Mathematical Survey Lectures 1943-2004

In my long professional life as a mathematician I have had to deliver various survey lectures. They were of different character according to the occasion. A selected number are reproduced in this volume. They were, with few exceptions, printed in books or in periodicals, and are reproduced here without any modification. I started as a student at the ETH Zurich in 1935 and have spent my working Ufe there, with the exception of the period 1942-1948 (lecturer then associate professor at the University of Lausanne) and 1947 and 1951/52 (Institute for Advanced Study Princeton). In 1948 I was appointed as a professor at the ETH; I retired in 1984 and have since then been professor emeritus. The surveys in this volume are lectures given at congresses and workshops, at international congresses of mathematicians (plenary or section lectures), and at special occasions like birthdays or commemorations. They all reflect the special interests of the respective times. Although they are in fields of topology, algebra and differential geometry they reveal the big changes mathematics has undergone over the years from 1943 to 2004. New thinking has been developed; it has created new problems, or simply has let old problems appear in a new light.

Includes supplementary material: sn.pub/extras

Klappentext

This collection traces the career of Beno Eckmann, whose work ranges across a broad spectrum of mathematical concepts from topology and differential geometry through homological algebra to group theory. One of our most influential living mathematicians, Eckmann has been associated for nearly his entire professional life with the Swiss Federal Institute of Technology Zurich (ETH), as student, lecturer, professor, and professor emeritus.

The lectures offer a fascinating account of advances in pure mathematics from 1943 to 2004, as new topics and methods are introduced, and gradually become routine. The penultimate lecture is a personal-historical overview of algebraic topology, delivered in connection with the 40-year jubilee of the Institute for Mathematical Research (FIM), which Eckmann founded at ETH in 1964. In the final article, Eckmann looks beyond pure mathematics to consider the application in concrete fields of intellectual enterprise.

Inhalt
L'idée de dimension.- Topologie und Algebra.- Complex-analytic manifolds.- Homotopie et dualité.- Groupes d'homotopie et dualité.- Homotopy and cohomology theory.- Simple homotopy type and categories of fractions.- Some recent developments in the homology theory of groups.- Poincaré duality groups of dimension two are surface groups.- Continuous solutions of linear equations An old problem, its history, and its solution.- Mathematics: Questions and Answers.- Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity.- Birth of fibre spaces, and homotopy.- 4-Manifolds, group invariants, and ? 2-Betti numbers.- The Euler characteristic a few highlights in its long history.- Topology, algebra, analysis relations and missing links.- to ?2-methods in topology: Reduced ?2-homology, harmonic chains, ?2-Betti numbers.- Die Zukunft der Mathematik Ein Rückblick auf Hilberts programmatischen Vortrag vor 100 Jahren.- Kolmogorov and contemporary mathematics.- Is algebraic topology a respectable field?.- Social choice and topology. A case of pure and applied mathematics.