On the nature of mathematical reasoning -- Mathematical magnitude and experience -- Non-Euclidian geometries -- Space and geometry -- Experience and geometry -- Classical mechanics -- Relative and absolute motion -- Energy and thermodynamics -- Hypotheses in physics -- Theories of modern physics -- Probability calculus -- Optics and electricity -- Electrodynamics -- The end of matter.

Poincaré tries to tackle the question "Can science sway us into materialism?". In other words, he analyzes if science - in particular Physics - and its theories are dependent on a materialistic ontological view of the world. His final answer appears to be "no". However, in order to reach this conclusion he resorts to a brief history of Physics, providing an insightful account on the evolution of the concept of atom from Democritus to the, then, recent discoveries on the composition (...) of the atom. In his opinion, science swung and will keep swinging between two opposing approaches over the constitution of nature: the discrete and the continuous approach. (shrink)

Nous reproduisons ici, avec l’aimable autorisation de la Hofbibliothek Aschaffenburg (Allemagne), la courte correspondance inédite entre Dingler et Henri Poincaré. Cette correspondance, conservée aux Archives Dingler dans la Hofbibliothek Aschaffenburg (et mentionnée dans le catalogue du Nachlass de Dingler [Wolters & Schroeder-Heister 1979]), consiste en trois documents : un brouillon en allemand de la main de Dingler, sa traduction française par une autre plume, mais avec des corrections ef...

During his lifetime, Henri Poincaré published three major philosophical books which achieved great success: "La science et l'hypothèse" (1902), "La valeur de la science" (1905) and "Science et méthode" (1908). After his death in 1913, a fourth volume of his philosophical works was published by his heirs as "Dernières pensées" (1913). The four books constitute the core of Poincaré's philosophic works and were given an ovation by scientific and general public. Around 1919, Gustave Le Bon wrote to Poincaré's widow. As (...) the director of the "Bibliothèque de Philosophie Scientifique at Flammarion", he asked her permission to publish a second posthumous volume. "L'Opportunisme scientifique" was intended to be the fifth and final volume of Poincaré's philosophical writings. Louis Rougier had elaborated the project, with the collaboration of Gustave Le Bon, and the approval of the philosopher Émile Boutroux and his son Pierre. Because of the reservations of the mathematician's heirs, this book was never published and Dernières pensées remained his last philosophical book. Nevertheless Poincaré's correspondence - which is kept in the Poincaré Archives at University Nancy 2 - contains a large amount of documents concerning the project, its justification and the discussions between Louis Rougier and the mathematician's heirs. The aim of this book is to restore this episode, which gives some crucial informations about editorial practices of Poincaré and about the posterity of his philosophic thinking. (shrink)

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote (...) for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. (shrink)