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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, , 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 in World War II 1990 3 Pete r L. Duren, editor, et al. A century of 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 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 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——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 : The 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 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 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 16 8 Professor o f 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 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 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 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 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. Thes e schools and their mathematical tra - ditions wer e obviousl y remot e geographicall y fro m lat e nineteenth-centur y America. The y wer e als o intellectuall y far-remove d fro m a countr y wher e institutions o f higher education functione d primaril y at a collegiate—as op- posed to a university—level and where basic mathematical research received little encouragement. Th e young and unproven America n Eliaki m Hasting s Moore serve d as the first Professor o f Mathematics a t the newl y establishe d University o f Chicag o beginnin g i n 1892 . A t thi s , hi s ow n develop - ment int o a majo r researche r wa s by n o mean s assured , an d h e ha d neve r taught student s at the graduate level. Furthermore , hi s youth, inexperience , and Midwestern vantage al l seemed to militate against his becoming a major voic e in a community o f which, insofar a s it was dis- cernible at all, had begun to coalesce on the East Coast around the fledgling Mathematical Society . On the , thes e three men—separated b y generation, mathematica l training, and cultural background—would appea r to be unlikely protagonist s in the stor y o f the emergence o f a mathematical researc h communit y i n the United States between 187 6 and 1900 . This period would also seem too early for th e detectio n o f significan t contribution s t o higher mathematic s fro m a country know n mor e fo r it s "Yanke e ingenuity " than fo r th e cultivatio n o f abstract ideas . Nevertheless , withi n thi s relativel y brie f spa n o f time , th e United State s succeede d i n puttin g itsel f o n th e mathematica l map , an d i t did s o spurred primarily by the efforts o f Sylvester , Klein, and Moore. This boo k look s a t th e confluenc e o f historica l trend s an d events whic h enabled this disparate trio to emerge as the dominant figures in the creatio n

IX X PREFACE of a community of mathematical researchers on American shores in the years from 187 6 t o 1900 . I t als o delve s int o th e mathematica l achievement s o f these thre e principal s i n orde r t o analyz e ho w thei r researc h inspire d th e subsequent wor k of many of their students. B y casting this research activit y in a broader scientifi c an d educationa l context , i t bot h addresse s issue s o f potential interes t t o a varied audience—an d mathematicians , historian s o f science, historians , amon g others—an d redresse s a seriou s omissio n i n th e literature on the history o f American science . In 198 6 the book Historical Writing on American Science: Perspectives and Prospects appeared as a result of an initiative taken by the Society. Representin g th e collectiv e effor t o f ove r a doze n specialists , thi s work aime d t o surve y th e various area s o f th e history o f America n scienc e as wel l a s to sugges t fruitfu l avenue s fo r furthe r research. 1 Indeed , i n th e volume's preface, editors and Margaret Rossiter ex- plained tha t b y the mid-1980s, "[s]evera l Americanists wer e ready to asses s the current state of various specialties and to indicate what 'needs and oppor- tunities' remained after more than a decade of significant activity. " I n their collective assessment , institutiona l histor y alon g wit h scienc e i n medicine , , and the federal governmen t constitute d the four so-calle d "classica l themes"; the "newer areas" of native American scientifi c knowledge in addi- tion to science and technology, war, and public policy were highlighted; an d the history of the scientific specialties of geology, , , biol- ogy, , and the social sciences received individua l attention. Notabl y absent fro m th e specialties treated? Mathematics . To be sure, the in general and the history of Ameri- can mathematics in particular have been relatively neglected in the last several decades by American historian s o f science . Th e "glor y days" of the 1930 s and 1940 s have long since passed when George Sarton, the father o f the his- tory of scienc e in America, declare d the primacy o f mathematics within th e

Sally Gregory Kohlstedt and Margaret W. Rossiter, Historical Writing on American Science: Perspectives and Prospects (Baltimore : Th e Johns Hopkins University Press , 1986) . Thi s work was originally published as Osiris, 2d ser., 1 (1985). 2Ibid., p. 7 . 3Ibid., pp. 9-15 . Uta Merzbach surveyed work done on the history of mathematics in America, including re- search on the history of American mathematics per se, in her article "The Study of the History of Mathematics in America: A Centennial Sketch," in A Century of Mathematics in America—Part III, ed. Pete r Duren et al (Providence : America n Mathematical Society , 1989) , pp. 639-666 . Although she dealt with the historical contributions from 196 9 to the present cursorily, Merzbach discussed in some detail the work done fro m th e publication of Floria n Cajori's The Teaching and History of Mathematics in the United States (Washington , D . C : Governmen t Printin g Office, 1890) , through the 1930s , when David Eugen e Smit h and Jekuthiel Ginsbur g produced theirs History of Mathematics in America before 190 0 (Chicago: The of America , 1934 ; reprint ed. , Ne w York : Arn o Pres s Inc., 1980) , an d up to th e foundin g b y Clifford Tniesdel l (i n 1960 ) o f th e Archive for History of Exact Sciences an d Kenneth O . May (in 1974 ) of Historia Mathematica, two journals which publish high-level research articles in the history of mathematics. PREFACE XI history o f scienc e from hi s loft y positivis t heights . "[T]h e history o f math - ematics should reall y be the kernel o f the history o f culture," he asserted i n 1937. "Tak e th e mathematica l development s ou t o f th e histor y o f science , and you suppress the skeleton which supported and kept together all the rest. Mathematics give s to scienc e it s innermos t unit y an d cohesion , whic h ca n never be entirely replaced with props and buttresses or with roundabout con- nections, no matter how many of these may be introduced."5 Yet despite such pronouncements, eve n durin g Sarton' s era , the histor y o f American mathe - matics and , i n fact , th e histor y o f America n scienc e faile d t o satisf y th e prescripts of a generation o f internalist historians of science which primarily adhered to a "great name" approach to the discipline. As historians o f scienc e know well, the discipline has increasingly broad - ened its purview since the 1950 s to embrace issues like the impact o f philo- sophical an d religiou s idea s o n science , th e rol e o f external , socia l factor s in the formation o f scientific thought, and the interrelations between science and societ y a t large. 6 Thi s change d historiographica l climat e ha s encour- aged man y ne w interests , bu t o f greates t importanc e t o th e presen t stud y has been th e increasin g concentratio n o n America n science . I n particular , those science s perceive d a s impingin g mos t upo n society—medicine , biol - ogy, and physics (particularly i n the twentieth centur y with relativity, quan - tum theory , an d nuclea r technologies)—hav e len t themselve s naturall y t o this sor t o f analysis . Mathematics , however , wit h it s abstruse languag e an d arcane symbolism , wit h it s seemingl y insulate d practitioners , an d wit h it s unapparent impac t o n publi c polic y o r dail y life , seem s uncongenial—an d so uninteresting—within suc h a n historiographica l framework. 7 Whil e thi s explanation ma y she d som e ligh t o n th e relativ e indifferenc e accorde d th e history o f America n mathematic s ove r the last twent y years, a period char - acterized b y Kohlsted t an d Rossite r a s on e o f "significan t activity " i n th e

George Sarton, The Study of the History of Mathematics (Cambridge, MA: Harvard Univer- sity Press , 1937 ; reprint ed., New York : Dove r Publications, Inc. , 1957) , p. 4 . Th e reprinte d edition als o contain s Sarton' s The Study of the History of Science (Cambridge, MA : Press, 1937) . These shifts i n emphasis came i n response initially to the diverse points of view reflecte d in work s suc h a s Alexandr e Koyre , Etudes galiliennes, 3 parts , 1935-1939 ; reprinte d i n on e volume ( : Hermann , 1939) ; an d Koyr e From the Closed World to the Infinite Universe (Baltimore: Th e Johns Hopkins Universit y Press , 1957) ; and , The Structure of Scientific Revolutions (Chicago: Th e Universit y o f Chicag o Press , 1962) . Fo r a concis e an d cogent discussio n o f thes e change s within th e histor y o f science , se e Alle n G . Debus , Science and History: A Chemist's Appraisal (Coimbra : Servic e d e Documentacji o e Publicagoe s d a Universidade d e Coimbra, 1984) , pp. 17-33 . 7 Here, w e refe r t o th e naiv e perceptio n o f pur e mathematics . I t goes without sayin g that applied probability and statistics have affected publi c policy in key and obvious ways. Perhap s due to their relatively short histories in the United States, not even these areas of the history of American mathematics have received much attention from the general population of historians of science. See , however, Stephen Stigler , "Mathematical Statistic s in the Earl y States," Annals of Statistics 6 (1978):239-265; and Stephen Stigler, ed., American Contributions to Mathematical Statistics in the Nineteenth Century, 2 vols. (Ne w York: Ara o Press, 1980). Xll PREFACE

history of American science, it fails to illuminate some of the deeper aspects of th e relatio n o f th e histor y o f mathematic s t o th e histor y o f scienc e a s a whole. In his 199 0 article, entitled "Does History of Scienc e Treat of the History of Science ? Th e Cas e o f Mathematics, " Ivo r Grattan-Guinnes s state d th e case bluntly: th e histor y o f mathematic s ha s bee n largel y ignored , makin g it on e o f th e leas t develope d subdiscipline s withi n th e histor y o f science. 8 In hi s view , historian s o f scienc e hav e neglecte d t o examin e th e historica l development bot h o f mathematic s per se and o f mathematic s a s related t o other sciences due to a fundamental fea r o f the subject. Moreover , the other constituency whic h migh t hav e advance d th e subdiscipline , th e mathemati - cians, hav e generall y faile d t o approac h th e subjec t wit h historiographica l sophistication o r sensitivity . A s Grattan-Guinnes s claimed , th e neglec t o f the historians o f science coupled with the mostly ahistorical approach o f the mathematicians have rendered the history of mathematics "a classical exam- ple of a ghetto subject: to o mathematical for historians and too historical fo r mathematicians. "9 Grattan-Guinness's critique , however, broaches only some of the complex issues which hav e le d to the marginalizatio n o f th e histor y o f mathematic s within th e histor y o f scienc e an d certainl y withi n th e wide r historica l dis - cipline. Par t o f th e blame fo r thi s lamentabl e situatio n als o rest s squarel y on the historians of mathematics themselves, many of whom have tended to pursue their work independently o f the trends that hav e shaped and altere d the historiograph y o f th e histor y o f scienc e ove r the las t severa l decades. 10 On the on e hand, this has made their mostl y internalisti c research see m in - creasingly outmoded and uninteresting to the wider community of historians of science ; o n th e other , i t ha s deprive d i t o f som e o f th e insight s issuin g

Ivor Grattan-Guinness, "Does History of Science Treat of the History of Science? Th e Case of Mathematics," History of Science 28 (1990):149-173. 9Ibid., p. 158 . The recent interest in empiricist approaches among of mathematics has opened up ne w possibilities fo r placin g historical studie s i n a broader context. See , fo r example , th e essays in The of Mathematics: Philosophical, Epistemological, and Historical Explorations, ed. Javie r Echeverria et al ( : Walte r de Gruyter, 1992) . Fo r a related study, see Revolu- tions in Mathematics, ed. Donal d Gillies ( : Clarendo n Press , 1992) . Thi s collection of new and reprinted essays deals with the issue of the legitimacy of the Kuhnian model of revolu- tions in the mathematical setting. Thi s theme received considerable attention from historians of science at least two decades ago, yet historians of mathematics have largely ignored its implica- tions for their subdiscipline. A s Herbert Mehrtens described the situation, "[t]he complaint .. . [of] historians of mathematics , that their field is too isolated from an d too little recognized by colleagues in the history of natural sciences, marks a problem, not of the inaccessibility of math- ematics, but rather of the inability of its historians to relate to issues of interest in general history of science. " Ibid., p. 42 . A n important counterexampl e to this trend is Mehrtens's ow n recent study, Moderne-Sprache-Mathematik (Frankfurt am Main: Suhrkam p Verlag, 1990). Thi s work represents a bold attempt to understand the debates over the foundations of mathematics in the early twentieth centur y i n term s of a struggl e ove r the rule s of mathematica l discours e within the (mostly German) mathematical community . PREFACE Xlll from th e newe r historiography. 11 Thi s i s certainl y no t t o sa y that histori - ans o f mathematic s shoul d abando n th e technica l analyse s s o crucia l fo r a deeper understandin g o f the history o f mathematica l ideas . I t doe s sugges t that mor e tha n th e idea s involve d i n thi s pivota l scientifi c disciplin e meri t historical illumination and that approaches other than the standard internal - istic technique s wil l be require d t o confron t thes e divers e historica l issues . The present book aims to move beyond—but not to ignore—technical aspects of mathematics through its exploration of a dynamic process that stimulate d the growt h o f th e disciplin e i n Americ a and , alon g wit h it , th e emergenc e of a community o f mathematica l researcher s durin g the las t quarte r o f th e 12 nineteenth century . The notion of periodization inherent in the preceding statement i s central both to the argument an d to the overall structure o f this study. B y targeting the period fro m 187 6 to 1900 , i t explicitl y delimit s th e boundaries o f tw o other period s i n th e histor y o f America n mathematics. 13 Thus , th e book' s discussion of this key quarter-century i s motivated by an examination o f the prior period , an d it s argument i s solidifie d b y mappin g the contour s o f th e one which followed . In th e first perio d i n th e histor y o f America n mathematics , th e centur y from 177 6 to 1876 , the field evolved no t a s a separate disciplin e but rathe r within the context of the general structure-building of American—as opposed to colonial—science . Th e college s forme d a primary locu s o f scientifi c ac - tivity, but, b y and large , they did littl e to encourage the pursuit o f researc h for th e advancemen t o f science . A t the sam e time, the concep t o f researc h in American science—a s i n othe r academi c disciplines—emerge d a s scien - tists looked toward Europ e a s their model and measure d themselve s agains t the yardstick o f Europea n scientifi c achievement . B y 1876 , these and othe r

The documentary foundation for much of the history of American mathematics has not yet even been laid. A s a result, the history of American mathematics, unlike other areas of American history or even of the history of American science, has not yet reached a stage of historiographical development whic h woul d mak e appropriat e o r pruden t th e examinatio n o f metatheme s lik e "moral judgment." Se e Pau l Forman' s cal l fo r th e stud y o f thi s issu e i n "Independence , No t Transcendence, for the Historian of Science," his 8 2 (1991):71-86. 1 Becaus e of the deficiency of the extant literature, we have also attempted to give the reader as complete a guide as possible to the pertinent source s both in mathematics and in the history of mathematic s an d America n science . (Du e t o th e scop e o f ou r study , however , w e d o no t feel i t is appropriate to go beyond this into, for example, the literature in American history in general.) W e accomplish thi s i n th e extensiv e footnote s t o th e various chapter s o f ou r book, although some of these are also explanatory in . actually suggeste d a periodization of th e history of America n mathematic s as earl y a s 190 5 i n hi s article, "Mathematica l Progres s in America, " Bulletin of the American Mathematical Society 1 1 (1905):238-246; reprinted in A Century of Mathematics in America— Part I, ed., Peter Duren et al. (Providence : America n Mathematica l Society , 1988) , pp. 3-11 . While he, too, defined a first period through 1876 , Fiske sa w the second period as "extending] from the establishment of the Johns Hopkins University up to 1891 , when the New York Math- ematical Society took on a national character and began the publication of its Bulletin" and the third as stretching "from 189 1 to the present [tha t is, 1905]. " (Se e p. 23 8 of his article.) XIV PREFACE

factors, suc h as the support o f certain types of scientifi c researc h within th e federal government , had resulte d i n the formation o f an American scientific community which, loosely characterized, earne d its living primarily throug h undergraduate teachin g bu t whic h define d itsel f b y th e extracurricula r re - search it presented before genera l scientific societie s and published in books or general scientifi c journals. As the essay s in Historical Writing on American Science show, a substan - tial amoun t o f wor k ha s been don e ove r th e las t tw o decade s o n precisel y these aspect s o f nineteenth-centur y America n science . Unfortunately , littl e of this research touche s eve n lightly on mathematics, i n spit e of the crucia l and recognized rol e that American mathematics ha s played in, for instance , the emergence o f the American researc h communities i n physics and chem - istry.14 Thi s neglect is mirrored in the work done during that sam e time pe- riod on the history of American mathematics per se, virtually none of which was informe d b y th e contemporaneou s studie s issuin g fro m th e histor y o f science community. Chapte r 1 addresses this fals e dichotom y by anchorin g the history of American mathematics firmly in the history of American scien- tific and educational institutions.15 B y viewing mathematics as a special case within this broader context, it provides an historical baseline for studying the changes which define the next period in the history of American mathematics, the two-and-a-half decade s from 187 6 to 1900 . As noted above, three men and the institutions within which they worked largely shape d thi s secon d period: th e Englishman , Jame s Joseph Sylvester , at the Johns Hopkins University; 16 th e German, Feli x Klein, first at Leipzi g but more crucially at Gottingen; and the American, Eliakim Hastings Moore, at th e Universit y o f Chicago . Thei r respectiv e period s o f involvemen t i n

14In "Mathematic s an d the Physical Science s in America, 1880-1930, " Isis 11 (1986):611- 629, Joh n Servo s argue d tha t th e leve l an d characte r of America n mathematica l trainin g had a large—an d primaril y negative—impac t o n th e characte r o f America n researc h i n th e othe r sciences. 15 One of the issues we explore is professionalization. I t goes without saying that there is an ex- tensive literature on professionalization in the other scientific, academic, and even non-academic areas within American culture. Fo r an idea of its extent, see, for example, Daniel J. Kevles, The Physicists: The History of a Scientific Community in Modern America (Cambridge, MA: Harvard University Press , 1971) ; Peter Novick, That Noble Dream: The "Objectivity Question" and the American Historical Profession (Ne w York: Cambridg e University Press , 1988) ; Dorothy Ross, The Origins of American Social Science (New York : Cambridg e Universit y Press , 1991) ; and Olivier Zunz , Making America Corporate 1870-1920 (Chicago : Universit y o f Chicag o Press , 1990). I n keeping with one of the goals of ou r book, namely , the establishment o f a firm doc- umentary foundation fo r one process and one er a in the history of American mathematics, we confine ourselve s primaril y t o the literatur e of mathematic s an d the histor y of America n sci - ence. W e would hope that, informed by our work, subsequent studies might draw well-founded generalizations concerning the developments in American mathematics and those in other areas of American culture. 16 Throughout this book, w e adopt the convention used in the nineteenth century, as well as today, of distinguishin g th e Johns Hopkins University (o r simply the Johns Hopkins) fro m its benefactor, Johns Hopkins. W e will, however, use the short form "Hopkins" from time to time in reference to the university, when no confusion wil l result. PREFACE xv the American scene clearly define three distinct phases centered around three programs of mathematical research. A n analysis of these programs and of the nature of the influence o f their progenitors reflects the progressive deepening of research standards and output in the United States throughout the twenty- five-year period a s wel l a s the generationa l difference s separatin g Sylvester , Klein, an d Moore . I t furthe r accentuates , b y focusin g o n th e student s an d research issuing from these schools, the process of maturation of an American mathematical research community which had full y emerge d by 1900 . Imported fro m Britai n i n 1876 , Sylvester assumed th e first professorshi p in mathematic s i n 187 6 at Hopkins , a n institution pivota l i n the history o f higher educatio n i n America and , b y extension , i n the history o f America n mathematics. Wit h Sylvester' s return t o Britain i n 1883 , however, Hopkin s lost its momentum as a center of advanced mathematical training, and Amer- icans desirous of suc h training turned elsewher e fo r thei r inspiration. The y chose as their mentor another foreigner, but this time a foreigner abroad, Fe- lix Klein. Fo r roughly a decade following Sylvester's departure, Klein actively served as the standard-bearer fo r a dynamic o f American mathemati - cians, many of whom studied under him in Germany. Hi s influence reache d its clima x i n 189 3 during hi s seven-wee k visi t t o th e Unite d States , whic h began with a lavish reception at the Mathematical Congres s held in conjunc - tion wit h Chicago' s World' s Columbia n Expositio n . Somewha t ironicall y perhaps, Klein' s appearanc e a t th e latte r even t foreshadowe d hi s desir e t o step back from hi s involvement i n American developments and heralded the arrival o f a new figure, E. H. Moore. Togethe r wit h hi s Chicag o colleague s Oskar Bolz a an d Heinric h Maschke , Moor e establishe d a n environmen t a t Chicago conducive to the training of research-leve l mathematicians back o n American soil . Moore , i n particular , als o consciousl y directe d hi s effort s toward strengthenin g severa l institutional an d organizationa l structure s tha t ultimately played crucial roles in cementing a national community . Chapters 2 , 4, and 9 center o n Sylvester , Klein , an d Moore—o n th e for - mative influence s i n thei r lives , o n thei r approache s t o mathematics , an d on their actual research—i n orde r to motivate and trace their influence s o n the first generation o f America n mathematica l researcher s an d t o char t th e growing maturity o f the community the y helped define . Thes e chapters als o place thes e three me n withi n th e institutiona l setting s that activel y encour - aged the m t o trai n student s a t a n advance d leve l an d t o pursu e thei r ow n personal researc h objectives . I n a ke y shif t whic h serve s t o delineat e par - tially the first and second periods in the history of American mathematics, a o f influentia l academi c institutions i n the United States , led by the Johns Hopkins , adopte d an d adapte d th e researc h ethi c which ha d becom e firmly entrenched in German higher education earlie r in the nineteenth cen - tury. Thi s translated into an increasing emphasis on research as an officiall y sanctioned an d supporte d endeavo r i n th e emergen t universit y settin g and , by intimate association, in the emergent mathematical community . XVI PREFACE

