Titles in This Series Volume 8 Kare n Hunger Parshall and David £. Rowe The emergenc e o f th e America n mathematica l researc h community , 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moore 1994 7 Hen k J. M. Bos Lectures in the history of mathematic s 1993 6 Smilk a Zdravkovska and Peter L. Duren, Editors Golden years of Moscow mathematic s 1993 5 Georg e W. Mackey The scop e an d histor y o f commutativ e an d noncommutativ e harmoni c analysis 1992 4 Charle s W. McArthur Operations analysis in the U.S. Army Eighth Air Force in World War II 1990 3 Pete r L. Duren, editor, et al. A century of mathematics in America, part III 1989 2 Pete r L. Duren, editor, et al. A century of mathematics in America, part II 1989 1 Pete r L. Duren, editor, et al. A century of mathematics in America, part I 1988 This page intentionally left blank https://doi.org/10.1090/hmath/008 History of Mathematics Volume 8 The Emergence o f the American Mathematical Research Community, 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moor e Karen Hunger Parshall David E. Rowe American Mathematical Societ y London Mathematical Societ y 1991 Mathematics Subject Classification. Primary 01A55 , 01A72, 01A73; Secondary 01A60 , 01A74, 01A80. Photographs o n th e cove r ar e (clockwis e fro m right ) th e Gottinge n Mathematisch e Ges - selschafft, Feli x Klein, J. J. Sylvester, and E. H. Moore. The background photograph is the Court of Honor at the Chicago World's Fair in 1893 . A list of photograph an d figure credits is included at the beginning o f this volume. Library of Congress Cataloging-in-Publication Dat a Parshall, Karen Hunger, 1955 — The emergence of the American mathematical research community, 1876-1900 : J. J. Sylvester, Felix Klein, and E . H. Moore/Karen Hunge r Parshall, David E . Rowe. p. cm . Includes bibliographical reference s an d index. ISBN 0-8218-9004-2 (acid-free ) 1. Mathematics—Research—United States—History—19t h century . 2 . Mathematics — —Study an d teachin g (Higher)—Unite d States—History—19t h century . I . Rowe , Davi d E. , 1950-. II . Title. QA13.P37 199 4 94-221 8 510/.720973/09034—dc20 CI P Copying an d reprinting. Individua l reader s o f thi s publication , an d nonprofi t librarie s actin g fo r them, are permitted to make fair us e of the material, such as to copy a chapter fo r us e in teaching or research. Permissio n is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment o f the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts ) i s permitte d onl y unde r licens e fro m th e America n Mathematica l Society . Requests for suc h permission shoul d be addressed to the Manager of Editorial Services , American Mathematical Society , P.O . Bo x 6248 , Providence, Rhod e Islan d 02940-6248 . Request s ca n als o be made by e-mail to reprint-permissionQmath.ams.org . © Copyrigh t 199 4 by the American Mathematica l Society . Al l rights reserved. Reprinted wit h corrections , 1997 . Printed i n the United State s of America. The American Mathematical Societ y retains all rights except those granted to the United State s Government . © Th e paper used in this book is acid-free an d fall s within the guidelines established to ensure permanence and durability . The London Mathematical Societ y is incorporated under Roya l Charter and i s registered with the Charity Commissioners . This publication wa s typeset by the authors with technica l and editorial assistance from th e American Mathematical Society . 10 9 8 7 6 5 4 3 2 0 2 01 00 99 98 97 Contents Preface i x Acknowledgements xi x Photograph and Figure Credits xx i Chapter 1. An Overview of American Mathematics: 1776-1876 1 British and French Influences 2 Mathematics an d the American College: The Cases of Harvar d and Yale 1 5 German Influences: J. Willard Gibbs at Home an d Abroad 2 3 Mathematics in the Federal Government 3 3 Mathematics an d Scientific Professionalizatio n 4 0 Table 1 .1 Cours e o f Stud y i n Mathematic s an d Astronom y unde r Benjamin Peirc e at the Lawrence Scientifi c Schoo l (1848 ) 5 0 Table 1. 