By Bertrand Duplantier, Vincent Rivasseau

This 13th quantity of the Poincaré Seminar sequence, Henri Poincaré, 1912-2012, is released at the celebration of the centennial of the dying of Henri Poincaré in 1912. It provides a scholarly method of Poincaré’s genius and creativity in mathematical physics and arithmetic. Its 5 articles also are hugely pedagogical, as befits their foundation in lectures to a vast clinical viewers. Highlights comprise “Poincaré’s gentle” by means of Olivier Darrigol, a number one historian of technology, who makes use of gentle as a guiding thread via a lot of Poincaré ’s physics and philosophy, from the applying of his stronger mathematical talents and the speculation of diffraction to his next reflections at the foundations of electromagnetism and the electrodynamics of relocating our bodies; the authoritative “Poincaré and the Three-Body challenge” by way of Alain Chenciner, who deals an exquisitely designated, hundred-page point of view, peppered with bright excerpts from citations, at the huge paintings of Poincaré in this topic, from the recognized (King Oscar’s) 1889 memoir to the principles of the fashionable concept of chaos in “Les méthodes nouvelles de los angeles mécanique céleste.” A profoundly unique and scholarly presentation of the paintings via Poincaré on likelihood idea is given through Laurent Mazliak in “Poincaré’s Odds,” from the incidental first visual appeal of the be aware “probability” in Poincaré’s well-known 1890 theorem of recurrence for dynamical platforms, to his later recognition of the unavoidability of chance calculus in technology, as built to an exceptional volume via Emile Borel, Poincaré’s major direct disciple; the thing through Francois Béguin, “Henri Poincaré and the Uniformization of Riemann Surfaces,” takes us on a desirable trip in the course of the six successive types in twenty-six years of the prestigious uniformization theorem, which exemplifies the Master’s unique signature within the foundational fusion of arithmetic and physics, on which conformal box thought, string idea and quantum gravity a lot count these days; the ultimate bankruptcy, “Harmony and Chaos, at the determine of Henri Poincaré” through the filmmaker Philippe Worms, describes the homonymous poetical movie during which eminent scientists, via mathematical scenes and actual experiments, reveal their emotional dating to the customarily elusive clinical fact and common “harmony and chaos” in Poincaré’s legacy.

This e-book could be of large common curiosity to physicists, mathematicians, philosophers of technology and historians.