The first of Henri Poincar?'s several path-breaking contributions to mathematics was the theory of Fuchsian functions discovered in 1880. Poincar? 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 Poincar?'s 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 Fuchs' 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 Poincar?'s first major discovery.
- ISBN10 3527401474
- ISBN13 9783527401475
- Publish Date 18 October 1999
- Publish Status Out of Print
- Out of Print 23 May 2001
- Publish Country DE
- Imprint Wiley-VCH Verlag GmbH
- Format Hardcover
- Pages 114
- Language English