2 America n Mathematic s Journals 1800–190 0 5 1 Chapter 2. A New Departmental Prototype : J. J. Sylveste r and the Johns Hopkins Universty 5 3 A New Experiment in Baltimore: The Johns Hopkins University 5 3 The Johns Hopkins's First Professor of Mathematic s 5 9 The Department of Mathematics a t the Johns Hopkins University 7 5 The American Journal of Mathematics 8 8 Table 2.1 Th e Mathematica l Offering s a t th e John s Hopkin s University 1876-188 4 9 5 Table 2.2 Th e Mathematic s Fellow s a t th e John s Hopkin s University 1876-188 4 9 7 Chapter 3. Mathematics at Sylvester's Hopkins 9 9 Sylvester and Invariant Theory 10 0 Geometrical Researc h at Johns Hopkins University 10 8 From Invariant Theory to the Theory of Partitions 11 6 vi CONTENT S Research i n Mathematical Logi c at the Johns Hopkins University 13 0 Sylvester and the Theory of Matrix Algebra 13 5 Denouement 13 8 Chapter 4. German Mathematics an d the Early Mathematical Caree r of Felix Klein 14 7 The Göttingen Mathematical Traditio n 15 0 Klein's Educational Journey 15 4 Anschauung, Riemann Surfaces , and Geometric Galois Theory in Klein's Early Work 16 8 Professor o f Geometry i n Leipzi g 17 5 The Ascension o f a New Star 18 2 Chapter 5. America's Wanderlust Generation 18 9 Klein's Leipzig Students 19 1 Two German Emigre s 19 7 The Kleinian Connection i n American Mathematic s 20 2 Stepping to the Podium: Two Seminar Lectures by Henry White 22 3 Studying Outside Göttingen 22 9 Studying with Sophus Lie in Leipzig 23 4 The Women Make Their Mark 23 9 The Kleinian Legac y 25 3 Table 5. 1 Lecture s Delivere d i n Klein' s Seminar s 1881-189 6 25 5 Table 5. 2 Doctora l Dissertation s Writte n b y Americans unde r Klein's Supervisio n 25 8 Table 5. 3 Student s o f Klei n a t the American Mathematica l Societ y 25 9 Chapter 6. Changes on the Horizon 26 1 Changes on the American Scen e after 187 8 26 1 Mathematics at Cornell and Clar k Universities 26 9 The Founding of the University o f Chicago 27 5 Building a Department o f Mathematics at Chicag o 27 9 Chapter 7. The World's Columbian Exposition of 1893 and the Chicago Mathematical Congress 29 5 The Chicago World's Columbian Expositio n 29 6 Felix Klein at the Chicago World's Fair 30 4 The Chicago Mathematical Congres s 30 9 The Congress Adjourns 32 6 Table 7. 1 Progra m o f the Chicag o Mathematica l Congres s 32 8 Chapter 8. Surveying Mathematical Landscapes : The Evanston Colloquium Lectures 33 1 The Evanston Colloquiu m Lecture s 33 3 Touring the American Mathematica l Scen e 35 4 The Aftermath 35 9 CONTENTS vi i Chapter 9. Meeting the Challenge: The University of Chicago and the American Mathematical Researc h Community 36 3 Running the Chicago Department o f Mathematics 36 3 The Mathematical Interest s of Moore and His Students 37 2 The Mathematical Interests of Bolza, Maschke, and Their Students 39 3 Mathematical Activism: The Role of the Chicagoans in the American Mathematical Societ y 40 1 Table 9. 1 Mathematica l Clu b Lectures: Winte r an d Sprin g 189 3 42 0 Table 9. 2 E . H. Moore' s Earl y Chicag o Student s 42 3 Table 9.3 Dickson' s Earl y Chicag o Student s 42 4 Table 9. 4 Bolza' s Chicag o Students 42 5 Table 9.5 Maschke' s Chicag o Student s 42 6 Chapter 10. Epilogue: Beyond the Threshold: The American Mathematical Researc h Community, 1900-1933 42 7 Mathematics at the Johns Hopkins and at Yale 43 2 The Emergence of "The Bi g Three" 43 5 Hilbert's Göttingen and the Impact o f World War I 43 9 The Interwar Years: Sustaining the Momentum 44 5 The Flight fro m Europ e and the Dawn of a New Era 45 1 Bibliography 45 5 Subject Index 487 This page intentionally left blank Preface James Josep h Sylvester , a Britis h algebraist , worke d a s a n actuar y an d then taught a t the Royal Military Academy in Woolwic h until his forced re - tirement i n 1870 . I n neithe r o f thes e post s di d h e hav e a n opportunit y t o train his countrymen, muc h less aspiring Americans, in research-level math - ematics. Preparatio n a t that leve l simply did not form par t o f the universit y mission i n nineteenth-centur y Britain . Th e geomete r Christia n Feli x Klei n taught an d conducte d hi s mathematica l researc h a t various educationa l in - stitutions in his native Germany.