In Chapter s 3 , 5 , and 9 , the emphasi s shift s t o the student s o f Sylvester , Klein, and Moor e and to the actual training they received. A n examinatio n first o f their teachers' commitment t o research an d o f their varied, eve n id - iosyncratic, style s o f instillin g thi s commitmen t set s th e stag e fo r a close r 17 look a t th e researc h produce d b y these youn g men an d women . A s ofte n as feasible , thi s wor k i s place d withi n th e large r contex t o f th e histor y o f nineteenth- an d earl y twentieth-centur y mathematic s i n orde r t o asses s th e rapid changes made in the United State s between 187 6 and 1900 . Although the training of mathematicians at the research-level represents a critical ingredient i n the historical proces s documented here , the actual for - mation o f a community—an interactin g group o f people linked by common interests—required mor e than just advanced training in mathematics. Chap - ters 6 through 9 describe ho w members o f this firs t generatio n o f research - oriented s reforme d th e academic environments a t a number of American universities . Thes e chapters als o investigate the organizationa l activities which engendered publication outlet s for research-leve l mathemat - ics, a specialized professiona l society , the firs t majo r mathematica l meetin g which als o drew influential foreig n participation , an d the firs t research-leve l colloquium lectures open to and designed for a wide variety of mathematical listeners. Th e historical conjunction durin g the last quarter of the nineteenth century o f thes e various innovation s an d thei r innovators , o f change d atti - tudes a s to the value and desirabilit y o f researc h a t both a n individua l an d institutional level , an d o f th e existenc e o f a critica l mas s numberin g som e 1000 practitioner s ha d produced, b y 1900 , a firmly grounde d mathematica l research community i n the United States. 1 As this las t statemen t suggests , thi s communit y clearl y extende d beyon d the defined b y Sylvester, Klein, and Moore . Thus , while the presen t study centers on the influenc e o f these three "grea t men," it is by no mean s limited t o thei r contributions . O n th e contrary , i t use s their career s a s the points o f departur e fo r a n examinatio n o f a broad spectrum—althoug h b y no means the complete roster—of participant s in the fiel d a t the turn o f the twentieth century . Chapter s 3 , 5 , 9 , an d 1 0 identify thei r student s and , t o some extent, their students' students and colleagues. Wh o studied and taught mathematics? Wher e did they come from an d where did they go? What di d they do mathematically? Thes e are among the questions examined. B y pene- trating beneath the top layer, the investigation underscores the existence of an One subtheme which recurs throughout ou r book concerns women an d the obstacles they faced in breaking into mathematics at the research level. 18 Delia Dumbaug h Fenste r an d Kare n Hunge r Parshal l hav e recentl y complete d a quanti- tative stud y of th e America n mathematica l researc h communit y durin g the perio d fro m 189 1 to 1906 , o r the first fifteen years of publicatio n o f th e Bulletin of the American Mathematical Society. They uncovered some 100 0 distinc t members of this community at all levels of partic- ipation. Se e Delia Dumbaug h Fenste r and Karen Hunger Parshall, " A Profile o f the American Mathematical Researc h Community: 1891-1906, " in The History of Modern Mathematics, vol. 3, ed. Eberhar d Knobloch and David E . Rowe ( : Academi c Press, 1994) , to appear. PREFACE xvii extended population of mathematicians—some talented and some not, some well know n an d som e obscure—base d a t college s an d universitie s through - out the United State s who actively shared an interest in mathematics a t the research level. Clearl y much more could—and should—be done to flesh out this community fully, to examine it completely from the top down and from the bottom up. Thi s book, however, aims to explore and document the emer- gence of th e community. I t leaves to futur e researcher s the stud y of i t a s a community per se} 9 Likewise, the tenth and final chapter mainly suggest s lines of inquir y fo r further historical research. I t outlines the fuller conception of the periodiza- tion of th e history of America n mathematics an d provides some indicatio n of the parameters which delineate a third period of consolidation and growth from the second emergent period. Wit h this sketch of our book's underlying structure and overall argument, we now turn to examine the American math- ematical landscap e durin g the first period i n its historical development , th e century from 177 6 to 1876 .

1 Fo r a n indication o f wha t suc h researc h migh t entail , se e th e comparativ e stud y o f th e structure an d functio n o f physic s communitie s durin g thi s perio d b y Pau l Forman , Joh n L . Heilbron, and Spencer Weart, "Physics circa 1900 : Personnel and Productivity of the Academic Establishments," Historical Studies of the Physical Sciences 5 (1975):1-185. This page intentionally left blank Acknowledgments

The centennia l o f th e foundin g o f th e America n Mathematica l Societ y in 198 8 gav e us the initia l ide a o f writin g a history o f th e dynami c events that forge d a vibrant communit y o f mathematical researcher s in the United States durin g th e las t quarte r o f th e nineteent h century . A s we have sinc e come to appreciate, a joint effor t o f this kind and scope, which strives to give a coheren t presentatio n o f a comple x phenomeno n tha t too k plac e o n tw o continents, poses considerable intellectual difficulties a s well as organizational problems for the collaborators. Ha d w e anticipated al l of these complexitie s and difficulties a t the outset, this book might have appeared sooner. Instead , it evolved through various forms over a five-year period during which we had the opportunity to reorient our own perspectives as we familiarized ourselve s with ne w source s pertinen t t o importan t idea s an d individual s connecte d with the American mathematica l scene . I n offerin g th e present stud y a s the culmination of our collaborative efforts, w e take satisfaction in knowing that, after much brainstorming and countless revisions, this book could never have been written by either o f us alone. It als o could neve r hav e been complete d withou t th e assistanc e and sup - port o f man y others. Indeed , s o many people have taken a n interest i n thi s project that it would be nearly impossible to mention them all here. Firs t and foremost, however , we would like to thank the entire Publication Committe e of the joint AMS/LMS series on the history of mathematics, but particularl y Peter Duren, Dick Askey, Ed Edwards, Jeremy Gray, and Charlie Curtis, fo r not onl y their encouragemen t bu t als o their carefull y considere d comment s and critiques of our manuscript. I f they sometimes differed wit h us regarding how the history o f mathematics shoul d be written and what issues it shoul d involve, their flexibility has allowe d u s to produc e a book which , w e hope, will be of interest to mathematicians and historians alike. In addition to the members of the Publication Committee , severa l o f ou r friends and colleagues read and commented on all or part of our manuscript. Bob Cross , Jo e Dauben , Te d Feldman , Deli a Dumbaug h Fenster , Susan n Hensel, "Mike " Hunger , Jo e Kett , Arnol d Koslow , Joh n McCleary , Elliot t Mendelsohn, Bria n Parshall , an d Pau l Wolfso n helpe d u s t o appreciat e

XIX XX ACKNOWLEDGMENTS better the points of view of the mathematicians, historians o f science, histo- rians, an d more general readers who might chance to open our book. Give n the demand s o f thei r ow n work, w e sincerel y appreciat e th e time tha t the y devoted to their careful reading s of our text. We would als o lik e to acknowledg e th e hospitalit y o f th e man y librarie s we worked in during the course of our research on this project. I n particular, we exten d ou r thank s t o th e John s Hopkin s University ; th e Universit y o f Chicago; the Library of Congress; the Smithsonian Institution; Smith College; the Universit y o f Texa s a t Austin ; th e Maste r an d Fellow s o f St . John' s College, Cambridge; the Niedersachsische Staats- und Universitatsbibliothek , Gottingen; th e Mathematische s Institu t de r Universita t Gottingen ; an d th e Universitetsbiblioteket, Osl o fo r permissio n t o quot e fro m document s hel d in their archival collections. Much o f th e researc h fo r thi s boo k wa s conducte d i n conjunctio n wit h grants fro m variou s sources . Th e first autho r i s indebte d t o th e Nationa l Science Foundation fo r support in the form o f grants SES 8509795 and DIR 9011625, which allowe d her to gather much o f the material o n the Hopkin s and Chicag o schools , an d t o a Fourth-Yea r Researc h Fellowshi p fro m th e University o f Virginia . Th e secon d autho r receive d suppor t fro m Nationa l Science Foundation gran t DI R 882142 1 a s well as a two-year stipen d fro m the Alexander vo n Humbold t Foundation , whic h gav e him th e opportunit y to do archival research in Germany . Finally, the first author would like to express her debt o f gratitude to her parents, "Mike" and Maurice Hunger, for all of their encouragement, support, and advice ; to her advisers , I. N. Herstein an d Alle n G. Debus , fo r al l that they taught her about scholarship and friendship; an d to her husband, Bria n Parshall, for hi s tireless and selfles s devotion. Th e second author would like to thank his wife, Hilde, his son, Andy, and his other good friends wh o have helped to remind him that there is more to life than scholarship .

CHARLOTTESVILLE, VIRGINI A AND MAINZ , GERMAN Y July 199 3 Photograph and Figure Credits

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Photo of Georg e Birkoff; p. 391 Photo of Gilber t Bliss; p. 397 Photo of Maxime Bocher; p. 206 xxiv PHOTOGRAP H AND FIGURE CREDITS Photo of Henry Fine; p. 19 5 Photo of Josiah W. Gibbs; p. 25 Photo of Georg e Hill; p. 37 Photo of Rober t Moore; p. 388 Photo of Simo n Newcomb; p. 36 Photo of William F. Osgood; p. 205 Photo of ; p. 216 Photo of William Story ; p. 10 9 Photo of ; p. 385 Photo of Edwar d Van Vleck; p. 215 Photo of Henry White; p. 332 This page intentionally left blank Bibliography

Adams, Henry, The Education of , Boston : Houghto n Miffli n Co. , 1961. Albers, Donald J . an d Alexanderson , Geral d L. , ed., Mathematical People, Chicago: Contemporary Books , Inc., 1985 . Albers, Donald J.; Alexanderson, Gerald L.; and Reid, Constance, International Math- ematical Congresses: An Illustrated History, New York: Springer-Verlag , 1987 . Albert, A . Adrian, "Leonar d Eugen e Dickso n 1874-1954, " Bulletin of the American Mathematical Society 61 (1955):331-345. Alexandrov, P . S. , ed. , Die Hilbertschen Probleme, Ostwalds Klassike r de r exakte n Wissenschaften, vol . 252 , Leipzig : Akademisch e Verlagsgesellschaf t Gees t & Portig, 1979 . Andrews, George E. , "Generalizations o f the Durfee Square, " Journal of the London Mathematical Society 3 (1971):563-570. , "O n a Partition Proble m o f J . J . Sylvester, " Journal of the London Mathe- matical Society 2 (1970):571-576. , The Theory of Partitions, Encyclopedia o f Mathematics and its Applications, vol. 2, Reading: Addison-Wesle y Publishing Co., 1976 . Appelbaum, Stanley, The Chicago World's Pair o/1893: A Photographic Record, New York: Dove r Publications, Inc., 1980 . Archer, William, America To-Day, London: Willia m Heinemann, 1900 . Archibald, Raymon d Clare , "Materia l Concernin g Jame s Josep h Sylvester, " Studies and Essays in the History of Science and Learning Offered in Homage to George Sarton on the Occasion of His Sixtieth Birthday, 3 1 August 1944 , Ne w York : Schuman, n.d., pp. 209-217. , A Semicentennial History of the American Mathematical Society, 1888-1938 , New York: American Mathematical Society, 1938 , reprinted., New York: Arn o Press, 1980 . , "Unpublished Letters of James Joseph Sylvester and Other New Informatio n Concerning His Life and Work," Osiris 1 (1936):85-154. Archibald, Raymond Clare, ed., Semicentennial Addresses of the American Mathemat- ical Society, New York: America n Mathematical Society , 1938 . Archibald, Raymond Clare et ah, "Benjamin Peirce," American Mathematical Monthly 32(1925):l-30. Aris, R.; David, H. T.; and Stuewer, R. H., ed., Springs of Scientific Creativity. Essays on Founders of Modern Science, Minneapolis: Universit y o f Minnesot a Press , 1983. Aspray, William , "Th e Emergenc e o f Princeto n a s a Worl d Cente r fo r Mathemati -

455 456 BIBLIOGRAPHY

cal Research, 1896-1939, " in History and of Modern Mathematics, ed. William Aspray and Philip Kitcher, Minneapolis : Universit y o f Minnesot a Press, 1988 , pp. 346-366. Aspray, Willia m an d Kitcher , Philip , ed., History and Philosophy of Modern Mathe- matics, Minneapolis: Universit y o f Minnesota Press , 1988 . Badger, Reid , The Great American Fair: The World's Columbian Exposition and American Culture, Chicago: Nelso n Hall, 1979 . Baker, H. F., "Biographical Notice," in The Collected Mathematical Papers of James Joseph Sylvester, ed. H. F. Baker, 4 vols., Cambridge: Universit y Press , 1904 - 1912, reprint ed. , New York: Chelse a Publishing Co., 1973 , 4:xv-xxxvii. Beach, Mark , "Wa s There a Scientific Lazzaroni?, " in Nineteenth-Century American Science: A Reappraisal, ed. George H. Daniels, Evanston : Northwester n Uni - versity Press, 1972 , pp. 115-132 . Beardsley, Edwar d A. , The Rise of the American Chemical Profession, 1850-1900 , Gainesville: Universit y of Florida Press, 1964 . Beckert, Herber t an d Schumann , Horst , ed. , 10 0 Jahre Mathematisches Seminar der Karl-Marx-Universitdt Leipzig, Berlin : VE B Deutscher Verla g der Wissen - schaften, 1981 . Bedini, Silvi o A. , The Life of Benjamin Banneker, Ne w York : Charle s S . Scribner' s Sons, 1971. Beetle, K. D. and Wilder, C . E., "John Wesley Young: In Memoriam," Bulletin of the American Mathematical Society 38 (1932):603-610. Belhoste, Bruno , Augustin-Louis Cauchy: A Biography, trans. Fran k Ragland , Ne w York: Springer-Verlag , 1991. , Cauchy: U n Mathematicie n legitimist e a u XIX * Siecle , Paris : Librairi e Classique Eugen e Belin, 1985 . Bell, Eric Temple, The Development of the History of Mathematics, Ne w York: Mc - Graw-Hill, 1945 . , "Fifty Year s of Algebra in America, 1888-1938, " in Semicentennial Addresses of the American Mathematical Society, ed. Raymond C . Archibald, Ne w York: American Mathematica l Society , 1938 , pp. 1-34 . Bellot, H . Hale, University College London 1826-1926 , London : Universit y o f Lon - don Press , Ltd., 1929 . Benson, Keith R., "American Morpholog y in the Late Nineteenth Century : Th e Biol- ogy Department at Johns Hopkins University," Journal of the History of Biology 18 (1985):163-205. Bers, Lipman , "Th e Europea n Mathematicians ' Migratio n t o America, " i n A Cen- tury of Mathematics in America—Part I , ed . Pete r Dure n et al, Providence : American Mathematical Society , 1988 , pp. 231-243. Betsch, Gerhard, "Alexander von Brill (1842-1935)," Bausteine zur Tubingen Univer- sitatsgeschichte 3 (1989):71-90. Biermann, Kurt-R. , "Johan n Pete r Gusta v Lejeun e Dirichlet , Dokument e fu r sei n Leben und Wirken," Abhandlungen der deutschen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik 2 (1959):2-88. , Die Mathematik und ihre Dozenten an der Berliner Universitdt, 1810-1933, Berlin: Akademie-Verlag , 1988 . "Biographical Sketc h o f th e Presiden t o f th e Associatio n [Huber t Anso n Newton]," Stance 6 (1885):161-162. Birkhoff, Garrett , "Mathematic s a t Harvard , 1836-1944, " i n A Century of Mathe- matics in American —Part II , ed . Pete r Dure n et al, Providence : America n Mathematical Society , 1989 , pp. 3-58. BIBLIOGRAPHY 457

Birkhoff, Georg e David, "Boundary Value and Expansion Problems of Ordinary Lin - ear Differential Equations, " Transactions of the American Mathematical Society 9 (1908):373-395. , Collected Mathematical Papers, 3 vols., New York: America n Mathematica l Society, 1950 . , "Fifty Year s of American Mathematics, " in Semicentennial Addresses of the American Mathematical Society, ed. Raymond C . Archibald, New York: Amer - ican Mathematical Society , 1938 , pp. 270-315. , "On the Asymptotic Character of the Solutions of Certain Linear Differentia l Equations Containing a Parameter," Transactions of the American Mathemati- cal Society 9 (1908):219-231. , "Review of The New Haven Colloquium. By Eliakim Hastings Moore, Ernest Julius Wilczynski, Max Mason. Press, 1910 . x + 22 2 p.'," Bul- letin of the American Mathematical Society 1 7 (1911):414-428. , "Th e Scientifi c Wor k o f Maxim e Bocher, " Bulletin of the American Mathe- matical Society 25 (1919): 197-215. Blichfeldt, Han s F., "The Finite, Discontinuous Primitive Groups of Collineations in Four Variables," Mathematische Annalen 6 0 (1905):204-231. , "Th e Minimu m Valu e o f Quadrati c Form s an d th e Closes t Packin g o f Spheres," Mathematische Annalen 10 1 (1929):605-608. , "On a Certain Class of Groups of Transformations i n Space of Three Dimen- sions," American Journal of Mathematics 2 2 (1900): 113-120. Bliss, Gilbert A. , "Eliakim Hasting s Moore," Bulletin of the American Mathematical Society, 2nd. ser., 3 9 (1933):831-838. , "The Geodesic Lines on the Anchor Ring," Annals of Mathematics 4 (1902- 1903):1-21. , "—In Memoriam," Bulletin of the American Mathematical Society 50 (1944):478-489 . , "The Scientifi c Wor k o f Eliaki m Hasting s Moore," Bulletin of the American Mathematical Society 40 (1934):501-514 . Blondheim, David S., "James Joseph Sylvester," Jewish Comment 2 3 (May 25, 1906). Bocher, Maxime, "The Theorems of Oscillation o f Sturm and Klein," Bulletin of the American Mathematical Society 4 (1898):295-313, 365-376 and 5 (1898):22-43. , Ueber die Reihenentwicklungen der Potentialtheorie, Leipzig: B . G. Teubner , 1894. Boi, Luciano; Flament, D.; and Salanski, J.-M., ed., 1830-1930 : A Century of Geom- etry, Berlin: Springer-Verlag , 1992 . Bolza, Oskar, "A n Application o f the Notions o f 'General Analysis ' to a Problem i n the of Variations," Bulletin of the American Mathematical Society 1 6 (1910):107-110. , Aus meinem Leben, Munchen: Verla g Ernst Reinhardt, 1936 . , "Einfuhrung i n E . H. Moore's 'General Analysis' und deren Anwendun g auf die Verallgemeinerun g de r Theori e de r lineare n Integralgleichungen, " Jahres- bericht der deutschen Mathematiker-Vereinigung 2 3 (1914):248-303. , "Heinric h Maschke : Hi s Lif e an d Work, " Bulletin of the American Mathe- matical Society 1 5 (1908):85-95. , Lectures on the Calculus of Variations, Chicago: University of Chicago Press, 1904. , "New Proof o f a Theorem o f Osgood's in the Calculus of Variations," Trans- actions of the American Mathematical Society 2 (190 1 ):422-427. , "O n th e Theor y o f Substitutio n Group s an d It s Application s t o Algebrai c 458 BIBLIOGRAPHY

