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Henri Poincare

Henri Poincare: A Scientific Biography

Copyright Date: 2013
Pages: 320
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    Henri Poincare
    Book Description:

    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 Poincaréexplores 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 Poincarédemonstrates how one man's work revolutionized math, science, and the greater world.

    eISBN: 978-1-4008-4479-1
    Subjects: Mathematics, History, Physics, Technology

Table of Contents

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  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. List of Figures
    (pp. ix-x)
  4. Preface
    (pp. xi-xvi)
  5. Introduction
    (pp. 1-26)

    Although there have been several excellent studies of aspects of Poincaré’s work this book is the first full-length study covering all the main areas of his contributions to mathematics, physics, and philosophy. It presents an introduction to his work, an overview of its many fields and interconnections, and an indication of how Poincaré was able to tackle so many different problems with such success. What emerges is a picture of Poincaré as a man with a coherent view about the nature of knowledge, one that he expressed in many of his popular philosophical essays and applied in the conduct of...

  6. 1 The Essayist
    (pp. 27-152)

    On 20 January 1889 the ambitious Swedish mathematician Gösta Mittag-Leffler went to the Court of King Oscar II of Sweden to announce the judges’ decision concerning the prize competition the King had announced in 1885. Mittag-Leffler had administered it, and would have been feeling very pleased, for the competition had been a success: the result would surely play well with the King and would add, as intended, to the celebrations for the King’s 60th birthday. Moreover, it would be popular with professional mathematicians; none of this could do other than advance Mittag-Leffler’s own career.

    King Oscar II was an enlightened...

  7. 2 Poincaré’s Career
    (pp. 153-206)

    Jules Henri Poincaré was born in Nancy on 29 April 1854. His father, Léon, a professor of medicine at the University of Nancy, was then 26 and Henri’s mother Eugénie was 24. Henri’s sister Aline was born two years later (his cousin Raymond was born in 1860). In 1909 Dr. Toulouse reported that Henri resembled his mother and his maternal grandmother more than his father, and that his maternal grandmother was thought to have a real, but undeveloped gift for mathematics.

    The children had a happy childhood. Based on Poincaré’s recollections Toulouse recorded that Henri spoke at nine months, and...

  8. 3 The Prize Competition of 1880
    (pp. 207-252)

    On 10 March 1879 the Académie des sciences in Paris announced the topic for many of its customary essay competitions. Candidates for the Grand Prize for the mathematical sciences were asked

    to improve in some important way the theory of linear differential equations in a single independent variable. (CR1879, 88, 511)

    The prize was a medal to the value of 3,000 francs. On 12 April 1880 the academy announced that the panel of judges would comprise Bertrand, Bonnet, Puiseux, and Bouquet, with Hermite as rapporteur. Joseph Bertrand, then 58, was a professor at the École polytechnique who lectured at...

  9. 4 The Three Body Problem
    (pp. 253-299)

    Poincaré was interested all his life in celestial mechanics, and made original and lasting contributions in every decade from his early work on flows on surfaces to his last geometric problem. The particular case of the three body problem had long been regarded as the most important; Whittaker in his (1937, 339) estimated that over eight hundred papers on the subject had been written since 1750. Those which investigate the stability of the solar system largely assumed that it was stable, as the majestic long-term behavior of the planets so eloquently suggests, and that the only risk was collisions. Poincaré’s...

  10. 5 Cosmogony
    (pp. 300-317)

    There are many reasons for caring about the motion of a rotating fluid mass, most notably that we live on one, but the most spectacular sight of the problem is Saturn’s rings. They had first been detected by Galileo in 1610, who saw them as handles on either side of the planet; in 1655 Huygens, with an improved telescope of his own design, saw them as a disk surrounding it. Robert Hooke was able to see shadows cast on them, and in 1675 Domenico Cassini was the first to see gaps in the disk and therefore to see them as...

  11. 6 Physics
    (pp. 318-381)

    The study of magnetism and electricity in the second half of the 19th century was marked by disagreement at every level. There were at least two theories popular in continental Europe, Wilhelm Weber’s and the later theory of Hermann von Helmholtz. They were followed by the much more sophisticated theory of James Clerk Maxwell, which was the first fully mathematical theory of the static and dynamic aspects of the complex interrelations between electricity and magnetism. It also held out the prospect of explaining light by treating it as an electromagnetic wave. For reasons to be discussed, it was never fully...

  12. 7 Theory of Functions and Mathematical Physics
    (pp. 382-426)

    The core discipline in French mathematical education was that of analysis, particularly the theory of ordinary and partial differential equations, but also of Fourier series and the evaluation of integrals. It covered everything from the rigorous foundations of the calculus after the manner of Cauchy, to applications of analysis to geometry and mechanics. Originally analysis meant the study of real functions of a real variable with only modest excursions into functions of a complex variable, but complex or analytic function theory was one of the great growth areas of mathematics in the 19th century. Indeed, it grew much faster, and...

  13. 8 Topology
    (pp. 427-466)

    Topology became one of the central, and most fundamental, branches of mathematics in the 20th century, very much as a result of Poincaré’s pioneering achievements—which means, of course, that it was not regarded as a truly significant way of approaching mathematical problems before he began. Even the name of the subject shows this evolution, Poincaré, like many before him, called it “analysis situs,” after an analogy with some vague ideas of Leibniz about a subject more general than Euclidean geometry. The name “topology,” meaning the study orlogosof places (topoi) was introduced by Listing in 1847, but does...

  14. 9 Interventions in Pure Mathematics
    (pp. 467-508)

    One of the most important subjects in 19th-century mathematics was number theory. This had been rewritten by Gauss in hisDisquisitiones Arithmeticae(1801) on the back of considerable work by Euler, Lagrange, and Legendre, and had become something of a German specialty. Almost every major German mathematician of the period sought to contribute to it—Weierstrass is the most notable exception—and they collectively gave the subject a strong algebraic aspect, although Jacobi, Dirichlet, and Riemann also developed profound analytical methods.

    The simplest topic in this rapidly growing field was that of binary quadratic forms. These are expressions of the 𝑎𝑥²+𝑏𝑥𝑦+𝑐𝑦², where...

  15. 10 Poincaré as a Professional Physicist
    (pp. 509-524)

    Whatever the reasons that led to Poincaré taking up a chair in physics in 1886, he took his duties as a professor of physics not only very seriously but much more imaginatively than his predecessors, so much so that in barely a decade he had published a dozen volumes on different topics. While these largely took the form of lectures edited by some of his students they are nonetheless clear and speak with Poincaré’s voice. The lectures on the interrelated topics of thermodynamics and probability are the most interesting apart from the accounts of electricity, magnetism, and optics, but all...

  16. 11 Poincaré and the Philosophy of Science
    (pp. 525-542)

    The philosophical stance for which Poincaré is best remembered is his geometric conventionalism, but in his day he was also accused of being both too much and too little of a skeptic about science, and he was willing to charge others with undue skepticism. He was also said to be more of an idealist than a realist about the knowledge claims of science, and once called himself a pragmatic idealist (as opposed to a Cantorian realist).

    There are four questions to ask about Poincaré’s philosophy of science. The first concerns his distinction between geometric conventionalism and other forms of conventionalism...

  17. 12 Appendixes
    (pp. 543-552)
  18. References
    (pp. 553-584)
  19. Name Index
    (pp. 585-588)
  20. Subject Index
    (pp. 589-592)