Andre and Eveline Weil (photo by Lucien Gillet, May 2, 1948)

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2 Andre and Eveline Weil (photo by Lucien Gillet, May 2, 1948)

3 Andre Weil The Apprenticeship of a Mathematician Translated from the French by J ennifer Gage Springer Basel AG

4 Author's address Prof. Or. Andre Weil Institute for Advanced Study School of Mathematics Princeton, NJ 08540, USA This work was originaliy published as: Souvenirs d'apprentissage; Basel: Birkhăuser AII illustrations were kindly provided by Professor A. Weil, Princeton. Library of Congress Cataloging-in-Publication Data Weil, Andre, [Souvenirs d'apprentissage. EnglishJ The apprenticeship of a mathematician / Andre Weil; translated from the French by Jennifer Gage. Translation of: Souvernirs d'apprentissage. Includes index. ISBN ISBN (ebook) DOI / Weil, Andre, Mathematicians-France-Biography. 1. Title QA29.W455A '.92 - dc20 Deutsche Bibliothek Cataloging-in-Publication Data Weil, Andre: The apprenticeship of mathematician / Andre Weil. Transl. from the French by Jennifer Gage. - Basel ; Boston; Berlin : Birkhăuser, 1992 Franz. Ausg. u.d.t.: Weil, Andre: Souvenirs d'apprentissage ISBN This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law where copies are made for other than private use a fee is payable to "Verwertungsgesellschaft Wort", Munich Springer Basel AG Originally published by Birkhauser Verlag Basel in 1992 Softcover reprint of the hardcover 1 st edition 1992 ISBN

5 Translator's acknowledgments I am grateful for the continuing support and encouragement of Rosanna Warren. For assistance with mathematical terminology my thanks go to Thanasis Kehagias - a true scion of Bourbaki. Finally, I am deeply indebted to Dr. Weil himself for his patient and generous assistance. J.G.

6 Table of Contents Foreword Chapter I Chapter II Chapter III Chapter IV Chapter V Chapter VI Growing Up At the Ecole Normale First Journeys, First Writings India... Strasbourg and Bourbaki The War and I: A Comic Opera in Six Acts. Prelude... Finnish Fugue.... Arctic Intermezzo.. Under Lock and Key Serving the Colors. A Farewell to Arms Chapter VII The Americas; Epilogue. Index of Names

7 CONIUGIS DILECTAE MANIBUS Pero nadie guerra mirar tus ojos porgue te has muerto para siempre. FEDERICO GARCIA LORCA

8 Foreword 11 My life, or at least what deserves this name - a singularly happy life, its diverse vicissitudes withal - is bounded by my birth on May 6, 1906, and the death on May 24, 1986, of my wife and companion Eveline. If she figures rather little in these pages which I dedicate to her, it is not that she did not count for much in my life and thought; on the contrary, she was so intimately a part of these, almost from our very first meeting, that to speak of myself is also to speak of her: her presence and her absence form the warp on which the entire weft of my life was woven. What shall I say, but that our marriage was one of those which give the lie to La Rochefoucauld?l Fulsere vere candidi mihi sales... My sister, too, is not much mentioned in these memoirs. Some time ago, in any case, I recounted my memories of her to Simone Petrement, who recorded them in her fine biography, Simone Weil: A Life;2 it would be superfluous to repeat herein those many details on our childhood which are included in Petrement's book. As children, Simone and I were inseparable; but I was always the big brother and she the little sister. Later on we saw each other only rarely, speaking to one another most often in a humorous vein; she was naturally bright and full of mirth, as those who knew her have attested, and she retained her sense of humor even when the world had added on a layer of inexorable sadness. In truth we had few serious conversations. But if the joys and sorrows of her adolescence were never known to me at all, if her behavior later on often struck me (and probably for good cause) as flying in the face of common sense, still we remained always close enough to one another so that nothing about her really came as a surprise to me - with the sole exception of her death. This I did not expect, for I confess that I had thought her indestructible. It was not until quite late that I came to understand that her life had unfolded according to its own laws, and thus also did it end. I was little more than a distant observer of her trajectory. All I am attempting here is to retrace the intellectual itinerary of a mathematician - a mathematician who has perhaps become too longwinded for the amusement (benevolent, I hope) of the younger generation. In the case of a writer or an artist, apparently nothing matters more than to Maximes 113: "II y a de bons mariages, mais il n'y en a point de delicieux" (there are good marriages, but there are no delicious ones). 2 Translated by Raymond Rosenthal (New York: Pantheon, 1976).

9 12 ANDRE WElL scrutinize the first gurglings of his infancy, after which the modem reader expects to be admitted into the most intimate recesses of the character's love life. But I have neither the temperament nor the talent of a Jean-Jacques Rousseau; and his is not the way to account for the life of a mathematician. I had first planned to end these memoirs with my arrival in New York harbor in March of 1941 with my wife and her son Alain. But my years of apprencticeship (my Lehrjahre, which were also Wanderjahre) did not end so early. What am I saying? I am still learning today: I am learning to live in my memories. May the kindly reader accompany me with all good will... his presence will be precious to me.