Equations," American Journal of Mathematics 1 3 (1891):59—144 . , "O n Weierstrass ' System s o f Hyperellipti c s o f th e Firs t an d Sec - ond Kind, " i n Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et at., New York: Macmilla n & Co., 1896 , pp. 1-12 . , "Uber de n 'Anormale n Fall ' beim Lagrangesche n un d Mayersche n Proble m mit gemischte n Bedingunge n un d variablen Endpunkten, " Mathematische An- nalenlA (1913):430-446 . , Vorlesungen uber Variationsrechnung, Leipzig : B . G. Teubner, 1909 . Boole, George , "Exposition o f a General Theor y o f Linea r Transformations," Cam- bridge Mathematical Journal 3 (1841-1842):l-2 0 an d 106-119 . Borel, Armand, "The School of Mathematics at the Institute for Advanced Study," in A Century of Mathematics in America—Part III, ed. Peter Duren et al, Provi - dence: America n Mathematical Society , 1989 , pp. 119-148 . Bottazzini, Umberto, The Higher Calculus: A History of Real and from Euler to Weierstrass, trans . Warre n Va n Egmond , Ne w York : Springer - Verlag, 1986 . , "Urspriinge der Riemannschen Theorie der Funktionen eine r veranderlichen komplexen Grosse," unpublished manuscript . Bourbaki, Nicolas, Elements d'Historire des mathematiques, Paris : Masson , 1984 . , Groupes et Algebres de Lie: Chapitres IV, V, et VI, Paris: Hermann , 1968 . Bouton, Charles L., "Invariants of the General Linear Differential Equatio n and Their Relation to the Theory of Continuous Groups," American Journal ojMathemat- ics 21 (1899):25-84. Bowditch, Henr y Ingersoll , "Memoir, " i n Pierr e Simo n d e l a Place , Celestial Me- chanics, trans. Nathaniel Bowditch, 4 vols., New York: Chelse a Publishing Co., 1966. Bowditch, Nathaniel, American Practical Navigator, Washington: Governmen t Print - ing Office , 1802 , reprin t ed. , n . p. : Defens e Mappin g Agenc y Hydrographic / Topographic Center, 1984 . Brent, Joseph, : A Life, Bloomington: Indian a University Press, 1993. Brieskorn, Egber t and Knorrer , Horst , Plane Algebraic Curves, trans. John Stillwell , Boston: Birkhause r Verlag , 1986 . Brill, Alexander , "Ma x Noether, " Jahresbericht der deutschen Mathematiker- Vereinigung 32 (1923):211-233 . Brill, Alexander and Noether, Max , "Die Entwicklun g der Theorie de r algebraische n Functionen i n altere r un d neuere r Zeit, " Jahresbericht der deutschen Mathe- matiker-Vereinigung 3 (1892):107-566 . Brocke, Bernhar d vom , "De r deutsch-amerikanische n Professorenaustausch . PreuBische Wissenschaftspolitik, international e Wissenschaftsbeziehungen un d die Anfang e eine r deutsche n auswartige n Kulturpoliti k vo r dem erste n Welt - krieg," Zeitschrift fur Kulturaustausch 31 (1981): 128-182. Browder, Felix , ed. , Mathematical Developments Arising from Hilbert's Problems, Symposia i n , vol. 28, Providence: America n Mathematica l Society, 1976 . Brown, Ernest W., "Theorie des Erdmondes," Encyklopadie der mathematischen Wis- senschaften vol. VI-2 (1915):667-728. Brualdi, Richar d A. , Introductory , 2n d ed. , Ne w York : North - Holland, 1992 . BIBLIOGRAPHY 459

Bruce, Rober t V. , The Launching of Modern American Science: 1846-1876 , Ne w York: Alfre d A . Knopf, 1987 . , " A Statistica l Profil e o f America n Scientists , 1846-1876, " i n Nineteenth- Century American Science: A Reappraisal ed . Georg e H . Daniels , Evanston : Northwestern Universit y Press, 1972 , pp. 63-94. Buel, James William, The Magic City: A Massive Portfolio of Original Photographic Views of the Great World's Fair and Its Treasures of Art, Including a Vivid Presentation of the Famous Midway Plaisance, St. Louis: Historica l Publishin g Co., 1894 , reprint ed. , New York: Arn o Press, 1974 . Bumstead, H . A. , "Josia h Willar d Gibbs, " The Scientific Papers of .. . , 2 vols., Ne w York : Longmans , Green , & Co., 1906 , reprin t ed. , New York: Dove r Publications, Inc., 1961 , l:xi-xxvi. , "Josiah Willard Gibbs," American Journal of Science, ser. 4, 1 6 (1903) : 187- 202. Burkhardt, Heinrich , "Grundziig e eine r allgemeine n Systemati k de r hyperellipti - schen Funktione n erste r Ordnung : Nac h Vorlesunge n vo n F . Klein, " Mathe- matische Annalen 3 5 (1890) : 198-296. , "Uebe r einig e mathematisch e Resultate n astronomische r Untersuchungen , insbesondere tiber irregular e Integral e lineare r DifFerentialgleichungen, " i n Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et al, Ne w York: Macmilla n & Co., 1896 , pp. 350-366. Burckhardt, J . J. , "De r Briefwechse l vo n E . S . von Federo w un d F . Klein , 1893, " Archive for History of Exact Sciences 9 (1972):85-93 . , "De r Briefwechse l vo n E . S . von Federo w un d A . Schoenflies, " Archive for History of Exact Sciences 7 (1971):91-141 . Burke, Colin B., American Collegiate Population: A Test of the Traditional View, New York and London: Ne w York University Press, 1982 . Butler, Loren , "Mathematica l Physic s and the American Mathematica l Community : Disciplinary Values , Professiona l Interests , an d th e Plac e o f Borderlan d Re - search 1880-1940, " unpublishe d Ph.D . dissertation , Universit y o f Chicago , 1992. Cairns, W. D., "Herbert Ellswort h Slaught—Edito r an d Organizer," American Math- ematical Monthly 4 5 (1938):l-4 . Cajori, Florian, The Teaching and History of Mathematics in the United States, Wash- ington: Governmen t Printin g Office , 1890 . Caldi, D . G . an d Mostow , G . D. , ed. , Proceedings of the Gibbs Symposium: Yale University, May 15-17 , 1989 , Providence : America n Mathematica l Society , 1990. Cartan, Elie , Oeuvres completes, 3 vols , i n 6 pts. , Paris : Gauthier-Villars , 1952 - 1955. Cattell, James McKeen, American Men of Science: A Biographical Directory, 1st ed., New York: Scienc e Press, 1906 . , American Men of Science: A Biographical Directory, 2nd ed. , Ne w York : Science Press, 1910 . Cayley, Arthur, The Collected Mathematical Papers of , ed. Arthur Cay- ley and A. R. Forsyth, 1 4 vols., Cambridge: Universit y Press , 1889-1898 . , "An Introductory Memoir Upon Quantics," Philosophical Transactions of the Royal Society of London 14 4 (1854):244-258 . , "A Ninth Memoi r on Quantics," Philosophical Transactions of the Royal So- ciety of London 16 1 (1871):17-50. 460 BIBLIOGRAPHY

, "On Linear Transformations," Cambridge and Dublin Mathematical Journal 1 (1846):104-122 . , "On the Theory of Linear Transformations," Cambridge Mathematical Jour- nal 4 (1845) : 193-209. , "A Second Memoir Upon Quantics," Philosophical Transactions of the Royal Society of London 14 6 (1856):101-126 . , " A Sixt h Memoi r Upo n Quantics, " Philosophical Transactions of the Royal Society of London 14 9 (1859):61-90. , " A Third Memoi r Upo n Quantics, " Philosophical Transactions of the Royal Society of London 14 6 (1856):627-647. Chandrasekharan, Komaravolu, Elliptic Functions, New York: Springer-Verlag , 1985 . Chauvenet, William, A on Elementary Geometry, : J . B. Lippin- cott, 1870 . , Treatise on Plane and Spherical Trigonometry, Philadelphia: Hogan , Perkin s &Co., 1850 . Chessin, Alexander S. , "The Preliminary Meetin g of the Southwestern Section, " Bul- letin of the American Mathematical Society 1 3 (1907 ) :213-223. Chittenden, Russel l H. , History of the Sheffield Scientific School of Yale University: 1846-1922, 2 vols., New Haven: Yal e University Press, 1928 . Clebsch, Alfred, "Uber die Anwendung der Abel'schen Functionen in der Geometrie," Journal fur die reine und angewandte Mathematik 6 3 (1864) : 189-243. , Vorlesungen uber Geometrie, ed . Ferdinan d Lindemann , Leipzig : B. G. Teubner, 1876 . Clebsch, Alfred an d Gordan, Paul, Theorie der Abelschen Functionen, Leipzig : B . G. Teubner, 1866 . Clifford, Willia m Kingdon , Mathematical Papers by , ed. Robert Tucker , London : Macmilla n an d Co. , 1882 , reprin t ed. , Ne w York : Chelsea Publishing Company, 1968 . Coble, Arthur B., "Virgil Snyder, 1869-1950, " Bulletin of the American Mathematical Society 56 (1950):468-471 . Cochrane, Rexmond C, The National Academy of Sciences: The First Hundred Years, 1863-1963, Washington: Th e Academy, 1978 . Cole, Frank N., "A Contribution t o the Theory o f the General Equatio n o f the Sixt h Degree," American Journal of Mathematics 8 (1886):265-286 . , "Klein's Ikosaeder," American Journal of Mathematics 9 (1887):45-61 . , "On a Certain Simpl e Group," in Mathematical Papers Read at the Interna- tional Mathematics Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et al, Ne w York: Macmilla n & Co., 1896, pp. 40-43. , "Simple Groups As Far As Order 660," American Journal of Mathematics 1 5 (1893):303-315. Condit, Car l W. , The Chicago School of Architecture: A History of Commercial and Public Building in the Chicago Area, 1875-1925 , Chicago : Universit y o f Chicago Press, 1964 . Cooke, Roger, "Abel's Theorem," i n The History of Modern Mathematics, ed . David E. Row e an d Joh n McCleary , 2 vols. , Boston : Academi c Press , Inc. , 1989 , 1:389-421. , The Mathematics of Sony a Kovalevskaya, New York: Springer-Verlag , 1984 . Cooke, Roge r an d Rickey , V . Frederick , "W.E . Stor y o f Hopkin s an d Clark, " i n A Century of Mathematics in America-Part III , ed. Peter Duren et al, Providence : American Mathematica l Society , 1989 , pp. 29-76. BIBLIOGRAPHY 461

Coolidge, Julian Lowell, A History of Geometrical Methods, Oxford: Clarendo n Press, 1940. , A History of the Conic Sections and Quadric Surfaces, Oxford : Clarendo n Press, 1945 . , The Mathematics of Great Amateurs, Oxford : Clarendo n Press , 1949 . , "Rober t Adrain , an d th e Beginning s o f America n Mathematics, " American Mathematical Monthly 3 3 (1926):61-76 . , A Treatise on Algebraic Plane Curves, Oxford: Clarendo n Press , 1931. Cordasco, Francesco , and the Protean Ph.D.: The Shaping of American Graduate Education, Leiden: E . J. Brill, 1960 . Courant, Richard, "Felix Klein," Die Naturwissenschaften 37 (1925):765-772 . Courant, Richar d an d Hilbert , David , Methoden der mathematischen Physik, Berlin: Springer-Verlag , 1924 . Coxeter, H. S . M., "The Complete Enumeration o f Finite Groups of the Form R- = (RiRj)kiJ = 1," Journal of the London Mathematical Society 10 (1935):21-25 . , "Discret e Group s Generate d b y Reflections, " Annals of Mathematics 3 5 (1934):588-621. , Regular Complex Polytopes, Cambridge : Universit y Press , 1974 . , Regular Polytopes, New York: Th e Macmilla n Company , 1963 , reprint ed. , New York: Dove r Publications, Inc., 1973. Craig, Gordan, The Germans, New York: Ne w American Library, 1983 . Craig, Thomas , "Th e Counter-Peda l Surfac e o f th e Ellipsoid, " American Journal of Mathematics 4 (1881):358-378. , "On the Parallel Surface to an Ellipsoid," Journal fur die reine und angewandte Mathematik 9 3 (1882):251-270 . , "Orthomorphic Projection o f an Ellipsoid on a ," American Journal of Mathematics 3 (1880):114-127 . , "Som e Ellipti c Functio n Formulae, " American Journal of Mathematics 5 (1882):62-75. , A Treatise on Projections, Washington: Unite d State s Coas t an d Geodeti c Survey, 1882 . Cremin, Lawrenc e A. , The Transformation of the School: Progressivism in American Education 1876-1957 , New York: Alfre d A . Knopf, 1961. Crilly, Anthon y James , "Th e Mathematic s o f Arthu r Cayle y wit h Particula r Refer - ence to Linea r Algebra" , unpublishe d Ph.D . dissertation, Middlese x Polytech - nic, June 1981. , "Th e Declin e o f Cayley' s Invarian t Theor y (1863-1895), " Historia Mathe- matica 1 5 (1988):332-347. , "The Rise of Cayley's Invariant Theory (1841-1862)," Historia Mathematica 13 (1986):241-254 . Crowe, Michae l J. , A History of : The Evolution of the Idea of a Vectorial System, Notr e Dame: Universit y o f Notre Dame Press, 1967 . Crozet, Claude , A Treatise on Descriptive Geometry for the Use of the Cadets of the United States Military Academy, Ne w York: A . T. Goodrich & Co., 1821. Currey, J . Seymour , A Century of Marvelous Growth, 5 vols., Chicago : Clark e Pub - lishing Co., 1912 , especially volume 3 , Chicago and Its History and Builders. Curtis, Charle s W . an d Reiner , Irving , of Finite Groups and Associative , New York: Interscienc e Publishers, 1962 . Dalmedico, Am y Dahan, Mathematisations: Augustin-Louis Cauchy et VEcole fran- caise, Argenteuil: Edition s du Choi x and Paris: Alber t Blanchard, 1993 . Daniels, Georg e H. , American Science in the Age of Jackson, Ne w York: Columbi a University Press , 1968 . 462 BIBLIOGRAPHY

, "Th e Proces s o f Professionalizatio n i n America n Science : Th e Emergen t Period, 1820-1860, " Isis 58 (1967):151-166 . Daniels, George H., ed., Nineteenth-Century American Science: A Reappraisal, Evan- ston: Northwester n Universit y Press , 1972 . Davies, Charles , Elementary Algebra : Embracing the First Principles of the Science, New York: A . S. Barnes & Burr, 1862 . Day, Jeremiah, An Introduction to Algebra, Being the First Part of a Course of Math- ematics, Adapted to the Method of Instruction in the American Colleges, New Haven: How e & Deforest, 1814 . , The Mathematical Principles of Navigation and Surveying, with the Mensura- tion of Heights and Distances, Being the Fourth Part of a Course of Mathemat- ics, Adapted to the Method of Instruction in the American Colleges, New Haven: Steele & Gray, 1817 . , A Practical Application of the Principles of Geometry to the Mensuration of Superficies and Solids, Being the Third Part of a Course of Mathematics, Adapted to the Method of Instruction in the American College, New Haven: Olive r Steele, 1814. , A Treatise of Plane Trigonometry to Which is Prefixed a Summary View of the Nature and Use of Logarithms, Being the Second Part of a Course of Math- ematics, Adapted to the Method of Instruction in the American Colleges, New Haven: How e & Deforest, 1815 . Dedekind, Richard , "Schreibe n a n Herr n Borchard t iibe r di e Theori e de r ellipti - schen Modulfunktionen, " Journal fur die reine und angewandte Mathematik 83(1877):265-292. Delambre, Jean-Baptiste , Rapport historique sur les Progres des Sciences mathe- matiques depuis 1789, et sur leur Etat actuel, Paris: Imprimerie imperiale, 1810 , reprint ed. , Amsterdam: N . V. Boekhandel & Antiquariaat B . M. Israel, 1966 . Demidov, Serge i S. ; Folkerts, Menso ; Rowe, David E. ; Scriba, Christoph , eds. , Am- phora: Festschrift fur zu seinem 65. Geburtstag, Basel: Birkhause r Verlag, 1992 . Dewey, John , Lectures in the Philosophy of Mathematics: 1899, ed . Reginal d D . Archimbault, Ne w York: Rando m House, 1966 . Dickson, Leonar d E. , "The Analyti c Representatio n o f Substitution s o n a Power o f a Prime Number o f Letters with a Discussion o f the Linear Group," Annals of Mathematics 1 1 (1897):65-143 . , The Collected Mathematical Papers of , ed. A. Adrian Albert, 6 vols., New York: Chelse a Publishing Company, 197 5 and 1983 . , "Definitions of a Group and a Field by Independent Postulates," Transactions of the American Mathematical Society 6 (1905) : 198-204. , "Eliakim Hastings Moore," Science 11 (1933):79-80 . , Linear Groups with an Exposition of the Galois Field Theory, Leipzig: B . G. Teubner, 1901 , reprint ed., New York: Dove r Publications, Inc., 1958 . Dieudonne, Jean, A History of Algebraic and Differential Topology, 1900-1960 , Boston: Birkhauser Verlag , 1989 . , "The Tragedy o f Grassmann," Linear and Multilinear Algebra 8(1) (1979 — 1980):1-14. Dieudonne, Jea n an d Carrell , James B. , Invariant Theory, Old and New, New York : Academic Press, Inc., 1971. Dirichlet, Pete r Lejeune , Vorlesungen iiber Zahlentheorie, ed. Richard Dedekind , 1s t ed., Braunschweig: F . Vieweg und Sohn , 1863 . Donaldson, Jame s A. , "Blac k American s i n Mathematics, " i n A Century of Math- BIBLIOGRAPHY 463

ematics in America—Part III, ed . Pete r Dure n et al., Providence : America n Mathematical Society , 1989 , pp. 449-469. Dorwart, Harold, "Mathematics and Yale in the Nineteen Twenties," in A Century of Mathematics in America—Part II, ed. Peter Duren et al., Providence: America n Mathematical Society , 1989 , pp. 87-98. Douglas, Jesse, "" , Biographical Memoirs of the National Academy of Sciences, 31 1958 , pp. 180-209 . Dresden, Arnold , " A Report o n th e Scientifi c Wor k o f th e Chicag o Section , 1897 - 1922," Bulletin of the American Mathematical Society 28 (1922):303-307 . Dronke, Adolf , Julius Pliicker, Professor der Mathematik und Physik an der Rheini- schen Friedrich Wilhelms-Universitat in Bonn, Bonn: Adol f Marcus, 1871. Dugac, Pierre, Richard Dedekind et les Fondements des Mathematiques, Collectio n des Travaux d e l'Academi e international e d'Histoir e de s Sciences , vol . 24 , Paris : Librairie philosophique J. Vrin, 1976 . Dunnington, G. Waldo, : Titan of Science, New York: Expositio n Press, 1955 . Dupree, A . Hunter , Science in the Federal Government: A History of Policies and Activities, Baltimore: John s Hopkins University Press, 1986 . Duren, Pete r et al, ed. , A Century of Mathematics in America—Part I, Providence : American Mathematical Society , 1988 . , A Century of Mathematics in America—Part II, Providence: America n Math- ematical Society , 1989 . , A Century of Mathematics in America—Part III, Providence: American Math- ematical Society , 1989 . Durfee, William Pitt, "Tables of the Symmetric Functions of the Twelfthic," American Journal of Mathematics 5 (1882):45—61 . , "The Tabulation of Symmetric Functions," American Journal of Mathematics 5 (1882):348-349 . Dyck, Walther von, ed., Amtlicher Bericht iXber die Weltausstellungen in Chicago 1893, erstattet von Reichskommisar, 2 vols., Berlin: Reichsdruckerei , 1894 . , Deutsche Unterrichtsausstellung in Chicago, 1893: Special-Katalog der math- ematischen Ausstellung, Berlin: n.p. , 1893. , Katalog mathematischer und mathematische-physikalischer Modelle, Apparate und Instrumente, Munich : C . Wolf, 1892 . Echeverria, Javier et al., ed., The Space of Mathematics: Philosophical, Epistemolog- ical, and Historical Explorations, Berlin: Walte r de Gruyter, 1992 . Eddy, Henry T., Neue Constructionen aus der graphischen Statik, Leipzig: B . G. Teub- ner, 1880 . , "Modern Graphica l Developments, " in Mathematical Papers Read at the In- ternational Mathematical Congress Held in Conjunction with the World's Colum- bian Exposition Chicago 1893, ed. E. H. Moore et al, Ne w York: Macmilla n & Co., 1896 , pp. 58-71. , Researches in Graphical , New York: D . Van Nostrand, 1878 . Edwards, Harold M., Fermat's Last Theorem: A Genetic Approach to Algebraic Num- ber Theory, New York: Springer-Verlag , 1977 . Eisenhart, Luther P., Non-, New York: America n Mathematical Society, 1927 . , Riemannian Geometry, Princeton: Universit y Press , 1926 . Elliott, Clar k A. , Biographical Dictionary of American Science: The Seventeenth through the Nineteenth Centuries, Westport: Greenwoo d Press , 1979 . Elliott, Edwin Bailey, An Introduction to the Algebra ofQuantics, Oxford : Universit y 464 BIBLIOGRAPHY

