Jean-Paul Pier - Böcker

For several centuries, analysis has been one of the most prestigious and important subjects in mathematics. The present book sets off by tracing the evolution of mathematical analysis, and then endeavours to understand the developments of main trends, problems, and conjectures. It features chapters on general topology, 'classical' integration and measure theory, functional analysis, harmonic analysis and Lie groups, theory of functions and analytic geometry, differential and partial differential equations, topological and differential geometry. The ubiquitous presence of analysis also requires the consideration of related topics such as probability theory or algebraic geometry. Each chapter features a comprehensive first part on developments during the period 1900-1950, and then provides outlooks on representative achievements during the later part of the century. The book provides many original quotations from outstanding mathematicians as well as an extensive bibliography of the seminal publications. It will be an interesting and useful reference work for graduate students, lecturers, and all professional mathematicians and other scientists with an interest in the history of mathematics.

This volume grew out of the preparation and achievements of the Symposium organized by the Luxembourg Mathematical Society in June 1992, at Chateau Bourglinster (Luxembourg). We express our best thanks to Monsieur Marc Fischbach, ministre de I 'Education nationale, Luxembourg Monsieur Rene Steichen, ministre delegue aux Affaires culturelles, Luxem- bourg, Academie des sciences, Paris, Academie roya1e des sciences, des lettres et des beaux-arts de Belgique, Section des sciences de l'Institut grand-ducal, Luxembourg, and all lecturers and participants. We hope that this contribution may ease a better understanding of the vitality in mathematics during the first half of the present century and provide clues for the explanation of its influence on later developments. We say our gratitude to persons who assisted us with their advice and help for the technical realization of the volume, especially Mrs. Suzanne D' Addato-Mues, Mr. Fran~ois Gaillard, Mr. Hubert Glesener. We are also grateful to Birkhauser- Verlag for having accepted this publication. Now the book should speak for itself ...