Poincare : Three Supplementary Essays

The first of Henri Poincaré2s several path-breaking contributions to mathematics was the theory of Fuchsian functions discovered in 1880. Poincaré pioneered the study of differential equations on Riemann surfaces by means of geometry and group theory, thereby establishing new fields of mathematical research which are still highly active. The three supplementary essays transcribed here originally accompanied a long essay submitted for the Grand Prix des Sciences Mathimatiques offered by the Paris Academy. They document Poincaré2s discovery of Fuchsian functions, showing in detail how he made and exploited a series of insights relating non-Euclidean geometry to complex function theory. An introductory essay considers both the original and supplementary essays in context, and discusses, among other topics, their relation to Lazarus Fuchs2 earlier work on the integration of linear differential equations with rational coefficients, the correspondence with Fuchs and Felix Klein, and the traces of German and French mathematical traditions in Poincaré2s first major discovery.Gray, Carol is the author of 'Poincare : Three Supplementary Essays' with ISBN 9783527401475 and ISBN 3527401474.