Press, 1895 , reprint ed. , Bronx, N. Y.: Chelse a Publishing Co., 1964 . Ely, Georg e S. , "Bibliograph y o f Bernoull i , " American Journal of Mathe- matics 5 (\&&2):22&-235. Engel, Friedrich , "Zu r Erinnerun g a n Sophu s Lie, " Berichte uber die Verhandlun- gen der koniglichen sdchsischen Gesellschaft der Wissenschaften zu Leipzig 5 1 (1899):11-61. Enros, Phili p C, "Th e Analytica l Society : Mathematic s a t Cambridg e i n th e Earl y Nineteenth Century" , doctoral dissertation, Universit y o f Toronto, 1979 . , "The Analytical Society (1812-1813): Precurso r of the Revival of Cambridge Mathematics," Historia Mathematica 1 0 (1983):24-47 . , "Cambridg e Universit y an d the Adoptio n o f Analytic s i n Earl y Nineteenth - Century England, " i n Social History of Nineteenth Century Mathematics, ed . Herbert Mehrtens , Hen k Bos , an d Iv o Schneider , Boston : Birkhause r Verlag , 1981, pp. 135-148 . Ernst, Wilhelm , Julius Pliicker: Eine zusammenfassende Darstellung seines Lebens und Wirkens als Mathematiker und Physiker aufGrund unveroffentlicher Briefe und Urkunden, Bonn: Universitats-Buchdruckerei , 1933 . Faa de Bruno, Francesco, Theorie des Formes binaires, Turin: P . Marietti, 1876 . Farrar, Joh n an d Emerson , George , First Principles of Differential and Integral Cal- culus, or The Doctrine of .. . Taken Chiefly from the Mathematics of Bezout, Cambridge : Hilliar d & Metcalf, 1824 . Fenster, Deli a Dumbaug h an d Parshall , Kare n Hunger , " A Profil e o f th e America n Mathematical Researc h Community , 1891-1906, " i n The History of Modern Mathematics, vol. 3, ed. an d David E . Rowe, Boston: Aca - demic Press, Inc., 1994 , pp. 179-227. , "Women i n the American Mathematica l Researc h Community," in The His- tory of Modern Mathematics, vol. 3, ed. Eberhard Knobloch and David E. Rowe, Boston: Academi c Press, Inc., 1994 , pp. 229-261. Feuer, Lewi s S. , "America' s Firs t Jewis h Professor : Jame s Josep h Sylveste r a t th e University o f Virginia," American Jewish Archives 36 (1984) : 151 -201. , "Sylvester i n Virginia," The Mathematical Intelligencer 9(2) (1987) : 13-19. Fine, Henr y B. , "Kronecke r an d hi s Arithmetica l Theor y o f Algebrai c Equations, " Bulletin of the New York Mathematical Society 1 (1892) : 173-184. Fischer, Gerd , ed., Mathematische Modelle, 2 vols., Berlin: Akademi e Verlag , 1986 . Fischer, Ger t et ai, ed. , Fin Jahrhundert Mathematik, 1890-1990 . Festschrift zum Jubildum der DMV, Braunschweig : Vieweg , 1990 . Fiske, Thomas S. , "," Bulletin of the American Mathematical Soci- ety 33 (1927):773-777 . , "Mathematical Progres s in America," Bulletin of the American Mathematical Society 1 1 (1905):238-246 . Forman, Paul; Heilbron, John L. ; and Weart, Spencer, "Physics circa 1900 : Personne l and Productivit y o f th e Academi c Establishments, " Historical Studies of the Physical Sciences 5 (1975) : 1-185. Franklin, Fabian , The Life of Daniel Coit Oilman, New York: Dodd , Mead and Co., 1910. , "On the Calculation o f the Generating Functions and Tables of Groundform s for Binar y Quantics," American Journal of Mathematics 3 (1880) : 128-153. , "On a Problem o f Isomerism, " American Journal of Mathematics 1 (1878) : 365-368. , "Sur le Developpement d u Produit infin i ( 1 —x)(\ -x 2)(l -x 3)(l -x 4) • • ," Comptes rendus 82 (1881):448-450 . BIBLIOGRAPHY 465

Frei, Gunther, ed., Der Briefwechsel David Hilbert-Felix Klein (1886-1918), Arbeiten aus der niedersachsischen Staats- und Universitatsbibliothek Gottingen, vol. 19, Gottingen: Vandenhoec k & Ruprecht, 1985 . French, Joh n C , History of the University Founded by Johns Hopkins, Baltimore : Johns Hopkins University Press, 1946 . Frobenius, Ferdinan d Georg , Ferdinand Georg Frobenius: Gesammelte Abhandlun- gen, ed. Jean-Pierre Serre , 3 vols., Berlin: Springer-Verlag , 1968 . , "Uebe r linear e Substitutione n un d bilinear e Formen, " Journal fur die reine und angewandte Mathematik 8 4 (1878) : 1-63. Gauss, Car l Friedrich , Disquisitiones arithmetical, trans . Arthu r A . Clarke , rev . William C . Waterhouse et al., New York: Springer-Verlag , 1966 . Gibbs, Josiah Willard, Elementary Principles of Statistical , New York: C . Scribner's Sons, 1902 . , "," American Journal of Science, 4th ser. 3 (1897):358 - 378. , The Scientific Papers of J. Willard Gibbs, Ph.D., LL.D. formerly Professor of in Yale University, 2 vols., New York: Longmans , Green, & Co., 1906 , reprint ed. , New York: Dove r Publications, Inc., 1961. Giedion, Sigfried , Space, Time, and Architecture, 3rd ed. , Cambridge , MA: Harvard University Press, 1954 . Gillies, Donald, ed., Revolutions in Mathematics, Oxford : Clarendo n Press , 1992 . Gillispie, Charle s C, ed. , Dictionary of Scientific Biography, 1 6 vols., 2 supps., New York: Charle s Scribner's Sons, 1970-1990 . Gilman, Danie l Coit , The Launching of a University and Other Papers: A Sheaf of Remembrances, Ne w York: Dodd , Mead & Co., 1906 . Goldstine, Herman H., A History of the Calculus of Variations from the Xlth through the \9th Century, New York: Springer-Verlag , 1980 . Goodspeed, Thoma s Wakefield , A History of the University of Chicago Founded by John D. Rockefeller: The First Quarter-Century, Chicago: University of Chicago Press, 1916 . Gordan, Paul, "Beweis, dass jede Covariante und Invariante einer binaren Form eine ganze Functio n mi t numerisch e Coefhciente n eine r endliche n Anzah l solche n Formen ist," Journal fur die reine und angewandte Mathematik 6 9 (1868) : 323- 354. , Vorlesungen uber Invariantentheorie, ed . Geor g Kerschensteiner , 2 vols. , Leipzig: B . G. Teubner, 1885-1887 . Gorenstein, Daniel , "Th e Classificatio n o f th e Finit e Simpl e Groups . A Persona l Journey: Th e Earl y Years, " i n A Century of Mathematics in America—Part I, ed . Pete r Dure n et al, Providence : America n Mathematica l Society , 1988 , pp. 447-476. Gould, Joseph E., The Chautauqua Movement: An Episode in the Continuing Ameri- can Revolution, n.p.: Stat e University o f New York, 1961. Goursat, Edouard, " A Simple Proof o f a Theorem in the Calculus of Variations (Ex - tract o f a Letter to Mr. W. F. Osgood)," Transactions of the American Mathe- matical Society 5 (1904) : 110-112. Grabiner, Judith V., "Mathematics in America: Th e First Hundred Years," in The Bi- centennial Tribute to American Mathematics, 1776-1976 , ed. Dalton Tarwater , n.p.: Th e Mathematical Associatio n o f America, 1977 , pp. 9-24 . , The Origins ofCauchy 's Rigorous Calculus, Cambridge, MA: MIT Press, 1981. Grassmann, Hermann, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik dargestellt und durch Anwendungen auf die ubrigen Zweigen der Mathematik, 466 BIBLIOGRAPHY

me auch aufdie Statik, Mechanik, die Lehre vom Magnetismus und die Krys- tallonomie erlautert, Leipzig : O . Wigand, 1844 . Grattan-Guinness, Ivor , Convolutions in French Mathematics, 1800-1840 : From the Calculus and Mechanics to and Mathematical Physics, 3 vols., Basel: Birkhause r Verlag , 1990 . , The Development of the Foundations of Mathematical Analysis from Euler to Riemann, Cambridge , MA: MIT Press, 1970 . , "Doe s Histor y o f Scienc e Trea t o f th e Histor y o f Science ? Th e Cas e o f Mathematics," History of Science 28 (1990) : 149-173. , "A Mathematical Union: Willia m Henry and ," Annals of Science 29 (1972):105-183 . Graustein, William C, "Invarian t Methods in Classical , " Bul- letin of the American Mathematical Society 36 (1930):489-521 . Graves, Lawrenc e M. , "Gilber t Ame s Blis s 1876-1951, " Bulletin of the American Mathematical Society 58 (1952):251-264 . Gray, Jeremy, " in the late Nineteenth Century," in The History of Modern Mathematics, ed . David E . Rowe and John McCleary , 2 vols., Boston: Academic Press, Inc., 1989 , 1:361-385 . , Linear Differential Equations and from Riemann to Poincare, Boston: Birkhause r Verlag , 1986 . Greene, Joh n C, American Science in the Age of Jefferson, Ames: Th e Iow a Stat e University Press, 1984 . Green, Judy , "Christin e Ladd-Frankli n (1847-1930), " in Women of Mathematics: A Biobibliographic Sourcebook, ed. Louise S. Grinstein and Paul J. Campbell, New York: Greenwoo d Press, 1987 , pp. 121-128 . Green, Judy and LaDuke, Jeanne, "Women in the American Mathematical Commu - nity: Th e Pre-1940 Ph.D.'s," The Mathematical Intelligencer 9(1) (1987) : 11 - 23. Gregory, Frederick , "Kant , Schilling , and th e Administratio n o f Scienc e i n th e Ro- mantic Era, " in Science in Germany. The Intersection of Institutional and In- tellectual Issues, ed. Kathryn Olesko , Osiris, 2nd ser. , 5 (1989): 17-35. Grinstein, Louis e S . and Campbell, Paul J., ed. Women of Mathematics: A Biobibli- ographic Sourcebook, New York: Greenwoo d Press , 1987 . Guralnick, Stanley M., "The American Scientist in Higher Education: 1820-1910, " in The Sciences in the American Context: New Perspectives, ed . Nathan Reingold , Washington: Smithsonia n Institutio n Press , 1979 , pp. 99-141. Haas, Arthur, ed., A Commentary on the Scientific Writings of J. Willard Gibbs Ph.D., LL.D. formerly Professor of Mathematical Physics in Yale University, 2 vols., New Haven: Yal e University Press, 1936 . Hall, G . Stanley , Life and Confessions of a Psychologist, Ne w York : Appleton - Century-Crofts, Inc. , 1923. Halphen, Georges , Traite des Fonctions elliptiques et de leurs Applications, 3 vols., Paris: Gauthier-Villars , 1886-1891. Halsted, Georg e Bruce , "Th e Betweennes s Assumptions, " American Mathematical Monthly 9 (\902)m-\0\. , "Bibliography of Hyper-Space and Non-," American Jour- nal of Mathematics 1 (1878):261-276 an d 384-385 ; 2 (1879):65-70. Hamilton, William Rowan , "On , or on a New System of Imaginaries i n Algebra," Philosophical Magazine, 3r d ser., 2 9 (1846):26-31 . Hancock, Harris, Foundations of the Theory of Algebraic Numbers, 2 vols., New York: Macmillan & Co., 1932 . BIBLIOGRAPHY 467

Hankins, Thomas, Sir , Baltimore : John s Hopkins Univer - sity Press, 1980 . Harmon, P. M., ed., Wranglers and Physicists: Studies on Cambridge Physics in the Nineteenth Century, Manchester: Universit y Press, 1985. Harper, Willia m Rainey , The President's Report: Administration —The Decennial Publications, 1st ser., vol. 1 , Chicago: Universit y o f Chicag o Press, 1902 . Haskell, Mellen W., "Uber die zu der Kurve A 3//+/J3I/+I/3A = 0 i m projektiven Sinne gehorende mehrfache Uberdeckung der Ebene," American Journal of Mathemat- ics 13 (1890) : 1-52. Hathaway, Arthu r S. , "Some Papers o n the Theory o f Numbers," American Journal of Mathematics 6 (1884):316-330 . Hawkins, Hugh , Pioneer: A History of the Johns Hopkins University, 1874-1889 , Ithaca: Cornel l University Press , 1960 . Hawkins, Thomas, "Anothe r Loo k a t Cayle y an d th e Theory o f Matrices, " Archives Internationales d'Histoire des Sciences 26 (1977):82-112 . , "Hypercomplex Numbers, Lie Groups, and the Creation of Group Represen- tation Theory," Archive for History of Exact Sciences 8 (1972):243-287 . , Lebesgue's Theory of Integration: Its Origins and Development, Ne w York : Chelsea Publishing Company, 1970 . , "Lin e Geometry , Differentia l Equations , an d th e Birt h o f Lie' s Theor y o f Groups," in The History of Modern Mathematics, ed . David E. Rowe and John McCleary, 2 vols., Boston: Academi c Press, Inc., 1989 , 1:275-329 . , "The Theory of Matrices in the 19t h Century," in Proceedings of the Interna- tional Congress of Mathematicians: Vancouver, 1974, 2 vols., n.p.: Canadia n Mathematical Congress , 1975 , 2:56-70. , "Weierstrass an d th e Theory o f Matrices, " Archive for History of Exact Sci- ences 17 (1977): 119-163. Hedrick, Ear l Raymond, Ueber den analytischen Character des Losungen von Differ- entialgleichungen, Gottingen: n.p. , 1901. Heilbron, John L., The Dilemmas of an Upright Man: as Spokesman for German Science, Berkeley: Universit y o f California Press , 1986 . Heims, Steve J., andNorbert Wiener, Cambridge, MA: MIT Press, 1980. Hellinger, Ernst , "Hilbert' s Arbeite n ube r Integralgleichunge n un d unendlich e Gleichungssysteme," in David Hilbert, Gesammelte Abhandlungen, 3 vols., Ber- lin: Springer-Verlag , 1932-1935 , 3:94-145. Hensel, Susann , "Di e Auseinandersetzungen u m di e mathematisch e Ausbildun g de r Ingenieure an den Technischen Hochschulen in Deutschland Ende des 19 . Jahr- hunderts," in S. Hensel, K.-N. Ihmig, and M. Otte, Mathematik und Technik im 19. Jahrhundert in Deutschland, Studien zu r Wissenschafts- , Sozial- , un d Bil - dungs geschichte der Mathematik, vol. 6, Gottingen: Vandenhoec k & Ruprecht, 1989, pp. 1-111 . Hensel, Susann; Ihmig, K. -N.; and Otte, M., Mathematik und Technik im 19 . Jahrhun- dert in Deutschland, Studie n zu r Wissenschafts- , Sozial- , un d Bildungs - geschichte der Mathematik, vol. 6, Gottingen: Vandenhoec k & Ruprecht, 1989 . Herstein, I . N., Noncommutative Rings, n.p.: Mathematica l Associatio n o f America , 1968. Hilbert, David, The , trans. E. J. Townsend, 2d ed., Chicago: The Open Court Publishing Company , 1910 . , Gesammelte Abhandlungen, 3 vols., Berlin: Springer-Verlag , 1932-1935 . 468 BIBLIOGRAPHY

, Grundlagen der Geometrie, Leipzig: B . G. Teubner, 1899 . , "Mathematica l Problems : Lectur e Delivere d Befor e th e Internationa l Con - gress of Mathematicians at Paris in 1900, " trans. Mary F. Winston, Bulletin of the American Mathematical Society 8 (1902):437-479 . , "Mathematisch e Probleme, " Archiv fur Mathematik und Physik 1 (1901) : 44-63. , Natur und mathematisches Erkennen, ed . David E . Rowe, Basel: Birkhauser , 1991. , "Di e Theori e de r algebraische n Zahlkorper, " Jahresbericht der deutschen Mathematiker-Vereinigung 4 (1897):175—546 . , "Ueber di e Theorie de r algebraische n Formen, " Mathematische Annalen 3 6 (1890):473-534. , "Ueber di e Theorie de r algebraischen Invarianten, " i n Mathematical Papers Read at the International Mathematical Congress Held in Conjunction with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et al, Ne w York: Macmillan & Co., 1896 , pp. 116-124 . Hill, George William, Collected Mathematical Works of , 4 vols., Washington: Carnegi e Institution, 1905-1907 . Hindle, Brooke, The Pursuit of Science in Revolutionary America, 1735-1789, Chapel Hill: Universit y of North Carolina Press, 1956 , reprint ed., New York: Norton , 1974. Hines, Thomas S. , Burnham of Chicago, Architect and Planner, Chicago: Universit y of Chicag o Press, 1979 . Hofstadter, Richard , "Th e Revolutio n i n Highe r Education, " i n Paths of American Thought, ed. Arthur M. Schlesinger, Jr. and Morton White, Boston: Houghto n Mifflin Company , 1970 , pp. 269-290. Hofstadter, Richar d an d Smith , Wilson , ed. , American Higher Education: A Docu- mentary History, 2 vols., Chicago: University o f Chicago Press, 1961. Hogan, Edwar d R. , "Georg e Baro n an d th e Mathematical Correspondent," Historia Mathematical (1976):403-415 . , "Th e Mathematica l Miscellan y (1836-1839), " Historia Mathematica 1 2 (1985):245-257. , "Robert Adrain: America n Mathematician," Historia Mathematica 4 (1977) : 157-172. , "Theodore Strong and Ante-Bellum American Mathematics," Historia Math- ematical (1981):439-455 . Holder, Otto , "Di e einfache n Gruppe n i m erste n un d zweite n Hunder t de r Ord - nungszahlen," Mathematische Annalen 4 0 (1892):55-88 . , "n Die Gruppen der Ordnungen p 3, pq 1, pqr, p 4 , " Mathematische Annalen 43 (1893):301-412 . , "Ueber einfache Gruppen, " Mathematische Annalen 4 0 (1892):55-88 . Howard, Michael, The Franco-Prussian War: The German Invasion of France, 1870- 1871, London: Ruper t Hart-Davis, 1961. Huntington, Edwar d V. , "A Second Definition o f a Group," Bulletin of the American Mathematical Society 8 (1902):388-391 . , "Simplifie d Definitio n o f a Group," Bulletin of the American Mathematical Society % (1902):296-300. Husemoller, Dale , Elliptic Curves, New York: Springer-Verlag , 1986 . Jacobi, Car l G . J. , C. G. J. Jacobi's Gesammelte Werke, ed. Car l W . Borchardt an d , 7 vols., Berlin: Verla g von G. Reimer, 1881-1891 . Johns Hopkins University Celebration of the Twenty-Fifth Anniversary of the Founding BIBLIOGRAPHY 469

of the University and Inauguration of Ira Remsen, LL.D. As President of the University, Baltimore: John s Hopkins University Press, 1902 . Jordan, Camille , Traite des Substitutions et des Equations algebriques, Paris: Gau - thier-Villars, 1870 . Jungnickel, Christ a an d McCormach , Russell , Intellectual Mastery of Nature: Theo- retical Physics from Ohm to Einstein, 2 vols., Chicago: Universit y o f Chicag o Press, 1986 . Kaplansky, Irving , "Abraham Adria n Albert, " Biographical Memoirs of the National Academy of Sciences 51 (1980):3-22 . Kaufmann-Buhler, Walter , Gauss: A Biographical Study, Ne w York : Springer - Verlag, 1981. Kellogg, Oliver Dimon, Foundations of Potential Theory, New York: Dove r Publishing Co., 1929 . Kelley, Brooks Mather, Yale: A History, New Haven: Yal e University Press, 1974 . Kenschaft, Patrici a C , "Charlott e Anga s Scott , 1858-1931, " College Mathematics Journal 18 (1987):98-110 . , "Charlotte Angas Scott (1858-1931)," in Women of Mathematics: A Biobibli- ographic Sourcebook, ed . Louise S . Grinstein and Paul J. Campbell, New York: Greenwood Press , 1987 , pp. 193-203. Kevles, Daniel J. , The Physicists: The History of a Scientific Community in Modern America, Cambridge, MA: Harvard Universit y Press, 1971. Klein, Felix, "A Comparative Revie w of Recent Researche s in Geometry," trans. M. W. Haskell, Bulletin of the New York Mathematical Society 2 (1893):215-249. , Einleitung in die hohere Geometric Vorlesungen gehalten im Wintersemester 1892-93 und Sommersemester 1893 , 2nd ed., Leipzig: B . G. Teubner, 1907 . , Elementarmathematik vom hoheren Standpunkte aus, Berlin: Springer-Verlag , 1928. , Elementary Mathematics from an Advanced Standpoint. Arithmetic, Algebra, Analysis, vol. 1 , trans. E. R. Hedrick and C . A. Noble, New York: Dove r Pub- lishing Co., 1932 . , Elementary Mathematics from an Advanced Standpoint. Geometry, vol . 2 , trans. E. R. Hedrick and C . A. Noble, New York: Dove r Publishing Co., 1939 . , The , Evanston Colloquium Lectures, and Other Selected Works, ed. Jeremy Gray and David E. Rowe, New York: Springer-Verlag , forth - coming. , "Erns t Ritter, " Jahresbericht der deutschen Mathematiker-Vereinigung 4 (1894-1895):52-54. , The Evanston Colloquium Lectures on Mathematics, Ne w York: Macmilla n & Co., 1893 , reprint ed. , New York: America n Mathematica l Society , 1911. , Gesammelte Mathematische Abhandlungen, 3 vols., Berlin: J . Springer, 1921- 1923. , "Gottinge r Professoren . Lebensbilde r vo n eigene r Hand, " Mitteilungen des Universitatsbundes Gottingen 5 (1923) : 11-36. , Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, trans. Georg e Gavi n Morrice , London : Kega n Paul , Trench , Trube r & Co., 1888. , The Mathematical Theory of the Top, New York : Charle s Scribner' s Sons , 1897. , "Neu e Beitrag e zu r Riemannsche n Funktionentheorie, " Mathematische An- nalen2\ (1882-1883) : 141-218. , "Th e Presen t Stat e o f Mathematics, " i n Mathematical Papers Read at the 470 BIBLIOGRAPHY

