poincaré's Popular Writings on Physics | p. 100 |
| The Future of Mathematics | p. 112 |
| Poincaré among the Logicians | p. 123 |
| Poincaré's Defenses of Science | p. 144 |
| 2 Poincaré's Career | p. 153 |
| Childhood, Schooling | p. 153 |
| The École Polytechnique | p. 157 |
| The École des Mines | p. 158 |
| Academic Life | p. 160 |
| The Dreyfus Affair | p. 165 |
| National Spokesman | p. 169 |
| Contemporary Technology | p. 177 |
| International Representative | p. 187 |
| The Noble Prize | p. 192 |
| 1911, 1912 | p. 200 |
| Remembering Poincaré | p. 202 |
| 3 The Prize Competition of 1880 | p. 207 |
| The Competition | p. 207 |
| Fuchs, Schwarz, Klein, and Automorphic Functions | p. 224 |
| Uniformization, 1882 to 1907 | p. 247 |
| 4 The Three Body Problem | p. 253 |
| Flows on Surfaces | p. 253 |
| Stability Questions | p. 265 |
| Poincaré's Essay and Its Supplements | p. 266 |
| Les Méthodes Nouvelles de la Mécanique Céleste | p. 281 |
| Poincaré Returns | p. 291 |
| 5 Cosmogony | p. 300 |
| Rotating Fluid Masses | p. 300 |
| 6 Physics | p. 318 |
| Theories of Electricity before Poincaré: Maxwell | p. 318 |
| Poincaré's Électricité et Optique, 1890 | p. 329 |
| Larmor and Lorentz: The Electron and the Ether | p. 338 |
| Poincaré on Hertz and Lorentz | p. 346 |
| St. Louis, 1904 | p. 356 |
| The Dynamics of the Electron | p. 361 |
| Poincaré and Einstein | p. 367 |
| Early Quantum Theory | p. 378 |
| 7 Theory of Functions and Mathematical Physics | p. 382 |
| Function Theory of a Single Variable | p. 382 |
| Function Theory of a Several Variables | p. 391 |
| Poincaré's Approach to Potential Theory | p. 402 |
| The Six Lectures in Göttingen, 1909 | p. 416 |
| 8 Topology | p. 427 |
| Topology before Poincaré | p. 427 |
| Poincare's Work, 1895 to 1905 | p. 432 |
| 9 Interventions in Pure Mathematics | p. 467 |
| Number Theory | p. 467 |
| Lie Theory | p. 489 |
| Algebraic Geometry | p. 498 |
| 10 Poincaré as a Professional Physicist | p. 509 |
| Thermodynamics | p. 513 |
| Probability | p. 518 |
| 11 Poincaré and the Philosophy of Science | p. 525 |
| Poincaré: Idealist, Skeptic, or Structural Realist? | p. 525 |
| 12 Appendixes | p. 543 |
| Elliptic and Abelian Functions | p. 543 |
| Maxwell's Equations | p. 545 |
| Glossary | p. 548 |
| References | p. 553 |
| Articles and Books by Poincaré | p. 554 |
| Other Authors | p. 564 |
| Name Index | p. 585 |
| Subject Index | p. 589 |