This book describes the life and work of Henri Poincaré, detailing most of his unique achievements in mathematics and physics. It is divided into two parts—the first on Poincaré’s life, and the second on his contributions to the mathematical sciences. Apart from biographical details, attention is given to Poincaré’s results on automorphic functions; differential equations and dynamical systems; celestial mechanics; mathematical physics, in particular the theory of the electron and relativity; and topology (analysis situs). A chapter on philosophy explains Poincaré’s conventionalism in mathematics and his view of conventionalism in physics. The book shows how Poincaré reached his fundamentally new results in many different fields, how he thought about problems, and how one should read his work. Simultaneously, it is made clear how analysis and geometry are intertwined in Poincaré’s thinking and work. In dynamical systems, this becomes clear in his description of invariant manifolds, his association of differential equation flow with mappings, and his fixed-point theory. There is no comparable book on Poincaré presenting such a relatively complete vision of his life and the working of his very original mind. Scientists and engineers as well as general readers interested in the history of science will find this book of interest. Reviews of this book:"The title of this biography is particularly well chosen : Henri Poincaré was a true genius, and he was impatient. It gives a fair picture of both the man and the scientist, completed by particularly well chosen illustrations. Jean Mawhin, Université Catholique de Louvain, Belgium "Ferdinand Verhulst has written a true scientific biography, introducing Poincaré the man, his cultural milieu, and his mathematics. This book shows why, a century after his death, Poincaré's ideas still shape a substantial part of the mathematical sciences." Philip J Holmes, Princeton University, USAThe discovery of relativity is considered one of his minor accomplishments.
Albert Einstein is considered the greatest genius who ever lived, primarily for his 1905 relativity paper. But he got the Lorentz transformations, constancy of the speed of light, local time, relativistic mass, and theorem of corresponding states from Lorentz, and the relativity principle, clock synchronization method, and E=mc2 from Poincare. Meanwhile, Poincare's 1905 relativity paper discovered the Lorentz group, covariance of Maxwell's equations, spacetime geometry, and relativistic gravity. Einstein completely missed these points, and did not even understand them until years later. Today relativity is taught based on Poincare's ideas.
The biography says:
The main priority controversy regarding the new mechanics, replacing Newtonian classical mechanics by relativity, is over special relativity, with prominent candidates Einstein, Lorentz, and Poincaré. [p.62] ...That is a polite way of saying that Einstein lied about the relativity story all his life. The obvious answer is that there was nothing that Einstein could have said about Poincare without diminishing his own status. He could not get away with saying that Poincare's work was deficient, or wrong, or unknown, or not influential, or not original, or anything like that. He just had to pretend that it did not exist.
In this respect, it is difficult to understand why Einstein, when describing the development of relativity in 1949 [Einstein 1950], mentions many scientists, in particular Lorentz, but omits Poincaré. [p.64]
Another biography last year was Henri Poincaré: A Scientific Biography. A recent AAAS Science magazine review (behind a paywall) says:
Despite his many brilliant interventions and mathematical virtuosity, Poincaré, Gray argues, made no great discovery in physics. Nonetheless, Gray emphasizes that for Poincaré “there is no valid or clear distinction to be made between mathematics and physics because the two are so intimately entangled.”The book seems to take the view that Poincare's discovery of special relativity as spacetime non-Euclidean geometry was a mathematical discovery, not a physical one, and it was perfected by Minkowski, not Poincare or Einstein. The book says:
He [Poincare] preferred a theory in which space and time were separate and Lorentz contractions really occurred, and argued, quite correctly, that because there could never be conclusions on this view that were incompatible with conclusions derived from a theory of space-time it was simple a matter of convenience which theory was adopted. [p.529]The book also discusses Poincare's many contributions to celestial mechanics and quantum mechanics.