International Mathematical Congress Held in Connection with the World's Co- lumbian Exposition Chicago 1893, ed. E. H. Moore et aL, New York: Macmilla n &Co., 1896 , pp. 133-135. , Riemannsche Fldchen. Vorlesungen, gehalten in Gottingen 1891/92, ed . Gunther Eisenreic h and Walter Purkert, Teubner-Archi v zu r Mathematik, vol. 5, Leipzig: B . G. Teubner, 1986 . , "Rieman n un d sein e Bedeutun g fu r di e Entwicklun g de r moderne n Mathe - matik," Jahresbericht der deutschen Mathematiker-Vereinigung4 (1894-1895) : 71-87. , "Uber Liniengeometri e un d metrisch e Geometrie, " Mathematische Annalen 5 (1872):257-277 . , "Uebe r ein e geometrisch e Representatio n de r Resolvente n algebraische r Gleichungen," Mathematische Annalen 4 (1871):346-358. , "Ueber eine neue Art der Riemannschen Flache n (Erst e Mitteilung)," Math- ematische Annalen 7 (1874):558-566 . , "Ueber eine neue Art der Riemannschen Flachen (Zweite Mitteilung)," Math- ematische Annalen 1 0 (1876):398-416 . , "Uebe r di e sogenannt e Nicht-Euklidisch e Geometrie, " Mathematische An- nalen 4 (1871):573-625 . , Ueber Riemanns Theorie der algebraische Funktionen und ihrer Integrate, Leipzig: B . G. Teubner, 1882 . , "Ueber die Transformation siebente r Ordnung der elliptischen Funktionen, " Mathematische Annalen 1 4 (1878-1879):428-471. , Vorlesungen iiber das Ikosaeder und dieAuflosung der Gleichungen vomfunften Grade, Leipzig: B . G. Teubner, 1884 . , Vorlesungen iiber das Ikosaeder und dieAuflosung der Gleichungen vomfunften Grade, ed. Peter Slodowy, Basel: Birkhauser, Verlag and Leipzig: B. G. Teubner Verlagsgesellschaft, 1993 . , Vorlesungen iiber die Entwicklung der Mathematik im 19 . Jahrhundert, 2 vols., Berlin: Springer-Verlag , 1926-1927 . , Vorlesungen iiber hohere Geometrie, ed. Wilhel m Blaschke , 3r d ed. , Berlin : Springer-Verlag, 1926 . , Vorlesungen iiber nicht-Euklidische Geometrie, ed. W. Rosemann, Berlin: Ver - lag von Julius Springer, 1928 . Klein, Felix et aL, "Rudolph Friedric h Alfre d Clebsch , Versuch einer Darlegung und Wurdigung seine r wissenschaftliche n Leistungen, " Mathematische Annalen 7 (1874):l-55. Klein, Felix and Fricke, Robert, Vorlesungen iiber die Theorie der automorphen Funk- tionen, 2 vols., Leipzig : B . G . Teubner , 1897-1912 , reprin t ed. , Ne w York : Johnson Reprint Corporation , 1965 . , Vorlesungen iiber die Theorie der elliptischen Modulfunctionen, 2 vols., Leipzig: B. G. Teubner, 1890 , 1892 , reprint ed. , New York: Johnso n Reprin t Corpora - tion, 1966 . Klein, Felix and Lie, Sophus, "Deux Notes sur une certaine Famille de Courbes et de Surfaces," Comptes rendus 70 (1870):1222-1226. , "Ueber diejenigen ebenen Kurven, welche durch ein geschlossenes System von einfach unendlich vielen vertauschbaren linearen Transformationen i n sich iiber gehen," Mathematische Annalen 4 (187 1 ):50-84. , "Ueber die Haupttangentenkurven de r Kummerschen Flach e vierten Grade s mit 1 6 Knotenpunkten, " Monatsberichte der Berliner Akademie der Wissen- schaften (1870):891-899. BIBLIOGRAPHY 471

Klein, Feli x an d Riecke , Eduard , Neue Beitrdge zur Frage des mathematischen und physikalischen Unterrichts an den hoheren Schulen, Leipzig : B . G . Teubner , 1904. Klein, Marti n J. , "Th e Scientifi c Wor k o f Josia h Willar d Gibbs, " in Springs of Sci- entific Creativity: Essays on Founders of Modern Science, ed. R . Aris , H . T . Davis, and R. H. Stuewer, Minneapolis: Universit y o f Minnesota Press, 1983, pp. 142-162 . Kline, Morris , Mathematical Thought from Ancient to Modern , Ne w York : Oxford Universit y Press, 1972 . Knobloch, Eberhar d an d Rowe , David E. , ed., The History of Modern Mathematics, vol. 3, Boston: Academi c Press, Inc., 1994 , forthcoming . Knorr, Wilbur R., The Evolution of the Euclidean Elements, Dordrecht: Reidel , 1975. Koblitz, Ann Hibner , A Convergence of Lives: Sofia Kovalevskaia, Scientist, Writer, Revolutionary, Boston: Birkhause r Verlag , 1983. Koebe, Paul, "Ueber di e Uniformisierung beliebige n analytische n Kurven, " Journal fur die reine und angewandte Mathematik 13 8 (1910) : 192-253. Koelsch, Willia m A. , Clark University 1887-1987: A Narrative History, Worcester : Clark University Press, 1987 . Kohlstedt, Sall y Gregory, The Formation of the American Scientific Community: The American Association for the Advancement of Science 1848-60 , Urbana: Uni - versity of Illinois Press, 1976 . Kohlstedt, Sall y Gregor y an d Rossiter , Margare t W. , Historical Writing on Ameri- can Science: Perspectives and Prospects, Baltimore : John s Hopkins Universit y Press, 1986 . Konigsberger, Leo , , trans . France s A . Welby , Ne w York : , Inc., 1965. Kowalewski, Gerhard, Bestand und Wandel: Meine Lebenserinnerungen zugleich ein Beitragzur neueren Geschichte der Mathematik, Munich : Verla g R. Oldenbourg, 1950. "The Krupp Exhibi t a t the Great Fair," Scientific American 6 9 (July-Dec . 1893):3 3 and 40. Ladd (-Franklin) , Christine, "On the Algebra o f Logic," in Studies in Logic by Mem- bers of the Johns Hopkins University, ed. Charles S . Peirce, Boston: Littl e an d Co., 1883 , pp. 17-71 . Ladd(-Franklin), Christine, "On De Morgan's Extension o f the Algebraic Processes," American Journal of Mathematics 3 (1880):210-225 . , "The Pascal Hexagram," American Journal of Mathematics 2 (1879) : 1-12. Langer, Rudol f E. , "Josia h Willar d Gibbs, " American Mathematical Monthly 4 6 (1939):75-84. Langer, Rudol f E . and Ingraham , Mar k H. , "Edwar d Bur r Va n Vleck , 1863-1943, " Biographical Memoirs of the National Academy of Sciences 30 (1957):399-409 . Layton, Edwin, "Mirror-Image Twins: The Communities o f Science and Technolog y in 19th-centur y America, " Technology and Culture 12 (1971):562-580 . Lefschetz, Solomon, Algebraic Topology, New York: America n Mathematical Society , 1942. , "Reminiscence s o f a Mathematica l Immigran t i n th e Unite d States, " i n A Century of Mathematics in America—Part I, ed. Peter Duren et ah, Providence: American Mathematical Society , 1988 , pp. 201-207. , Topology, New York: America n Mathematical Society , 1930 . Lehner, Joseph, Discontinuous Groups and Automorphic Functions, Mathematical Sur- veys, vol. 8, Providence: America n Mathematical Society , 1964 . 472 BIBLIOGRAPHY

Lewis, Alber t C , "Th e Buildin g o f th e Universit y o f Texa s Mathematic s Faculty , 1883-1938," in A Century of American Mathematics—Part III, ed. Peter Duren et ai, Providence : America n Mathematical Society , 1989 , pp. 205-239. , "George Bruce Halsted and the Development o f American Mathematics," in Men and Institutions in American Mathematics, ed . J. Dalto n Tarwater , Joh n T. White , an d Joh n D . Miller , Graduat e Studies , Texa s Tech University, No . 13, Lubbock: Texa s Tech Press, 1976 , pp. 123-129 . Lie, Sophus , Gesammelte Abhandlungen, ed . Friedric h Enge l and Pou l Heegaard , 7 vols., Oslo: H. Aschehoug & Co. and Leipzig: B . G. Teubner, 1922-1960 . , Theorie der Transformationsgruppen, 3 vols., Leipzig: B . G. Teubner, 1888 - 1893. , "Ueber die Grundlagen der Geometrie," Berichte tiber die Verhandlungen der koniglichen sdchsischen Gesellschaft der Wissenschaften zu Leipzig, 3 (1890) : 355-418. , "Uber Komplexe, insbesondere Linien- und Kugelkomplexe, mit Anwendung auf di e Theori e partielle r Differentialgleichungen, " Mathematische Annalen 5 (1872):145-256. , Vorlesungen uber Differentialgleichungen mit bekannten infinitesimalen Trans- formation, ed . , Leipzig : B . G. Teubner, 1891 . Lie, Sophu s an d Scheffers , Georg , Geometrie der Beriihrungstransformationen, Leipzig: B . G. Teubner, 1896 . Lindemann, Ferdinand , "Ube r di e Zah l % ," Mathematische Annalen 2 0 (1882) : 213-225. Lorey, Wilhelm, Das Studium der Mathematik an den deutschen Universitdten seit An- fang des 19 . Jahrhunderts, Abhandlungen uber den mathematischen Unterrich t in Deutschland, vol. 3, no. 9, Leipzig: Verla g B. G. Teubner, 1916 . Lovett, Edgar O., "The Theory of Perturbation and Lie's Theory of Contact Transfor - mations," The Quarterly Journal of Pure and Applied Mathematics 3 0 (1898) : 47-149. Liitzen, Jesper, "The Solution of Partial s by Separation o f Vari- ables," in Studies in the History of Mathematics, ed . Esther Phillips, MAA Stud- ies i n Mathematics , vol . 26 , Washington , D.C. : Mathematica l Associatio n o f America, 1987 , pp. 242-277. Liitzen, Jespe r an d Purkert , Walter , "Conflictin g Tendencie s i n th e Historiograph y of Mathematics : Morit z Canto r an d H . G . Zeuthen, " i n The History of Mod- ern Mathematics, vol . 3, ed. Eberhard Knobloc h an d Davi d E . Rowe, Boston : Academic Press, Inc., 1994 , forthcoming . Mac Lane, Saunders , "Mathematics a t the Universit y o f Chicago : A Brief History, " in A Century of Mathematics in America—Part II, ed. Peter Duren et ai, Prov - idence: America n Mathematica l Society , 1989 , pp. 127-154 . Magnus, Wilhelm and Chandler, Bruce , The History of Combinatorial Group Theory, New York: Springer-Verlag , 1982 . Maltbie, W. H., "The Undergraduate Mathematica l Curriculum : Repor t o f the Dis- cussion a t the Sevent h Summe r Meetin g o f th e America n Mathematica l Soci - ety," Bulletin of the American Mathematical Society 7 (1900) : 14-24. Manchester, William , The Arms of Krupp, 1587-1968 , Ne w York : Banta m Books , 1981. Manegold, Karl-Heinz, Universitdt, Technische Hochschule und Industrie. Ein Beitrag zur Emanzipation der Technik im 19 . Jahrhundert unter besonderer Berucksichtigung der Bestrebungen Felix Kleins, Berlin : Duncke r & Humblot, 1970. BIBLIOGRAPHY 473

Manin, Yu . I. , Cubic Forms: Algebra, Geometry, Arithmetic, Amsterdam : North - Holland Publishin g Company, 1974 . Masani, Pesi R., , 1894-1964, Vita Mathematica, vol . 5 , Basel: Birk - hauser Verlag, 1990 . Maschke, Heinrich , "Bestimmun g alle r ternare n un d quaternare n Collineations - gruppen, welch e mi t symmetrische n un d alternierende n Buchstabenver - tau schungsgruppe n holoedrisc h isomorp h sind, " Mathematische Annalen 5 1 (1899): 253-298 . , "Beweis des Satzes, dass diejenigen endliche n linearen Substitutionsgruppen , in welchen einige durchgehends verschwindende Coefficienten auftreten , intran - sitiv sind," Mathematische Annalen 5 2 (1899):363-368 . , "Th e Invariant s o f a Grou p o f 2-16 8 Linea r Quaternar y Substitutions, " in Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et aL, New York: Macmilla n & Co., 1896 , pp. 175-186 . , "Uebe r de n arithmetische n Charakte r de r Coefficiente n de r Substitutione n endlicher lineare r Substitutionsgruppen, " Mathematische Annalen 5 0 (1898) : 492-498. Matz, F . P. , "Professo r Thoma s Craig , C.E. , Ph.D., " The American Mathematical Monthly 8 (1901):183-187 . McClelland, Charles , State, Society, and University in Germany, 1700-1914 , Cam - bridge: Cambridg e University Press, 1980 . Mehrtens, Herbert , "Ludwi g Bieberbac h an d 'Deutsch e Mathematik', " i n Studies in the History of Mathematics, ed . Esthe r Phillips , MA A Studie s i n Mathemat - ics, vol . 26 , Washington , D.C. : Mathematica l Associatio n o f America , 1987 , pp. 195-241 . , Moderne—Sprache—Mathematik, Frankfur t a m Main: Suhrkamp , 1990 . Mehrtens, Herbert; Bos , Henk; and Schneider , Ivo , ed., Social History of Nineteenth Century Mathematics, Boston : Birkhause r Verlag, 1981. Meinhardt, Gunther, Die Universitdt Gottingen, Ihre Entwicklung und Geschichte von 1734-1974, Gottingen: Musterschmidt , 1977 . Merrill, Georg e P., The First One Hundred Years of American Geology, Ne w Haven: Yale University Press, 1924 . Merzbach, Uta, "The Study of the History of Mathematics in America: A Centennial Sketch," in A Century of Mathematics in America—Part III, ed. Peter Duren et aL, Providence: America n Mathematica l Society , 1989 , pp. 639-666. Meyer, Franz , "Tabelle n vo n endliche n continuierliche n Transformationsgruppen, " in Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et aL, New York: Macmilla n & Co., 1896 , pp. 187-200 . Miller, George A., The Collected Works of , 3 vols., Urbana, 111. : University o f Illinois Press, 1935-1946 . Miller, Georg e A. ; Blichfeldt, Han s F. ; and Dickson , Leonar d E. , Theory and Appli- cations of Finite Groups, Ne w York: Joh n Wiley , 1916 . Minkowski, Hermann, Geometrie der Zahlen, Leipzig : B . G. Teubner, 1896 . , "Ueber Eigenschafte n vo n ganzen Zahlen , di e durch raumlich e Anschauung erschlossen sind, " i n Mathematical Papers Read at the International Mathe- matical Congress Held in Connection with the World's Columbian Exposition Chicago 1893 , ed . E . H . Moor e et aL, Ne w York : Macmilla n & Co., 1896 , pp. 350-366 . Mitchell, Oscar H., "On Binomial Congruences; Comprising an Extension of Fermat's 474 BIBLIOGRAPHY

and Wilson' s Theorems , an d a Theore m o f Whic h Bot h Ar e Specia l Cases, r American Journal of Mathematics 3 (1880):294-315 . "Some Theorems in Numbers," American Journal of Mathematics 4 (1881) : 25-38. Mobius, August Ferdinand, Gesammelte Werke, 4 vols., Leipzig: B . G. Teubner, 1886 . Monna, A . F. , Dirichlet's Principle: A Mathematical Comedy of Errors and Its In- fluences on the Development of Analysis, Utrecht : Oosthoeck , Scheltema , an d Holkema, 1975 . Montgomery, Deane, "Oswald Veblen," Bulletin of the American Mathematical Society 69 (1963):26-36 . Montgomery, Deane and Veblen, Oswald, "Nels Johann Lennes," Bulletin of the Amer- ican Mathematical Society 60 (1954):264-265 . Moore, Eliakim Hastings, "The Betweennes s Assumptions," American Mathematical Monthly 9 (1902):152-153 . , "Concernin g th e Abstrac t Group s o f Orde r k\ an d ~ Holoedricall y Iso - morphic wit h th e Symmetri c an d th e Alternatin g Substitution-Group s o n k Letters," Proceedings of the London Mathematical Society 28 (1897):357-366 . , "Concerning Harnack's Theory of Improper Definite ," Transactions of the American Mathematical Society 2 (1901):296-330 . , "Concerning Triple Systems," Mathematische Annalen 4 3 (1893):271—285 . , "A Definition o f Abstract Groups," Transactions of the American Mathemat- ical Society 3 (1902):485-492 . , "Definition o f in General Integral Analysis," Proceedings of the National Academy of Sciences 1 (1915):628-632. , "A Doubly-Infinite Syste m of Simple Groups," in Mathematical Papers Read at the International Mathematics Congress Held in Connection with the World's Columbian Exposition: Chicago 1893 , ed . E . H . Moor e et al., Ne w York : Macmillan & Co., 1896 , pp. 208-242. , "Extensions of Certain Theorems of Clifford an d of Cayley in the Geometry of n-," Transactions of the Academy of Arts and Sciences 7 (1885-1886):9-26 . , "Introduction t o a Form o f General Analysis," The New Haven Colloquium, New Haven: Yal e University Press, 1910 . , "On a Definition o f Abstract Groups," Transactions of the American Mathe- matical Society 6 (1905) : 179-180. _, "O n a Form of General Analysis with Application to Linear Differentia l an d Integral Equations," in Atti 4 Congresso internazionale dei Matematici Rome 1908, 3 vols., Rome: Accademi a de i Lincei, 1909 , 2:98-114. _, "O n the Foundations o f Mathematics," Science 17 (1903):401-416 . -, "O n the Projective Axioms of Geometry," Transactions of the American Math- ematical Society 3 (1902):142-158 . "On the Theory of Improper Definite Integrals," Transactions of the American Mathematical Society 2 (1901):459-475 . Moore, Eliakim Hastings with Barnard, Raymond Walter , General Analysis:: Part 1, Philadelphia: Th e American Philosophical Society , 1935 . Moore, Eliakim Hastings; Bolza, Oskar; Maschke, Heinrich; and White, Henry S., ed., Mathematical Papers Read at the International Mathematics Congress Held in Connection with the World's Columbian Exposition Chicago 1893, New York: Macmillan & Co., 1896 . Moore, Eliakim Hastings and Smith, H. L., "A General Theory of Limits," American Journal of Mathematics 4 4 (1922) : 102-121. BIBLIOGRAPHY 475

