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Uta C. Merzbach a Mathematical Biography Uta C. Merzbach Dirichlet A Mathematical Biography Uta C. Merzbach Dirichlet A Mathematical Biography Uta C. Merzbach (Deceased) Georgetown, TX, USA ISBN 978-3-030-01071-3 ISBN 978-3-030-01073-7 (eBook) https://doi.org/10.1007/978-3-030-01073-7 Library of Congress Control Number: 2018958343 Mathematics Subject Classification (2010): 01-XX, 31-XX, 30E25, 11-XX © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Image made available by the University of Toronto—Gerstein Science Information Centre Preface Among the questions a potential reader frequently asks about a book, let me single out the following three: Why this subject? What brings the author to the subject? How is the subject presented? Dirichlet was a mathematician who shared responsibility for significant trans- formations in mathematics during the nineteenth century in Western Europe, a notable period in the history of mathematics. Yet there is no book-length study of his life and work and only a small percentage of his publications tends to be cited. I first saw his name in conjunction with Dedekind’s Eleventh Supplement to Dirichlet’s Lectures on Number Theory. As a graduate student in mathematics, interested in algebra, I was puzzled by what this Supplement might have to do with Dirichlet. Shortly thereafter, while assisting Garrett Birkhoff with the Sourcebook of Classical Analysis, I studied Dirichlet’s own writings on convergence, functions, and potential theory. That did not answer my original question but led me to give a series of talks on Dirichlet in the 1970s, including an invited lecture at a meeting of the American Mathematical Society. This in turn led to an encouraging con- versation with the late Saunders Mac Lane and numerous chats with the late Walter Kaufmann-Bühler of Springer-Verlag New York. It was he who urged me to expand my earlier research into a book. After some primary source studies in libraries and archives, I became enthusiastic about such a project, realizing that Dirichlet was a man who produced his conceptual contributions while living in an unusually fascinating intellectual environment. Although I had to lay aside this intended, expanded study because of numerous other commitments, I recently was able to return to Dirichlet, to relearn many things I had forgotten, but to take the same pleasure in learning more about the man, his mathematics, and his environment that I had been granted before. The presentation of a “mathematical biography” produces the same challenges as most biographies, especially with regard to the questions raised repeatedly among historians concerning the relationship of history to biography, of internal versus external studies, of psychohistory vis-a-vis a “factual” listing of events, or of the thematic content of a historical study. I have tried to avoid such methodological arguments. Rather, I have attempted to record as accurately as possible, using the vii viii Preface tools in my possession, the life of a man who loved mathematics, who through accidents of time and place was able to pursue it as a career, who did not promote himself but, as noted in our concluding chapter, had a strong support system throughout most of his life. Many of those who attended his lectures in Berlin and Göttingen were proud to call themselves his students, no matter how widely their subsequent fields of specialization diverged. As I realized the rare opportunity Dirichlet presents to convey to the contem- porary reader a sense for certain nineteenth-century lives, my originally intended more mathematically oriented study turned into a fuller biography. I hope the result may interest not only mathematical specialists but readers with other backgrounds. I have chosen to alternate the chapters dealing with Dirichlet’s publications with those discussing the corresponding biographical aspects of his life. This decision was based on an early conversation and the example of Walter Kaufmann-Bühler which persuaded me that this approach can facilitate the reading for both groups of readers. In writing about the individual publications, I chose to condense the main threads of Dirichlet’s mathematical discussions sufficiently to guide those who wish to work through his arguments and to suggest changes in his methodology vis-a-vis his main predecessors and his successors. Readers may find access to the full versions of his papers through the references in these chapters pointing to the bibliography at the end of the book. At the same time, I have described in greater detail his introductions to the mathematical memoirs, frequently non-technical and often including references, that reflect his own interest in history. These not only are largely understandable to the general reader but also shed considerable light on the development of the subject and on Dirichlet’s own thought processes. Though at times repetitive, they are stylistically more accessible than the technical parts of his publications. In contrast to the lectures published posthumously by some of his students, many of Dirichlet’s memoirs have been ignored in the secondary literature. While cov- ering his memoirs in the odd-numbered Chaps. 5 through 13, I have attempted to convey the purpose and major statements of each with only occasional details of his proofs sufficient to convey his methodology and to interest the curious general reader. More involved mathematical readers may attempt to fill in proof details or read up on them in the extensive multilingual bibliography at the end of this volume. It should be noted that Dirichlet was not an emulable stylist. He was careful in detailing his arguments, but this very care, combined with his adhering to termi- nology quite different from the smoother, generalized one developed by later generations, frequently resulted in a certain awkwardness. This may have been reinforced by a lack of interest and consequent experience in writing. As will be noted in the following, this was more evident in his formal presentations than it was in his lectures and conversations. Preface ix Acknowledgements Before acknowledging specific sources of support, I should like to call the reader’s attention to some comments at the beginning of the bibliography, where I single out the meticulous publications of Kurt-R. Biermann and the more recent, concise, biographical sketch by J. Elstredt. The original motivation for a detailed study of Dirichlet’s mathematics arose from a set of lectures I gave at the invitation in the 1970s from Judith Victor Grabiner and the organizers of a Southern California lecture series. A sabbatical leave from the Smithsonian Institution provided me with the opportunity to do research in the relevant archives and manuscript collections of Berlin, Göttingen, and Kassel named at the end of the bibliography. Special thanks are due to Dr. Haenel in Göttingen for many helpful services and to Rudolf Elvers in Berlin, who, among other courtesies, provided me with access to his typescript of Fanny Hensel’s diaries before their publication in 2002. Numerous conversations with Harold M. Edwards in Göttingen and Washington, DC, during the early phase of related studies furnished considerable food for thought. This volume benefitted considerably from the advice of Jeanne LaDuke, who read over large portions of the draft and provided needed grammatical, ortho- graphic, and stylistic advice. There would have been considerable delay in pro- ducing a readable copy without the assistance of Judy Green, who devoted many hours to translating my coded text to the appropriate LaTeX format. I owe special thanks to the Birkhäuser editor, Sarah A. Goob, for her unfailing patience and courtesy. It pleased me greatly that, in a conversation at one of the Joint Mathematics meetings, Dr. Anna Mätzener had expressed immediate interest in adopting this project that had been orphaned after the death of Walter Kaufmann-Bühler, the former New York editor of Springer-Verlag, New York. Georgetown, TX, USA Uta C. Merzbach June 2017 Publisher’s Acknowledgements This book would not have been possible without the dedication of Prof. Dr. Jeanne LaDuke and Prof. Dr. Judy Green. After Dr. Merzbach passed away in 2017, Dr. LaDuke and Dr. Green continued to proofread the manuscript and transfer the manuscript from Microsoft Word to LaTeX. They spent long hours reading through Dr. Merzbach’s notes and filling in the gaps to finalize the book, all in honor of their colleague and dear friend. We are grateful to these two mathematicians for pro- viding the mathematical community with a deeper understanding of Dirichlet all the while adding to Dr.
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