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Leonhard Euler Leonhard Euler Mathematical Genius in the Enlightenment Ronald S. Calinger Princeton University Press Princeton and Oxford Copyright © 2016 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu Jacket art: Detail of 19th century engraving of Leonhard Euler, private collection. Image © Look and Learn/Elgar Collection/Bridgeman Images All Rights Reserved Library of Congress Cataloging-in-Publication Data Calinger, Ronald. Leonhard Euler : mathematical genius in the Enlightenment / Ronald S. Calinger. pages cm Includes bibliographical references and index. ISBN 978-0-691-11927-4 (hardcover : alk. paper) 1. Euler, Leonhard, 1707–1783. 2. Mathematicians—Germany—Biography. 3. Mathematicians—Russia (Federation) —Biography. 4. Mathematicians—Switzerland—Biography. 5. Physicists—Germany— Biography. 6. Physicists—Russia (Federation)—Biography. 7. Physicists— Switzerland—Biography. 8. Mathematics—History—18th century. I. Title. QA29.E8C35 2015 510.92--dc23 [B] 2014045172 British Library Cataloging- in- Publication Data is available This book has been composed in Baskerville 10 Pro. Printed on acid- free paper. ∞ Printed in the United States of America 1 3 5 7 9 10 8 6 4 2 Contents Preface ix Acknowledgments xv Author’s Notes xvii Introduction 1 1. The Swiss Years: 1707 to April 1727 4 “Das alte ehrwürdige Basel” (Worthy Old Basel) 4 Lineage and Early Childhood 8 Formal Education in Basel 14 Initial Publications and the Search for a Position 27 2. “Into the Paradise of Scholars”: April 1727 to 1730 38 Founding Saint Petersburg and the Imperial Academy of Sciences 40 A Fledgling Camp Divided 53 The Entrance of Euler 65 3. Departures, and Euler in Love: 1730 to 1734 82 Courtship and Marriage 87 Groundwork Research and Massive Computations 90 4. Reaching the “Inmost Heart of Mathematics”: 1734 to 1740 113 The Basel Problem and the Mechanica 118 The Königsberg Bridges and More Foundational Work in Mathematics 130 Scientia navalis, Polemics, and the Prix de Paris 140 Pedagogy and Music Theory 150 Daniel Bernoulli and Family 160 5. Life Becomes Rather Dangerous: 1740 to August 1741 165 Another Paris Prize, a Textbook, and Book Sales 165 Health, Interregnum Dangers, and Prussian Negotiations 169 v vi | Contents 6. A Call to Berlin: August 1741 to 1744 176 “Ex Oriente Lux”: Toward a Frederician Era for the Sciences 176 The Arrival of the Grand Algebraist 185 The New Royal Prussian Academy of Sciences 189 Europe’s Mathematician, Whom Others Wished to Emulate 200 Relations with the Petersburg Academy of Sciences 211 7. “The Happiest Man in the World”: 1744 to 1746 215 Renovation, Prizes, and Leadership 215 Investigating the Fabric of the Universe 224 Contacts with the Petersburg Academy of Sciences 234 Home, Chess, and the King 237 8. The Apogee Years, I: 1746 to 1748 239 The Start of the New Royal Academy 241 The Monadic Dispute, Court Relations, and Accolades 247 Exceeding the Pillars of Hercules in the Mathematical Sciences 255 Academic Clashes in Berlin, and Euler’s Correspondence with the Petersburg Academy 279 The Euler Family 282 9. The Apogee Years, II: 1748 to 1750 285 The Introductio and Another Paris Prize 287 Competitions and Disputes 292 Decrial, Tasks, and Printing Scientia navalis 298 A Sensational Retraction and Discord 303 State Projects and the “Vanity of Mathematics” 308 The König Visit and Daily Correspondence 313 Family Affairs 316 10. The Apogee Years, III: 1750 to 1753 318 Competitions in Saint Petersburg, Paris, and Berlin 320 Maupertuis’s Cosmologie and Selected Research 325 Academic Administration 329 Family Life and Philidor 333 Rivalries: Euler, d’Alembert, and Clairaut 335 The Maupertuis- König Affair: The Early Second Phase 337 Two Camps, Problems, and Inventions 344 Contents | vii Botany and Maps 348 The Maupertuis- König Affair: The Late Second and Early Third Phases 350 Planetary Perturbations and Mechanics 359 Music, Rameau, and Basel 360 Strife with Voltaire and the Academy Presidency 363 11. Increasing Precision and Generalization in the Mathematical Sciences: 1753 to 1756 368 The Dispute over the Principle of Least Action: The Third Phase 369 Administration and Research at the Berlin Academy 374 The Charlottenburg Estate 384 Wolff, Segner, and Mayer 385 A New Correspondent and Lessons for Students 391 Institutiones calculi differentialis and Fluid Mechanics 395 A New Telescope, the Longitude Prize, Haller, and Lagrange 399 Anleitung zur Nauturlehre and Electricity and Optimism Prizes 401 12. War and Estrangement, 1756 to July 1766 404 The Antebellum Period 404 Into the Great War and Beyond 409 Losses, Lessons, and Leadership 415 Rigid- Body Disks, Lambert, and Better Optical Instruments 427 The Presidency of the Berlin Academy 430 What Soon Happened, and Denouement 432 13. Return to Saint Petersburg: Academy Reform and Great Productivity, July 1766 to 1773 451 Restoring the Academy: First Efforts 452 The Grand Geometer: A More Splendid Oeuvre 456 A Further Research Corpus: Relentless