Moore, Robert L. , "Sets o f Metrica l Hypotheses fo r Geometry, " Transactions of the American Mathematical Society 9 (1908):487-512 . Morrison, Samue l Eliot , ed., The Development of Harvard University Since the Inau- guration of President Eliot 1869-1929 , Cambridge : Harvar d Universit y Press , 1930. Morse, Marston , "Georg e Davi d Birkhof f an d hi s Mathematica l Work, " Bulletin of the American Mathematical Society 52 (1946):357-391. Moyer, Albert E. , A Scientist's Voice in American Culture: and the Rhetoric of Scientific Method, Berkeley: Universit y o f California Press , 1992 . Muir, Thomas , The Theory of in the Historical Order of Development, 4 vols., London: Macmilla n & Co., Ltd., 1906-1923 , reprint ed. , Ne w York : Dover Publications, Inc., 1960 . Netto, Eugen, Substitutionstheorie und ihre Anwendungen auf die Algebra, Leipzig: B. G. Teubner, 1882 . , The Theory of Substitutions and its Applications to Algebra,, trans. Fran k Nelson Cole , Ann Arbor: G . Wahr, 1892 , reprint ed. , Chelse a Publishing Co., n.d. Newton, Hubert , "O n th e Transcendenta l Curve s Whos e Equatio n I s si n y sin my = a sin x sin nx + b, Wit h 24 Plates," Transactions of the Connecticut Academy of Arts and Sciences 3 (1875):97-107 . Nicholson, Julia , "Ott o Holde r an d th e Developmen t o f Grou p Theor y an d Galoi s Theory," unpublished doctora l dissertation, Oxford University , 1993 . Novick, Peter, That Noble Dream: The "Objectivity Question" and the American His- torical Profession, New York: Cambridg e University Press , 1988. Olesko, Kathryn M. , Physics as a Calling: Discipline and Practice in the Konigsberg Seminar for Physics, Ithaca: Cornel l University Press, 1991. Olesko, Kathryn, ed. , Science in Germany: The Intersection of Institutional and In- tellectual Issues, Osiris, 2nd ser., vol. 5 (1989). Oleson, Alexandra and Brown, Sanborn C, ed. , The Pursuit of Knowledge in the Early American Republic: American Scientific and Learned Societies from Colonial Times to the Civil War, Baltimore: John s Hopkins University Press, 1976 . Oliver, Jame s E. ; Wait, Lucien ; an d Jones , George , A Treatise on Algebra, 2nd ed. , New York: Dudle y F. Finch, 1887 . , A Treatise on Trigonometry, 4th ed., Ithaca: G . W. Jones, 1890 . Olivier, Charles P., "Ormond Stone, " Popular Astronomy 4 1 (1933):294-298 . Osgood, Willia m Fogg , "The Lif e an d Service s o f Maxim e Bocher, " Bulletin of the American Mathematical Society 25 (1919):337—350. , "Th e Scientifi c Wor k o f Maxim e Bocher, " Bulletin of the American Mathe- matical Society 25 (1919): 197-215. , Lehrbuch der Funktionentheorie, vol. 1 , Leipzig: B . G. Teubner, 1907 . Osgood, Willia m F. ; Coolidge , Julia n L. ; an d Chase , Georg e H. , "Charle s Leonar d Bouton," Bulletin of the American Mathematical Society 28 (1922):123-124 . Page, Jame s M. , "O n th e Primitiv e Group s o f Transformation s i n Spac e o f Fou r Dimensions," American Journal of Mathematics 1 0 (1888):293-346 . , Ordinary Differential Equations: An Elementary Text Book with an Introduc- tion to Lie's Theory of the Group of One Parameter, London: Macmilla n & Co., 1897. Parshall, Kare n Hunger , "America' s Firs t Schoo l o f Mathematica l Research : Jame s Joseph Sylvester at The Johns Hopkins University 1876-1883, " Archive for His- tory of Exact Sciences 38 (1988) : 153-196. 476 BIBLIOGRAPHY , "A Century-Old Snapsho t o f American Mathematics," The Mathematical In- telligencer 1 2 (3) (1990):7-11 . , "Chemistry throug h Invarian t Theory? " James Joseph Sylvester' s Mathema - tization o f the Atomic Theory," i n Experiencing Nature: Proceedings of a Con- ference in Honor of Allen G. Debus, ed. Pau l H . Theerman an d Kare n Hunge r Parshall, Boston/Dordrecht: Kluwe r Academi c Publishers , 1997 , pp. 81-111 . , "Eliakim Hasting s Moor e and the Foundin g o f a Mathematical Communit y in America, 1892-1902, " Annals of Science 41 (1984):313-333 , reprinted i n A Century of Mathematics in America—Part II, ed. Peter Duren et al. Providence: American Mathematica l Society , 1989 , pp. 155-175 . , "In Pursuit o f the Finite Division Algebr a Theorem an d Beyond : Josep h H . M. Wedderburn, Leonar d E . Dickson, an d Oswal d Veblen, " Archives Interna- tionales d'Histoires des Sciences 33 (1983):274-299 . , "Joseph H . M. Wedderburn an d the Structure Theor y o f Algebras," Archive for History of Exact Sciences 32 (1985):223-349 . , "The One-Hundredth Anniversar y o f the Death o f Invarian t Theory?, " The Mathematical Intelligencer 12 (4) (1990):10-16 . , "Th e One-Hundredt h Anniversar y o f Mathematic s a t th e Universit y o f Chicago," The Mathematical Intelligencer 14 (2) (1992):39-44 . , Selected Correspondence of James Joseph Sylvester and His , forthcoming . , "A Study i n Group Theory: Leonar d Eugen e Dickson's Linear Groups" The Mathematical Intelligencer 13(1) (199 1 ):7-11. , "Toward a History o f Nineteenth-Century Invarian t Theory," in The History of Modern Mathematics, ed . David E. Rowe and John McCleary, 2 vols., Boston: Academic Press, 1989 , 1:157-206 . Parshall, Karen Hunger and Rowe, David E., "Embedded in the Culture: Mathematic s at the World's Columbian Exposition o f 1893, " The Mathematical Intelligencer 15(2) (1993):40-45 . Peckhaus, Volker , Hilbertprogramm und kritische Philosophic, Studien zu r Wissen - schafts-, Sozial- , un d Bildungsgeschicht e de r Mathematik , vol . 7 , Gottingen : Vandenhoeck & Ruprecht, 1990 . Peirce, Benjamin , An Elementary Treatise on Algebra: To Which Are Added Expo- nential Equations and Logarithms, Boston : J . Munroe & Co., 1837 . , An Elementary Treatise on Plane and Solid Geometry, Boston: J . Munro e & Co., 1837 . , An Elementary Treatise on Plane and Spherical Trigonometry with its Appli- cations to Heights and Distances, Navigation and Surveying, Boston: J . Munro e &Co., 1835 . , "Linear Associative Algebra with Notes and Addenda, by C. S. Peirce," Amer- ican Journal of Mathematics 4 (188 1 ):97-229. , "O n th e Use s an d Transformation s o f Linea r Algebra, " Proceedings of the American Academy of Arts and Sciences, n.s. 2 (1875):395-400 . Peirce, Bessi e Louise and Norris , Joe L. , ed., As Others See Chicago: Impressions of Visitors, 1673-1933, Chicago: Universit y o f Chicag o Press, 1933 . Peirce, Charles S., The New Elements of Mathematics, ed . Carolyn Eisele , 4 vols, in 5 pts., The Hague: Mouto n Publishers and Atlantic Highlands, N. J.: Humanitie s Press, 1976 . , "On the Algebras I n Which Divisio n I s Unambiguous," American Journal of Mathematics 4 (1881):225-229 . , "On the Application o f Logica l Analysis to Multiple Algebra," Proceedings of the American Academy of Arts and Sciences 10 (1875):392-394 . Peirce, Charles S. , ed., Studies in Logic by Members of the Johns Hopkins University, Boston: Little and Co. , 1883. BIBLIOGRAPHY 477

Phillips, Esther , ed. , Studies in the History of Mathematics, MA A Studies in Mathe- matics, vol. 26, Washington, D.C.: Mathematical Association of America, 1987. Pierpont, James , "Galoi s Theor y o f Equations," Annals of Mathematics, 2n d ser. , 1 (1900):22-56. Pitcher, Everett, A History of the Second Fifty Years: American Mathematical Society 1939-1988, America n Mathematica l Societ y Centennia l Publications , vol . 1 , Providence: America n Mathematical Society , 1988 . Poincare, Henri , Oeuvres de Henri Poincare, ed. Pau l Appel l et al, 1 1 vols., Paris: Gauthier-Villars et Cie., 1916-1956 . , Papers on Fuchsian Functions, trans . Joh n Stillwell , Ne w York : Springer - Verlag, 1985. , Science et Methode, Paris: Flammarion , 1908 . , "Sur le d e Hill," Bulletin astronomique 1 7 (1900):134-143 . , "Su r le s Fonction s uniforme s qu i s e reproduisen t pa r de s Substitution s lineaires," Mathematische Annalen 1 9 (1882):553-564 . "Sur l'Uniformisatio n de s Fonction s analytiques, " Acta Mathematica 3 1 (1907):l-63. Post, Robert, "Science, Public Policy, and Popular Precepts: Alexander Dallas Bache and Alfre d Beac h a s Symboli c Adversaries," in The Sciences in the American Context: New Perspectives, ed. Natha n Reingold , Washington : Smithsonia n Institution Press , 1979 , pp. 77-98. Purkert, Walter, "Die Mathematik an der Universitat Leipzig von ihrer Griindung bis zum zweiten Drittel des 19 . Jahrhunderts," in 100 Jahre Mathematisches Sem- inar der Karl-Marx-Universitdt Leipzig, ed . Herber t Becker t an d Hors t Schu - mann, Berlin: VE B Deutscher Verlag der Wissenschaften, 1981 , pp. 9-40. Pycior, Helena M., "Benjamin Peirce' s 'Linear Associative Algebra'," Isis 70 (1979) : 537-551. , "British Synthetic vs. French Analytic Styles of Algebra in the Early American Republic," in The History of Modern Mathematics, ed . David E. Rowe and John McCleary, 2 vols., Boston: Academi c Press, Inc., 1989 , 1:125-154. Pyenson, Lewis, Neohumanism and the Persistence of Pure Mathematics in Wilhelmian Germany, Philadelphia: America n Philosophical Society , 1983. Reid, Constance, Courant, New York: Springer-Verlag , 1976 . , Hilbert, New York: Springer-Verlag , 1970 . , Neyman—From Life, Ne w York: Springer-Verlag , 1982 . , "Th e Roa d No t Taken : A Footnote i n th e Histor y o f Mathematics, " The Mathematical Intelligencer 1 (1) (1978):21-23 . Reingold, Nathan, "Alexander Dallas Bache: Science and Technology in the American Idiom," Technology and Culture 11 (1970):163-177 . , "Definitions and Speculations: The Professionalization o f Science in America in the Nineteenth Century," in The Pursuit of Knowledge in the Early American Republic: American Scientific and Learned Societies from Colonial Times to the Civil War, ed. Alexandra Oleso n and Sanbor n C . Brown, Baltimore: John s Hopkins University Press, 1976 , pp. 33-69. "Refugee Mathematician s i n the United State s of America, 1933-1941 : Re- ception and Reaction," Annals of Science 38 (198 1 ):313-338. Reingold, Nathan , ed. , The Sciences in the American Context: New Perspectives, Washington: Smithsonia n Institution Press , 1979 . Science in Nineteenth-Century America: A Documentary History, Chicago : University o f Chicago Press, 1985. 478 BIBLIOGRAPHY

Richards, Joan, Mathematical Visions : The Pursuit of Geometry in Victorian England, Boston: Academi c Press, Inc., 1988 . Richardson, R . G . D. , "Th e Ph.D . Degre e an d Mathematica l Research, " American Mathematical Monthly 43 (1936) : 199-215. Richenhagen, Gottfried , (1856-1927) : Von der reinen Mathematik zur Numerik, Gottingen : Vandenhoec k & Ruprecht, 1985 . Rider, Robin , "A n Opportun e Time : Griffit h C . Evan s an d Mathematic s a t Berke - ley," in A Century of Mathematics in America—Part II, ed. Peter Duren et ah, Providence: America n Mathematical Society , 1989 , pp. 283-302. Riemann, Bernhard, 's Gesammelte Mathematische Werke, ed . Heinrich Weber, 2nd ed., Leipzig: B . G. Teubner, 1892 . , "Theorie de r Abel'schen Funktionen, " Journal fur die reine und angewandte Mathematik 5 4 (1857) : 115-155. , "Uebe r di e Hypothese n welch e de r Geometri e z u Grunde liegen, " Abhand- lungen der Koniglichen Gesellschaft der Wissenschaften zu Gottingen 13 (1868) : 132-152. Ringer, Fritz , The Decline of the German Mandarins: The German Academic Com- munity, Cambridge , MA: Harvard University Press, 1969 . Rohn, Karl , "Di e verschiedene n Gestalte n de r Kummer'sche n Flache, " Mathemat- ische Annalen 1 8 (1881):99-159 . Rosenbaum, Robert A., "There were Giants in those Days: Va n Vleck and his Boys," Wesleyan University Alumnus (November 1956):2-3 . Rosenfeld, Bori s A., A History of Non-Euclidean Geometry, trans. Abe Shenitzer, New York: Springer-Verlag , 1988 . Rosenstein, Georg e M. , Jr. , "Th e Bes t Method . America n Calculu s Textbook s o f the Nineteent h Century, " i n A Century of American Mathematics —Part III , ed. Pete r Dure n et ah, Providence : America n Mathematica l Society , 1989 , pp. 77-109. Ross, Dorothy, G. Stanley Hall: The Psychologist as Prophet, Chicago : Universit y o f Chicago Press, 1972 . , The Origins of American Social Science, New York : Cambridg e Universit y Press, 1991. Rossiter, Margaret W., Women Scientists in America: Struggles and Strategies to 1940, Baltimore: John s Hopkins University Press, 1982 . Rothrock, David A., "Mathematicians in War Service," American Mathematical Month- ly 26 (1919):40-44 . Rowe, Davi d E. , "De r Briefwechse l Sophu s Lie-Feli x Klein , ein e Einsich t i n ihr e personlichen und wissenschaflicthen Beziehungen, " NTM. Schriftenreihe fur Ges- chichte der Naturwissenschaften, Technik und Medizin 2 5 (1988):37-47 . , "The Early Geometrical Works of Sophus Lie and Felix Klein," in The History of Modern Mathematics, ed. David E. Rowe and John McCleary, 2 vols., Boston: Academic Press, Inc., 1989 , 1:209-273. , "Felix Klein's 'Erlanger Antrittsrede.' A Transcription wit h Englis h Transla - tion and Commentary," Historia Mathematica 1 2 (1985):123-141. , " A Forgotte n Chapte r i n th e Histor y o f Feli x Klein' s Erlanger Programm," Historia Mathematica 1 0 (1983):448-454. , "'Jewish Mathematics at Gottingen in the Era of Felix Klein," Isis 11 (1986) : 422-449. , "Klein , Hilbert , an d th e Gottinge n Mathematica l Tradition, " i n Science in Germany: The Intersection of Institutional and Intellectual Issues, ed. Kathry n M. Olesko, Osiris, vol. 5 (1989), pp. 189-213. BIBLIOGRAPHY 479

_, "Klein , Lie , and the 'Erlanger Programm, " in 1830-1930 : A Century of Ge- ometry, ed. Luciano Boi, D. Flament, and J.-M. Salanski, Berlin: Springer-Ver - lag, 1992 , pp. 45-54. _, "Klein , Mittag-Leffler , an d th e Klein-Poincar e Correspondenc e o f 1881 - 1882," i n Amphora: Festschrift fur Hans Wussing zu seinem 65 . Geburtstag, ed. Sergei S . Demidov, Menso Folkerts, David E. Rowe, and , Basel: Birkhause r Verlag , 1992 , pp. 597-618. "The Philosophica l View s o f Klei n an d Hilbert, " i n The Intersection of History and Mathematics, ed . Chikara Sasaki, Mitsuo Sugiura, and Joseph W . Dauben Basel * Birkhauser, 1994 , pp. 187-202 . Rowe, Davi d E . an d McCleary , John , ed. , The History of Modern Mathematics, 2 vols., Boston: Academi c Press, Inc., 1989 . Royden, Halsey , " A Histor y o f Mathematic s a t Stanford, " i n A Century of Math- ematics in America —Part II, ed . Pete r Dure n et al, Providence : America n Mathematical Society , 1989 , pp. 237-277. Rudolph, Frederick , The American College and University: A History, Ne w York : Alfred A . Knopf, 1962 . , Curriculum: A History of the American Undergraduate Course of Study since 1636, : Jossey-Bas s Publishers, 1978 . Rukeyser, Muriel, Willard Gibbs, Garden City : Doubleday, Doran & Company, Inc., 1942. Ryan, W . Carson , Studies in Early Graduate Education: The Johns Hopkins, Clark University, The University of Chicago, Ne w York: Carnegi e Foundation fo r th e Advancement o f Teaching, 1939 . Rydell, Robert W., All the World's a Fair: Visions of Empire at American International Expositions, 1876-1916 , Chicago: Universit y o f Chicag o Press, 1984 . Salmon, George, Lessons Introductory to the Modern Higher Algebra, 3rd ed., Dublin: Hodges, Foster, & Co., 1876 . , A Treatise on the of Three Dimensions, 4t h ed. , Dublin : Hodges, Figgis, and Co., 1882 , ,,A Treatise on Higher Plane Curves, 2nd ed., Dublin: Hodges , Foster, and Co., 1873. Sanford, Edmun d C, A Sketch of the History of Clark University, Worcester: Clar k University Press , 1923. Sarton, George , The Study of the History of Mathematics, Cambridge , MA : Harvard University Press, 1937 ; reprint ed., New York: Dove r Publications, Inc., 1957. Sasaki, Chikara , ed. , Proceedings of the 199 0 Tokyo Symposium on the History of Mathematics, Basel : Birkhause r Verlag , to appear. Scanlon, Michael , "Wh o Wer e th e America n Postulat e Theorists, " The Journal of Symbolic Logic 56 (1991):981-1002 . Schappacher, Norbert , "Fachverband-Institut-Staat, " i n Ein Jahrhundert Mathema- tik, 1890-1990 . Festschrift zum Jubildum der DMV, ed . Ger d Fische r et al, Braunschweig: Vieweg , 1990 , pp. 1-82 . Scharlau, Winfried , ed. , Richard Dedekind: 1831-1981 . Eine Wiirdigung zu seinem 150. Geburtstag, Wiesbaden : Vieweg , 1981. Scheffers, Georg , "Uebe r di e Berechnun g vo n Zahlensystemen, " Berichte uber die Verhandlungen der koniglichen sdchsischen Gesellschaft der Wissenschaften zu Leipzig 4 1 (1889):400-457 . , "Zu r Theori e de r au s n Haupteinheite n gebildete n complexe n Grossen, " Berichte uber die Verhandlungen der koniglichen sdchsischen Gesellschaft der Wissenschaften zu Leipzig 4 1 (1889):290-307 . 480 BIBLIOGRAPHY

