André Weil Bücher

)tPI(}jlOV, e~oxov (10CPUljlr1.'CWV Aiux., llpop. . . dsup.. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by Chevalley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very well. It contained a brief but essentially com plete account of the main features of classfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I included such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather closely at some critical points.

From the reviews „All of Weil’s works except for books and lecture notes are compiled here, in strict chronological order for easy reference. But the value … goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places (…) or not published at all. Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career. The sheer number of mathematical papers of fundamental significance would earn Weil’s Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential.“ Neal Koblitz in Mathematical Reviews „André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) “Collected papers„ emphasize this influence.“ O. Fomenko in Zentralblatt der Mathematik

From the reviews: „…All of Weil’s works except for books and lecture notes are compiled here, in strict chronological order for easy reference. But the value … goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places (…) or not published at all. Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career. The sheer number of mathematical papers of fundamental significance would earn Weil’s Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential.“ Neal Koblitz in Mathematical Reviews „…André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) “Collected papers„ emphasize this influence.“ O. Fomenko in Zentralblatt der Mathematik

„Der bedeutende Algebraiker André Weil, der ältere Bruder der ebenso berühmten Theologin Simone Weil, hat eines der schönsten wissenschaftlichen Memoirenbücher verfaßt, das jemals geschrieben wurde.“The Times, 3.4.1992.

This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.

Drawn from the (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).

From the reviews„…All of Weil’s works except for books and lecture notes are compiled here, in strict chronological order for easy reference. But the value … goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places (…) or not published at all. Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career. The sheer number of mathematical papers of fundamental significance would earn Weil’s Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential.“ Neal Koblitz in Mathematical Reviews„…André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) “Collected papers„ emphasize this influence.“ O. Fomenko in Zentralblatt der Mathematik

L'auteur, mathématicien aux horizons variés, retrace sa carrière à travers plusieurs continents : de l'Italie à l'Inde, où il croise Ghandi et Nehru, puis l'U.R.S.S. et Princeton. Il évoque ses péripéties, dont une incarcération en Finlande et ses travaux en prison, tout en participant à la fondation du groupe Bourbaki.