Ingenuity 471 The Kulibin Bridge, the Great Fire, and One Fewer Distraction 485 Persistent Objectives: To Perfect, to Create, and to Order 488 14. Vigorous Autumnal Years: 1773 to 1782 495 The Euler Circle 496 Elements of Number Theory and Second Ship Theory 497 The Diderot Story and Katharina’s Death 499 viii | Contents The Imperial Academy: Projects and Library 502 The Russian Navy, Turgot’s Request, and a Successor 504 At the Academy: Technical Matters and a New Director 506 A Second Marriage and Rapprochement with Frederick II 509 End of Correspondence and Exit from the Academy 515 Mapmaking and Prime Numbers 517 A Notable Visit and Portrait 518 Magic Squares and Another Honor 520 15. Toward “a More Perfect State of Dreaming”: 1782 to October 1783 526 The Inauguration of Princess Dashkova 526 1783 Articles 529 Final Days 530 Major Eulogies and an Epilogue 532 Notes 537 General Bibliography of Works Consulted 571 Register of Principal Names 625 General Index 657 Preface or his profound and extensive contributions across pure and applied Fmathematics, Leonhard Euler (1707–83) ranks among the four great- est mathematicians of all time, the other three being Archimedes, Isaac Newton, and Carl Friedrich Gauss. Euler is a principal figure in applying calculus to create the modern mathematical sciences of celestial mechan- ics, analytical mechanics, elasticity, and optics. In the twentieth century, six concise biographies of him were produced, beginning in 1927 with Louis du Pasquier’s Léonard Euler et ses amis (Leonhard Euler and his friends) and two years later Otto Spiess’s Leonhard Euler. In 1961 Vadim V. Kotek published a short biography in Russian, while in 1982 Adolf P. Yush kevich brought out another in English and Rüdiger Thiele a narra- tive in German. In 1995 Emil A. Fellmann supplied a text in German of fewer than two hundred pages. In 2007, the tercentenary of Euler’s birth, Fellmann’s text was translated into English by Erika and Walter Gautschi, and Philippe Henry published Leonhard Euler: “incomparable géomètre.” Yet in no language has a treatment of his life and work appeared that is full in length and scope. This book attempts to offer the first detailed and comprehensive account in the context of Euler’s life, research, computations, and pro- fessional interactions that centers on his achievements in calculus and analytical mechanics. The growing body in print of primary sources by Euler, many long inaccessible, together with the secondary literature on him and his research, are making this possible. Central to the first effort is the near completion of the more than eighty large volumes of Euler’s Opera omnia (Collected works). Series 1, on mathematics, comprises twenty- nine volumes; series 2, on mechanics and astronomy, comprises thirty- one volumes; and series 3 comprises twelve volumes on physics and varia. Series 4A will have eight volumes with annotated versions of his massive correspondence, and a planned Internet database provision- ally called Euler Heritage will make accessible his remaining manuscript catalog, including his twelve notebooks totaling four thousand pages. It has taken more than a century to near the finish of the Opera omnia. The catalog of Euler’s complex writings by Gustaf Eneström appears in Die Schriften Eulers chronologische nach den Jahren geordnet, in denen sie verfasst ix x | Preface worden sind (The Writings of Euler chronologically arranged, according to the year they were published), which was published in the Jahresber­ icht der Deutschen Mathematiker­ Vereinigung (Annual Report of the Ger- man Mathematical Society) from 1910 to 1913. Eneström lists 866 of Euler’s publications, which include eighteen books. Today each has a number indicating its ordered place from the time of appearance annu- ally in the Eneström index.1 Thus, E88 stands for “Nova theoria lucis & colorum,” which was printed in 1746 coming after his first 87 publica- tions. The Euler Archive, directed by Dominic Klyve, Lee Stemkoski, and Erik Tou has made the originals of almost all of these writings available on the Internet.2 One result of the scope and depth of Euler’s research is that most scholarship on him is fragmentary, centering on one or another particular subject. The thorough investigation of Euler’s correspondence and the subjects and reliability of his notebooks is at an early stage. Euler publications and letters span five languages. Most are in Latin and French, some are in German and Russian, and Euler himself trans- lated one book from English into German. Recent Euler scholarship, especially that published by the Mathematical Association of America, includes many articles and books in English. Research on Euler requires expertise ideally in at least the first three of these five languages and col- laboration among scholars who together address all of them. The bibliog- raphy in the present work indicates that competence in Italian, Spanish, Chinese, and Japanese also helps.
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