Schlesinger, Arthu r M. , Jr . an d White , Morton , ed. , Paths of American Thought, Boston: Houghto n Miffli n Company , 1970 . Schoenflies, Arthur, "Gruppentheorie und Krystallographie," in Mathematical Papers Read at the International Mathematics Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et at., New York: Macmillan & Co., 1896 , pp. 341-349. Scholz, Erhard , "Crystallographi c Symmetr y Concept s an d Grou p Theor y (1850 - 1880)," in The History of Modern Mathematics, ed . David E . Rowe and Joh n McCleary, 2 vols., Boston: Academi c Press, Inc., 1989 , 2:3-27. , Geschichte des Mannigfaltigkeitsbegriffs von Riemann bis Poincare, Basel : Birkhauser Verlag , 1980 . , Symmetric—Gruppe—Dualitat: Zur Beziehung zwischen theoretischer Mathe- matik undAnwendungen in Kristallographie undBaustatik des 19. Jahrhunderts, Science Networks—Historical Studies , vol. 1 , Basel: Birkhause r Verlag, 1989 . Schubring, Gert , "Pure and Applied Mathematics i n Divergent Institutional Setting s in Germany : Th e Role and Impact o f Feli x Klein," in The History of Modern Mathematics, ed. David E. Rowe and John McCleary, 2 vols., Boston: Academi c Press, Inc., 1989,2:171-220 . , "Th e Ris e an d Declin e o f th e Bon n Naturwissenschafte n Seminar, " i n Sci- ence in Germany. The Intersection of Institutional and Intellectual Issues, ed. Kathryn M . Olesko, Osiris, vol. 5 (1989), pp. 56-93. Schwarz, Herman n Amandus , Gesammelte Mathematische Abhandlungen, 2 vols. , Berlin: Akademi e der Wissenschaften, 1890 . , "Ueber diejenigen Falle , in welchen die Gaussische hypergeometrische Reih e eine algebraisch e Functio n ihre s vierte n Elemente s darstellt, " Journal fur die reine und angewandte Mathematik 7 5 (1872):292-335 . Serret, Joseph , Cours d'Algebre superieure, 2 vols., 3r d ed. , Paris : Gauthier-Villars , 1866. Servos, John, "Mathematic s and the Physical Science s in America, 1880-1930, " Isis 77 (1986):611-629 . , from Oswald to Pauling'. The Making of a Science in America, Princeton: Universit y Press, 1990 . Shafarevich, I . R. , "Zu m 150 . Geburtstag vo n Alfre d Clebsch, " Mathematische An- nalen 266 (1983):135-140 . Simons, Lao G. , "Th e Influenc e o f French Mathematician s a t the End o f the Eight - eenth Centur y upo n th e Teaching o f Mathematic s i n American Colleges, " Isis 15 (1931):104-123 . Slaught, Herbert , "Th e Cross-Rati o Grou p o f 12 0 Quadratic Cremon a Transforma - tions of the Plane," American Journal of Mathematics 2 2 (1900):343-388 . , "Th e Teachin g o f Mathematic s i n th e Colleges, " American Mathematical Monthly \b (1909) : 173-177. Slaught, Herber t E . and Bliss , Gilber t A. , "Th e Departmen t o f Mathematics, " The University Record, n.s . 15 (1929):97-104. Smith, David Eugen e and Ginsburg, Jekuthiel, A History of Mathematics in America Before 1900 , Chicago: Th e Mathematical Association o f America, 1934 . Smith, Perce y F. , "Josiah Willar d Gibbs , Ph.D., LL.D.: A Short Sketc h and Appre - ciation o f Hi s Mathematics, " Bulletin of the American Mathematical Society, 2nd. ser. 1 0 (1903-1904):34-39. , "On Sophus Lie's Representation o f Imaginaries in Plane Geometry," Amer- ican Journal of Mathematics 2 5 (1903):165-179 . Snyder, Virgil , "Review o f F. Klein, Gesammelte Mathematische Abhandlungen, vol. 1," Bulletin of the American Mathematical Society 28 (1922):125-129 . BIBLIOGRAPHY 481

, "Ueber die lineare Complexe der Lie'schen Kugelgeometrie," doctoral disser- tation, University o f Gottingen, 1895 . Spivak, Michael , Differential Geometry, 5 vols. , Boston : Publis h o r Peris h Press , 1970-1975. Springer, George , Introduction to Riemann Surfaces, Reading, MA : Addison-Wesle y Publishing Co., 1957. Springer, Ton y A., Invariant Theory, Berlin: Springer-Verlag , 1977 . Stigler, Stephen , ed. , American Contributions to Mathematical Statistics in the Nine- teenth Century, 2 vols., New York: Arn o Press, 1980 . , "Mathematica l Statistic s i n th e Earl y States, " Annals of Statistics 6 (1978): 239-265. Stone, Marshall, "Me n an d Institution s i n American Mathematics, " i n Men and In- stitutions in American Mathematics, ed . J . Dalto n Tarwater , Joh n T . White , and John D. Miller, Graduate Studies , no. 13, Lubbock: Texas Tech Press, 1976 , pp. 7-29. Storr, Richard J., The Beginnings of Graduate Education in America, Chicago : Uni - versity of Chicago Press, 1953. , A History of the University of Chicago: Harper's University, The Beginnings, Chicago: University o f Chicago Press, 1966 . Story, Willia m E. , "O n th e Non-Euclidean Geometry, " American Journal of Mathe- matics 5 (1882) : 180-211. , "On Non-Euclidean Properties of Conies," American Journal of Mathematics 5 (1882):358-381 . , "On the Non-Euclidean Trigonometry, " American Journal of Mathematics 4 (1881):332-340. , "On the Theory of Rational Derivation on a Cubic Curve," American Journal of Mathematics 3 (1880):356-387. Stringham, W . Irving, "Determination o f the Finite Quaternio n Groups, " American Journal of Mathematics 4 (1881):345-357 . , " A Formular y fo r a n Introductio n t o Ellipti c Functions, " i n Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et al, New York: Macmilla n & Co., 1896 , pp. 350-366. , "Regular Figures in ^-Dimensiona l Space," American Journal of Mathematics 3 (1880):1-14 . Strong, Theodore, "On Analytical Trigonometry," Proceedings of the American Philo- sophical Society 1 (1843):49-50 . , "Theory and Variation of the Arbitrary Constants in Elliptic ," Amer- ican Journal of Science 30 (1836):248-266 . Struik, Dir k J. , A Concise History of Mathematics, 4th rev . ed. , Ne w York : Dove r Publications, Inc., 1987 . , "Julian Lowell Coolidge in Memoriam," American Mathematical Monthly 6 2 (1955):669-682. , Lectures on Classical Differential Geometry, 2n d ed. , Reading , MA : Addi - son-Wesley Publishing Co., Inc., 1961 , reprint ed. , New York: Dove r Publica - tions, Inc., 1988 . , "The MIT Department o f Mathematics durin g its First Seventy-Fiv e Years: Some Recollections, " i n A Century of Mathematics in America—Part III , ed . Peter Duren^r a/., Providence: American Mathematical Society, 1989 , pp. 163 — 178. , Science in the Making, Boston : Littl e Brown, 1948 . 482 BIBLIOGRAPHY

Study, Eduard , "Alter e un d neuer e Untersuchunge n tibe r System e complexe r Zahlen," in Mathematical Papers Read at the International Mathematical Con- gress Held in Connection with the World's Columbian Exposition Chicago 1893 , ed. E. H. Moore et al, Ne w York: Macmilla n & Co., 1896 , pp. 350-366. , "tiber Systeme von complexen Zahlen," Nachrichten der Gesellschaft der Wis- senschaften zu Gottingen, Mathematisch-Physicalische Abteilung (1889):237 - 268. Sullivan, Louis , The Autobiography of an Idea, Ne w York : Pres s o f th e America n Institute o f Architects, Inc., 1926 . Sylvester, James Joseph, "Address on Commemoration Day at Johns Hopkins Univer- sity 22 February, 1877, " in The Collected Mathematical Papers of James Joseph Sylvester, ed. H . F . Baker , 4 vols, Cambridge : Universit y Press , 1904-1912 , reprint ed. , New York: Chelse a Publishing Co., 1973 , 3:72-87. , "Algebraical Researches, Containing a Disquisition on Newton's Rule for the Discovery o f Imaginar y Roots , an d a n Allie d Rul e Applicabl e t o a Particula r Class o f Equations , Togethe r wit h a Complete Invariantiv e Determinatio n o f the Character o f the Roots o f the General Equatio n o f the Fifth Degree , &c," Philosophical Transactions of the Royal Society of London 15 4 (1864):579-666 . , The Collected Mathematical Papers of James Joseph Sylvester, 4 vols., Cam- bridge: Universit y Press , 1904-1912 , reprint ed. , Ne w York: Chelse a Publish - ing Co., 1973. , " A Constructive Theor y o f Partitions , Arrange d i n Thre e Acts , an Interact , and an Exodion," American Journal of Mathematics 5 (1882):251-330 . , "Example s o f th e Dialyti c Metho d o f Eliminatio n a s Applie d t o Ternar y Systems of Equations," Cambridge Mathematical Journal 2 (1841):232-236 . , Fliegende Blatter: Supplement to the Laws of Verse, privately printed in Lon- don by Grant & Co., 1876 . , The Laws of Verse: or, Principles of Versification Exemplified in Metrical Translations: Together with an Annotated Reprint of the Inaugural Presidential Address to the Mathematical and Physical Sections of the British Association at Exeter, London : Longmans , Green, & Co., 1870 . , "Lectures on the Principle of Universal Algebra," American Journal of Math- ematics 6 (1884):270-286 . , "Note on the Algebraical Theory o f Points o f Curves of the Third Degree," Philosophical Magazine 1 6 (1858) : 116-119. , "O n a n Applicatio n o f th e Ne w Atomi c Theor y t o th e Graphica l Repre - sentation o f th e Invariant s an d Covariant s o f Binar y Quantics,—Wit h Thre e Appendices," American Journal of Mathematics 1 (1878):64- l 25. , "O n Certai n Ternar y Cubic-For m Equations, " American Journal of Mathe- matics 2 (1879):280-28 5 an d 357-393 ; 3 (1880):58-88 an d 179-189 . , "On th e Genera l Theor y o f Associate d Algebraica l Forms, " Cambridge and Dublin Mathematical Journal 6(1851 ):289-293. , "On the Principles o f the Calculus of Forms," Cambridge and Dublin Math- ematical Journal 1 (1852):52-9 7 an d 179-217 . , "On Quaternions , Nonions , Sedenions , etc.," Johns Hopkins University Cir- culars 2 (1883):7-9 . , "On a Rule fo r Abbreviatin g the Calculatio n o f th e Number o f In - and Co- variants o f a Given Orde r an d Weigh t i n the Coefficient s o f a Binary Quanti c of a Given Degree," Messenger of Mathematics 8 (1879) : 1-8. , "On a Theory of the Syzygetic Relations of Two Rational Integral Functions, Comprising a n Applicatio n t o th e Theor y o f Sturm' s Functions , an d Tha t o f BIBLIOGRAPHY 483

the Greatest Algebraical Common Measure, " Philosophical Transactions of the Royal Society of London 14 3 (1853):407-548 . , "Presidentia l Addres s t o Sectio n 'A ' o f th e Britis h Association, " The Col- lected Mathematical Papers of James Joseph Sylvester, ed. H. F. Baker, 4 vols., Cambridge: Universit y Press, 1904-1912 , reprint ed., New York: Chelse a Pub- lishing Co., 1973,2:650-661. , "Proof o f a Hitherto Undemonstrated Fundamental Theorem of Invariants," Philosophical Magazine 5 (1878):178-188 . , "Sur les Covariants fondamentaux d'un Systeme cubo-biquadratique binaire," Comptes rendus 87 (1878):242-24 4 an d 287-289. , "Tables of Generating Functions and Ground-Forms for the Binary Quantics of the First Ten Orders," American Journal of Mathematics 2 (1879):223-251 . , "Table s o f th e Generatin g s an d Ground-Form s fo r Simultaneou s Binary Quantics of the First Four Orders Taken Two and Two Together," Amer- ican Journal of Mathematics 2 (1879):293-30 6 an d 324-329 . Taber, Henry , "O n th e Theor y o f Matrices, " American Journal of Mathematics 1 1 (1889):337-395. Tait, Pete r Guthrie , Elementary Treatise on Quaternions, 3rd ed. , Cambridge : Uni - versity Press, 1890 . Tarwater, J . Dalton ; White , Joh n T. ; Miller , Joh n D. , ed. , Men and Institutions in American Mathematics, Graduat e Studie s Texas Tech University, no. 13 , Lub- bock: Texa s Tech Press, 1976 . Thompson, Henr y Dallas , "Hyperelliptische Schnittsystem e un d Zusammenordnun g der algebraischen und transcendentalen Thetacharakteristiken," American Jour- nal of Mathematics 1 5 (1893):91-123. Tobies, Renate, Felix Klein, Biographien hervorragender Naturwissenschaftler, Tech - niker und Mediziner 5 0 Leipzig: BS B B. G. Teubner Verlagsgesellschaft, 1981 . Tobies, Renat e an d Rowe , Davi d E. , ed. , Korrespondenz Felix Klein-Adolf Mayer, Auswahl aus den Jahren 1871-1907 , Teubner-Archiv zu r Mathematik, vol . 14 , Leipzig: BS B B. G. Teubner Verlagsgesellschaft , 1990 . Toepell, Michael-Markus , Uber die Entstehung von David Hilberts "Grundlagen der Geometrie", Gottingen: Vandenhoec k & Ruprecht, 1986 . Traylor, D . Reginal d et ah, Creative Teaching'. Heritage of R. L. Moore, Houston : University o f Houston Press , 1972 . Truesdell, Clifford, An Idiot's Fugitive Essays on Science: Methods, Criticisms, Train- ing, Circumstances, New York: Springer-Verlag , 1984 . Tucker, Alber t W. , " : A Reminiscence," in Mathematical People, ed. Donal d J . Alber s an d Geral d L . Alexanderson , Chicago : Contemporar y Books, Inc., 1985 , pp. 349-352. Turner, R . Steven , "Th e Growth o f Professiona l Researc h i n , 1818-1848 — Causes and Context," Historical Studies in the Physical Sciences 3 (1971): 137- 182. van der Waerden, B . L., Algebra, 2 vols., New York: Springer-Verlag , 1991. , A History of Algebra from al-Khwarizmi to , Berlin: Springer - Verlag, 1985 . , "Topologisch e Begriindun g de s Kalkiil s der abzahlend e Geometrie, " Mathe- matische Annalen 10 2 (1930):337-362. Van Vleck , Edwar d Burr , "Zu r Kettenbruchentwicklun g hyperelliptische r un d ahn - licher Integrale," American Journal of Mathematics 1 6 (1894) : 1-91. Veblen, Oswald , "Georg e Davi d Birkhof f (1884-1944), " Yearbook of the American Philosophical Society (1946):279-285. 484 BIBLIOGRAPHY

, "—In Memorium," Bulletin of the American Mathemat- ical Society 35 (1929):726-730 . , Invariants of Quadratic Differential Forms, Cambridge Tracts in Mathematics and Mathematical Physics , vol. 24, Cambridge: Universit y Press, 1927 . , Projektive Relativitatstheorie, Ergebnisse der Mathematik und ihrer Grenzge- biete, vol. 2, no. 1 , Berlin: Springer-Verlag , 1933 . , " A System o f Axiom s fo r Geometry, " Transactions of the American Mathe- matical Society 5 (1904):343-384 . Veblen, Oswald and Whitehead, J. H. C, The Foundations of Differential Geometry, Cambridge Tract s i n Mathematic s an d Mathematica l Physics , vol . 29 , Cam - bridge: Universit y Press, 1932 . Veblen, Oswal d and Young, John Wesley , , vol. 1 , Boston: Gin n and Co., 1910 . Veysey, Laurence R., The Emergence of the American University, Chicago: Universit y of Chicag o Press, 1965. Volkert, Klau s T. , Die Krise der Anschauung, Studie n zu r Wissenschafts- , Sozial- , und Bildungsgeschicht e de r Mathematik , vol . 3 , Gottingen : Vandenhoec k & Ruprecht, 1986 . Walsh, Josep h L. , "Willia m Fog g Osgood, " i n A Century of Mathematics in Amer- ica—Part II, ed. Peter Duren et al, Providence : America n Mathematical Soci- ety, 1989 , pp. 79-85. Webber, Samuel, Mathematics, Compiled from the Best Authors and Intended to Be a Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Boston: Harvar d College , 1801. Weber, Heinrich, Lehrbuch der Algebra, 2nd ed., 3 vols., Braunschweig: F . Vieweg & Sohn, 1899-1912 . Wedderburn, Josep h H . M. , " A Theorem o n Finit e Algebras, " Transactions of the American Mathematical Society 6 (1905):349-352. , "On Hypercomplex Numbers," Proceedings of the London Mathematical So- ciety, 2nd ser., 6 (1907):77-118 . Weierstrass, Karl , Mathematische Werke, 7 vols., Berlin : Maye r & Muller, 1894 — 1927, reprin t ed. , Hildesheim : Geor g Ohm s Verlagsbuchhandlun g an d Ne w York: Johnso n Reprint Corporation, 1967 . Weil, Andre, : An Approach though History from Hammurapi to Leg- endre, Boston: Birkhause r Verlag, 1984 . Weimann, Jeanne Madeline, The Fair Women: The Story of The Woman's Building, World's Columbian Exposition, Chicago 1893, Chicago: Academy , 1981. Weltausstellung in Chicago, 1893. Reichskommissar fur die amtlicher Bericht iXber die Weltausstellung in Chicago, 1893, Berlin: Reichsdruckerei , 1894 . Weyl, Hermann, Classical Groups: Their Invariants and Representations, Princeton : University Press, 1939 . , Die Idee der Riemannschen Flache, Leipzig: B . G. Teubner, 1913 . , Die Idee der Riemannschen Flache, 3rd ed., Stuttgart: B . G. Teubner Verlags- gesellschaft, 1955 . Wheeler, Lynd e Phelps , Josiah Willard Gibbs: The History of a Great Mind, Ne w Haven: Yal e University Press, 1952 . White, Henr y Seely , "Abel'sch e Integral e au f singularitatenfreien , einfac h uber - deckten, vollstandige n Schnittcurve n eine s beliebi g ausgedehnte n Raumes, " Nova Acta der kaiser lichen Leopoldinisch-Carolinischen deutschen Academie der Naturforscher 57 (1891):41-128. , "Autobiographical Memoir of (1861-1943)," Biographical Memoirs of the National Academy of Sciences 25 (1944):16-33 . BIBLIOGRAPHY 485

, " A Brie f Accoun t o f th e Congres s o n Mathematic s hel d a t Chicag o i n Au - gust, 1893, " in Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition Chicago 1893, ed. E. H. Moore et al, Ne w York: Macmilla n & Co., 1896 , pp. 350-366. , "Ueber zwei covariante Formen au s der Theorie der abePschen Integrate auf vollstandigen singularitatenfreie n Schnittcurve n zweie r Flachen," Mathematis- cheAnnalen 3 6 (1890):597-601. White, Henry S.; Woods, Frederick S.; Van Vleck, Edward B., The Boston Colloquium, AMS Colloquium Publications , vol. 1 , New York: Macmilla n and Co., 1905. Whitman, Betse y S. , "Mar y France s Winsto n Newson, " Mathematics Teacher 76 (1983):576-577. Whittaker, E . T. an d Watson, G . N., A Course of Modern Analysis: An Introduction to the General Theory of Infinite Process and of Analytic Functions; With an Ac- count of the Principal Transcendental Functions, 4th ed., Cambridge: University Press, 1927 , reprint ed. , Cambridge: Universit y Press, 1963. Wiener, Norbert , Generalized Harmonic Analysis and Tauberian Theorems, Cam- bridge, MA: MIT Press, 1964 . , I Am a Mathematician, Garde n City , NY: Doubleday, 1956 . , Selected Papers of Norbert Wiener, Cambridge , MA : MIT Press, 1964 . Wilczynski, Ernest J. , "The First Meeting of the Sa n Francisco Sectio n o f the Amer- ican Mathematica l Society, " Bulletin of the American Mathematical Society 8 (1902):429-437. Wilder, Raymon d L. , "Th e Mathematica l Wor k o f R . L . Moore : It s Background , Nature, and Influence," Archive for History of Exact Sciences 26 (1982):73-97 . , "Rober t Le e Moore , 1882-1974, " Bulletin of the American Mathematical Society 82 (1976):417-427 . Williams, L. Pearce, Michael Faraday. A Biography, New York: Basi c Books, 1965. Wilson, Edwin Bidwell, "The Contributions of Gibbs to Vector Analysis and Multiple Algebra," in Commentary on the Scientific Writings of J. Willard Gibbs ... , ed. Arthur Haas, 2 vols., New Haven: Yal e University Press , 1936 , pp. 127-160 . , Vector Analysis'. A Text-book for the Use of Students of Mathematics and Physics Founded upon the Lectures of J. Willard Gibbs ... , New York: Charle s Scribner's Sons, 1902 . Wilson, Louis N., Clark University Directory of Alumni, Faculty and Students, Worces- ter: Clark University Press , 1915 . Wilson, Woodrow , "Th e Preceptoria l Syste m a t Princeton, " Educational Review 3 9 (1910):385-390. Winston, Mary F., "Eine Bemerkung zur Theorie der hypergeometrischen Function, " Mathematische Annalen 46 (1895):159-160. , Ueber den Hermiteschen Fall der Lameschen Dijferentialgleichung, Gottingen: W. Fr. Kastner, 1897 . Woods, Frederick S . and Bailey, Frederick H., Course in Mathematics for Students of and Applied Science, 2 vols., Boston: Gin n and Co., 1907-1909 . Wussing, Hans, The Origin of the Abstract Group Concept, trans. Abe Shenitzer, Cam- bridge, MA: MIT Press, 1984 . Yaglom, I. M., Felix Klein and Sophus Lie: Evolution of the Idea of in the Nineteenth Century, trans. Sergei Sossinsky, Boston: Birkhause r Verlag, 1988 . Young, Jacob W. A., "On the Determination o f Group s Whose Order Is a Power of a Prime," American Journal of Mathematics 1 5 (1893):124-178. Ziegler, Renatus , Die Geschichte der geometrischen Mechanik im 19 . Jahrhundert, Stuttgart: Fran z Steine r Verlag, 1985 . This page intentionally left blank Subject Index

