Hermann Weyl 1885 - 1985 ; centenary lectures

Published for the Eidgenössische Technische Hochschule Zürich Foreword This volume marks the celebration of the Centenary of Hermann Weyl by the Swiss Federal Institute of Technology (ETH), Ziirich. That celebration was given a special substance and meaning by the three Centenary Lectures delivered here by Professor Chen Ning Yang, by Professor Roger Penrose, and by Professor Armand Borel. It is the purpose of this volume to make the text of those lectures available to a wider audience. The themes chosen represent only a fraction of Weyl’s mathematical interests. But they give us more than a glimpse of the mighty effulgence of his mind. Among all the mathematicians who began their research work in the twentieth century, Weyl was the one who made major contributions in the greatest number of different fields. He alone could stand comparison with the last great universalists of the nineteenth century, David Hilbert and Henri Poincaré. No one else bounds about among the peaks of mathematics with quite such dazzling aplomb. To Weyl the world ofideas and concepts was as real as the world of human beings. The force, the steadiness, the comprehensiveness, and the versatility of his intellect were matched by his generosity, sympathy, and support for striving young researchers spread around the globe. He was peerless in the part he played in the international world of mathematics and mathematicians, as adviser, inspirer, referee, bringer on, and godfather. And he was totally devoid of envy, rare even among the great. Incelebrating his Centenary, we are not just savouring the past, or savaging the present, but looking to the future with a sober idealism that transcends the personality. While inscribing a copy ofhis book on Classical Groups for one of his admirers, Weyl used a quotation from Gauss which said: ‘you have achieved nothing so long as there is something to be achieved’. There is much to be achieved. But the example of Weyl, as it flames and glows in our memory, will remain a source of inspiration for succeeding generations. The Centenary Lectures make this point in their own way. ETH Zurich, March 30, 1986 K. Chandrasekharan Table of Contents Opening Address by Prof. H. Ursprung (President, ETH Zirich) 1 Hermann Weyl Centenary Lectures Hermann Weyl’s Contribution to Physics by Prof. Chen Ning Yang 7 Hermann Weyl, Space-Time and Conformal Geometry by Prof. Roger Penrose 23 Hermann Weyl and Lie Groups by Prof. Armand Borel 33 Hermann Weyl Memorabilia 83 Appendix Report on the Celebration 95 List of Publications by Hermann Weyl 109