Abel's theorem , 44 , 157 , 209 , 224 , 225 , American Journal of Science and Arts, 15 , 228 45 Abel, Niels, 174 , 189 , 319 American Mathematical Monthly, 51,411- Abelian functions, 19 9 413,419,430 Abelian integrals, 180 , 209, 286 American Mathematical Society (AMS), 33, Aberdeen Proving Grounds, 444 51,207,211,267,268,358,360, Academic specialization, 1 6 363, 387 , 404 , 406 , 411 , 412, Acta Mathematica, 4 6 414, 416, 418, 419, 430, 451 Adams, Charles Kendall, 269, 270 Bulletin of the, 51, 268, 411, 412, 430, Adams, Henry B., 88, 302, 304, 360 431, 44 3 Adams, John Couch, 18 , 46, 50 Chicago section , 408 , 409 , 414 , 416 , Addams, Jane, 296 419, 430 Adler, Dankmar, 29 7 Colloquium, 394 , 395, 419, 434, 448 Adrain, Robert, 43, 44 Colloquium lectures , 354, 360 Agassiz, Louis, 27, 41, 48, 354 Colloquium publications , 406 Airy, George, 5 0 role of Chicagoans in, 401 Albert, A . Adrian, 44 5 San Francisco section, 410 Alexander duality, 44 9 Sections, 413 Alexander polynomial, 449 Southwestern section , 410 Alexander, James W., 444, 448, 449, 451 summer meetings, 404, 414 Algebra, theories of , 47 , 48, 99, 133 , 135 Transactions of the, 390, 392, 394, 413, Algebraic geometry, 372 . 375 414, 419, 430 Algebraic number fields, 369 American Philosophical Society , 41, 355 Algebraic surfaces, 36 8 American Physical Society , 42 Althoff, Friedrich , 247 , 274, 305, 358 Amringe, John H. van, 267, 268, 415 American Academ y o f Art s an d Sciences , Analyst, 85 41, 35 5 Analyst or Mathematical Museum, 44 , 51 American Association for the Advancement Analyst: A Monthly Journal of Pure and Ap- of Scienc e (AAAS) , 41, 42, 45, plied Mathematics, 5 1 404, 443 Anderson, R. D., 450 Proceedings of, 45, 378, 428 Andrews, George, 12 5 American Baptist Educatio n Society , 275 Angell, James B., 54, 55, 266 American Chemical Journal, 88 Annales de Mathematiques pures et appliquees, American Chemica l Society , 42 6 American Colon y in Gottingen, 44 4 Annals of Mathematics, 51, 411, 412, 430, American Ephemeris, 35, 38 450 American Geologica l Society, 42 Anschauung, 168 , 170, 175, 178, 183, 334, American Journal, 93, 94 336, 342 American Journal of Mathematics, 38 , 49, Appell, Paul, 443 51, 87-91 , 109 , 113 , 123 , 141, Applied mathematics, 6 , 19 , 266 142, 144 , 146 , 282 , 374 , 411, Archer, William, 40 7 412 Archibald, Raymond C, 404 , 419 American Journal of Philology, 8 8 Aronhold, Siegfried , 103 , 157 488 SUBJECT INDEX

Association of Collegiate Alumnae (ACA), Bocher Prize, 447 240, 242, 249 Bocher, Maxime, 159 , 196 , 204, 207, 211, Astronomy and the theory of linear differ - 212, 214 , 218 , 253 , 256 , 258 , ential equations, 312 259, 264 , 286 , 290 , 337 , 390 , Asymptotic expansion s o f ordinar y linea r 392, 406 , 407 , 410 , 412 , 414 , differential equations , 390 434,436,437,440,442,451 Asymptotic expansions of the solutions of Bolyai, J., 163 , 350 differential equations , 392 Bolza, Oskar, 197-201, 203, 222, 241, 255, August, King Ernst, 15 1 259, 274 , 286 , 287 , 289 , 290 , Ausarbeitungen, 202 , 208, 211, 247 293, 294 , 304 , 307 , 308 , 313 , Automorphic functions, 172 , 253, 345 320, 324 , 326 , 329 , 331 , 350 , Axiomatics, 37 2 354, 355 , 361 , 363 , 364 , 366 - Axiomization for a group, 386 372, 375 , 386 , 390 , 394 , 395 , Axiomization o f geometry , 382-384 , 386 , 401,408,416,420,425,436 393 lecture courses, 368 mathematical interests, 393 Babbage, Charles, 7 , 63 teaching style, 370 Bache, Alexande r Dallas , 34 , 40 , 41 , 48 , Bonn University, 155 , 156 , 438 428 Natural Sciences Seminar, 15 5 Baker, R. P., 423 Bonney, Charles C, 303 , 310 Bancroft, George , 46 Boole, George, 66-68, 100 , 132 , 334 Banneker, Benjamin, 9 Borchardt, Car l Wilhelm, 26 Barnard, Frederick, A . P., 266 Borger, R. L., 424 Barnard, Henry, 56 Bosworth, Anne Lucy, 440 Barnum, P. T., 297 Bounday-value problems, 390 Baron, George, 42, 43 Bourbaki, Nicolas, 295 Mathematical Correspondent, 42, 43 Bourdon, Louis P. M., 13 , 59, 61 Barrow, Si r Isaac, 3 Bouton, Charles Leonard, 237, 238 Battaglini, Guiseppe, 15 9 Bowditch, Nathaniel , 8 , 9 , 12 , 17 , 35 , 38, Baur, G., 28 9 40, 44, 50, 428, 429 Beaux-Arts style, 297, 300 American Practical Navigator, 9 Bell, Eri c Temple, 201, 204, 254 Boyd, James Harrington, 220-222, 256, 293 Beltrami, E. , 18 4 Brauer, Richard, 398 Benner, Henry, 415 Bravais, August, 322 Berlin Academy of Sciences , 46 Brill, Alexander , 157 , 159 , 170 , 224, 228, Bernstein, Felix, 440, 452 335 Bessel, F., 50 Brill, Ludwig, 17 1 Bezout, Etienne, 8 , 63 Brioschi, Francesco, 324, 349 Bianchi, Luigi , 191 , 217 British Associatio n fo r th e Advancemen t Bieberbach, Ludwig, 346, 452 of Science, 31 8 Binary quadratic forms, 34 8 British influences o n American mathemat- Bing, R . H., 450 ics, 2 Biot, Jean-Baptiste, 5 0 Polytechnic Institute, 404 Birational transformations, 15 7 Brougham, Lord, 70 Birkhoff, George David, 382, 390, 392, 393, Brouwer, L . E. J., 181 , 186 , 334, 449 423, 434 , 436 , 437 , 439 , 446 , Brown University, 392 , 435, 453 451,452 Brown, Ernest William, 38, 413, 414, 433 Bismark, Otto von, 15 5 Brown, George Lincoln, 400, 426 Bissing, Gustav, 9 7 Brown, George William, 5 5 Blakslee, T. M., 220, 415 Bryn Mawr College, 85, 241, 242, 249, 367, Blaschke, Wilhelm, 32 5 416, 432 Blichfeldt, Han s Frederik , 235 , 237 , 238 , Bucknell University, 29 2 444 Buffalo Bill' s Wild West Show, 300 Bliss, Gilber t Ames , 282 , 372 , 396 , 401 , Bunsen, Robert, 28, 15 6 425, 434 , 436 , 439 , 444 , 445 , Burkhardt, Heinrich , 208 , 312 , 320 , 329 , 451 349, 350 Bloom, Sol, 300 Burnham, Daniel, 297, 298 Blumenthal, Otto, 440 Burnside, William, 398, 399 Boas, Franz , 289 Bussey, William Henry, 424 SUBJECT INDEX 489

Byerly, William E. , 20, 76, 212 167, 168 , 170 , 189 , 209 , 223- 225,228,315,334-336,338 Cairns, William Deweese, 440 Clebsch School, 157, 161, 170, 183, 234, Calculus of variations, 274, 368, 373, 394, 335 395 Mathematische Annalen, 2 6 California Institut e of Technology, 453 Clifford, Willia m Kingdon, 315 , 352, 373 Cambridge Analytical Society, 7 , 61 Coble, Arthur Byron, 218, 433, 435 Cambridge Miscellany of Mathematics, Physics Colaw, JohnM, 41 1 and Astronomy, 45, 51 Cole, Fran k Nelson , 173 , 192 , 196 , 200 , Cambridge University, 5 , 7, 201, 213, 251, 203, 204 , 208 , 210 , 241 , 253, 267, 277, 292, 293, 433, 447 254, 259 , 264 , 266 , 268 , 321, Cantor, Georg , 16 8 324, 326 , 329 , 377 , 378 , 402 , Cantor, Moritz, 295 406,410,415,435 Cartan, Elie , 94 Collineation groups, 399, 400 Cassatt, Mary, 30 3 , 133 , 266, 267 , 307, Catholic University o f America, 273 355, 359 , 384 , 406 , 429 , 432 , Cauchy, Augustin-Louis, 6 , 18 , 50, 63 435, 444, 450 Cayley metric, 163 , 166 , 167 , 169 , 351 Combinatorial grou p theory, 18 2 Cayley's absolute figure, 166, 16 7 Confocal cyclides , 164 , 211 Cayley's theorem, 102 , 117 , 120 Congress of Representative Women, 30 3 Cayley, Arthur, 31 , 66-69, 71, 79, 85, 92, Congresses in mathematics, astronomy, and 93,100-104,106,107,110,111, astrophysics, 310 116, 120 , 124 , 129 , 135 , 138 , Connecticut Academy of Arts and Sciences 140, 143 , 167 , 189 , 213 , 228 , Transactions of the, 45 267, 315 , 319 , 321 , 334 , 338 , Contact transformations, 165 , 167 , 237 374, 433 Coolidge, Julian Lowell , 438, 446 , 429 Copenhagen University, 23 7 Chasles, Michel, 22, 27, 161 , 164 , 76 , 84, 145 , 202, 211, Chautauqua Literary and Scientific , 213, 217 , 218 , 249 , 261 , 269- 277 272, 307 , 317 , 355 , 367 , 393 , Chautauqua University, 276, 277, 279, 282, 432, 435, 439, 445 369 mathematics curriculum, 27 0 Chauvenet, William, 1 4 Courant, Richard, 148 , 440, 452, 453 Chessin, Alexander, 41 0 Court of Honor, 298 , 300, 360 Chicago Art Institute, 30 3 Covariant, 10 1 Chicago Congress, 222 Coxeter, H. S. M„ 40 0 Chicago School of Architecture, 32 6 Craig, Thomas , 77-79 , 84 , 92 , 97 , 113 , Chicago's Museu m o f Scienc e an d Indus - 144, 200, 201, 213, 433 try, 30 2 Crathorne, Arthur Robert, 440 Chisholm, Grace , 244, 246, 249-252 Cremona, Luigi, 317, 371 Chow, W. L., 19 4 Crilly, Tony, 10 6 Christoffel, Elwi n Bruno, 198 , 224 Crowe, Michael, 3 2 Church, Alonzo, 448 Crozet, Claude, 1 3 Circle-squarers, 34 8 A treatise on descriptive geometry for the City Beautiful Movement , 29 8 use of the cadets of the United City University of Ne w York, 450 States Military Academy, 13, 14 Clap, Thomas, 2 Crystal Palace, 297 Clark University, 144 , 201, 261, 269, 271, Culmann, Carl , 31 7 272, 275 , 279 , 286 , 287 , 289 , Current flows on a surface, 178 , 179 292, 326 , 355 , 367 , 375 , 429 , Curriculum 432, 435, 449 18th century, 1 5 Clark, John Emory , 21 19th century, 15 , 17 , 18 , 20, 21, 57 Clark, Jonas Gilman, 271-273, 275, 287 Curry, Haskell Brooks, 256, 440 Class curve, 16 9 Cyclotomic theorem, 398 , 399 Classification o f finite simple groups, 325 Czermak, J. N., 17 6 Clausius, Rudolf, 2 9 Clebsch's diagonal surface, 34 0 Daniels, Archibald L. , 97 Clebsch, Alfred, 26 , 43, 103, 110, 143, 148, Darboux, Gaston, 27, 164 , 211, 336, 337 154, 157 , 159 , 161 , 163 , 165 , Dartmouth College , 392, 439 490 SUBJECT INDEX

Darwin, G . H., 433 1848 Revolution, 15 4 Davies, Charles, 13 , 14 , 20 Einstein, Albert, 352, 452 Davis, Eller y William, 97, 145 , 410 Eisenhart, Luthe r Pfahler , 414 , 439 , 448 , Davis, Lieutenant Charle s Henry, 35 449 Day, Jeremiah, 1 5 Eisenstein, Gotthold, 103 , 15 2 Dedekind /-function, 17 4 Elective system, 17 , 1 9 Dedekind, Richard, 148 , 152 , 15 3 Electrical Congress, 306 Dehn, Max, 440, 452 Elimination theory, 62, 19 4 DeMorgan, Augustus, 59, 61-63, 13 2 Eliot, Charles W., 54, 55, 263, 267 Des Moines College, 415 Elliptic functions, 112 , 116 , 173, 192,274, Descriptive geometry, 170 , 317 319, 366, 367 Deutsche Mathematiker-Vereinigung, 168 , , 16 6 307 Elliptic integrals, 180 , 319 Dewey, John, 418 Elliptic modula r functions, 172-174 , 253, Dickinson College, 411 350 Dickson, Leonar d Eugene , 235 , 371 , 381, Ely, George Stetson, 97, 129 , 14 5 382, 387 , 393 , 412 , 414 , 418 , Emerson, George, 8 423,424,434,436,445,451 Encyklopddie der mathematischen Wissenschaften, early mathematical interests , 379 434, 437 Dihedral groups, 17 2 Engel, Friedrich, 177 , 192 , 236, 315, 323 Dirichlet Principle, 177 , 232, 335 Engineering scienc e i n th e Unite d States , Dirichlet, Pete r Gusta v Lejeune , 80 , 151 , 317,355 152, 177 , 309 Erlangen University, 167 , 168 , 170 , 229- Disquisitiones Arithmetics, 151 , 348 234 Disquisitiones generales circa superficies cur- Erlanger Programm, 166-168, 180,203, vas, 44 343, 438 d'Ocagne, Maurice , 330 Euclid, 438 Doctoral degrees in mathematics conferred Euclid's Elements, 3, 344, 428 in the United States , 429, 432, Euclidean geometry, 383 , 384 435-437, 448 Euler's theorem on pentagonal numbers, 121 Doubly infinit e syste m o f simpl e groups , Euler, Leonard, 1 , 63, 102 , 120 , 121 , 12 7 325 Eureka College, 367 Dresden, Arnold, 409, 425 Evans, Griffith C, 434 , 437, 444 Drury College, 411 Evanston Colloquium lectures, 90, 222, 242, Du Bois-Reymond, Paul , 28 294, 296 , 306 , 309 , 325 , 331 , Dual curve, 169 , 341 358, 360 , 363 , 371 , 377 , 394 , Duhamel, Jean Marie Constant, 27 404-406, 408, 417 Dupin cyclides, 212, 337 publication of, 40 2 Dupin's theorem, 16 5 Duren, Jr., William L., 396 Faa de Bruno, Francesco, 10 8 Durfee, Willia m Pitt , 81 , 82, 87 , 97, 126 , Faraday, Michael, 15 6 129, 14 5 Farrar, John, 7, 8 , 12-14 , 16 , 17 , 44 Durfee square , 126 , 12 8 Federov, Evgenii, 311, 323 Dyck, Walthe r von, 177 , 186 , 307 Fenster, Delia Dumbaugh, 431 Ferrers's theorem, 118 , 11 9 Echols, William H., 32 8 Ferrers, Norman M., 11 9 Ecole centrale, 44 9 Fiedler, Wilhelm, 16 3 Ecole Des Beaux-Arts, 297 Fields, J. C, 25 0 Ecole des Mines, 6 Findlay, William, 423 Ecole poly technique, 6, 13 , 297, 428 Fine, Henry Burchard, 192 , 196 , 203, 208, Economic depression of 1893-94, 300, 359 258, 259 , 264 , 356 , 358 , 438 , Eddy, Henr y Turner , 93 , 313 , 317 , 318 , 439,447,448,451 326, 328 , 354 Finite basis theorem, 313 Edison, Thomas Finite division algebr a theorem, 372, 378 Kinetograph, 30 2 Finite fields, 378, 379 Educational Times, 8 5 Finite group theory, 204, 393 Eidgenossische Technische Hochschule (ETH), Finite linear groups, 375, 378, 398 153 Finite simple groups, 377, 381 Eiffel Tower , 300 Finkel, Benjamin F., 411 SUBJECT INDEX 491

First main theorem of invariants, 10 4 German seminar system, 26, 19 0 Fischer, Otto, 19 2 German unification, 15 5 Fisher, George Egbert, 270 German universities, 429, 439 Fiske, Thomas , 267 , 268 , 405 , 406 , 411 , German Universities Exhibit, 307, 308, 310, 412,415 313,337, 35 8 Ford, Lester R., 437 Gesner, Johann Matthias, 15 0 Foster, Michael, 88 Gibbs Chair, 434 Foundations of geometry and analysis, 372, Gibbs lecturer, 434 383 , 437 Four color problem, 93 Gibbs, George, 42 , 371 Gibbs, Josiah Willard, 22, 23, 27-29, 31- Fourier, Joseph, 6, 15 2 33, 45, 94, 355, 357, 434, 446 Fox, Ralph, 450 Gildersleeve, Basil, 58 , 88 Franco-Prussian War , 165 Gill, Charles , 44 Franklin, Fabian, 79, 80, 85, 97, 105 , 107 , Gillespie, David Clinton, 440 116, 117 , 119 , 120 , 122-125 , Gillespie, William, 393, 425 129, 144 , 200 , 214 , 240 , 331 , Gilman, Danie l Coit , 28 , 38 , 53 , 55-58 , 356, 433 72-78, 84 , 85 , 88-92 , 94 , 99 , Franklin, Philip, 447, 448 113, 130 , 131 , 135 , 138-140 , Frechet, Maurice, 414 143, 148 , 186 , 266 , 273 , 277 , Fredholm, Erik, 387, 389, 392 279, 356 , 369 French influences on American mathemat- Girton College, 241, 244 ics, 2 Glaisher, James W. L., 213, 267 Fricke, Robert, 192 , 221, 253, 329, 350 Goethe, Johann, 15 1 Frobenius, Georg, 94, 224, 230, 315 Goldstine, Herman, 446 Fuchs, Lazarus , 182 , 183 , 199 , 208 , 292 , Goodspeed, Thomas W., 275 320, 36 4 Gordan, Paul , 104 , 108 , 157 , 159 , 167 , Function theory, 366 , 367 224, 229 , 230 , 232 , 234 , 315 , Functional analysis, 38 7 334, 335 , 348, 349, 414 Fundamental system , 104 , 106 , 12 0 finiteness theorem , 104-108 , 123 , 12 4 Fundamental syste m of covariants, 10 2 Gore, Joshua W., 78, 79, 97 Gottingen Auditorium building, 243 Galois resolvents, 172 , 17 3 Gottingen Seven, 15 1 Galois theory, 201, 349, 406 Gottingen University, 26, 27, 150, 151, 154, Galton, Francis, 346 157, 159 , 187 , 197 , 199 , 202 , Gates, Frederick T., 275 204, 208 , 209 , 213 , 214 , 217 , Gauss, Car l Friedrich , 50 , 67 , 148 , 151 , 220, 221 , 229 , 231 , 240-243 , 152, 154 , 173 , 189 , 309 , 310 , 246, 271 , 274 , 282 , 285 , 296 , 312, 343 , 347, 438 305, 325 , 347 , 353 , 366 , 367 , Geiser, Car l Friedrich, 340 370, 371 , 430 , 434 , 438 , 440 , General analysis, 387, 390 442, 452, 453 Generating functions, 102 , 119-121, 12 5 mathematics at, 148 , 150 , 15 1 Gentry, Ruth, 240, 241, 243 tradition, 343, 348 Genus p o f a surface, 17 9 Goursat, Edouard, 199 , 414, 443 Genus of an algebraic curve, 15 7 Graphical statics, 170 , 317 Geological Societ y of Pennsylvani a Grashof, Franz, 317 Transactions of the, 42 Grassmann, Hermann, 30, 32, 16 7 Geometric Galoi s theory , 168 , 172 , 173 , Ausdehnungstehre, 30 , 31, 46 209 Graustein, William C, 44 6 Geometry, 99 Greeley, Horace, 297 descriptive, 6 , 1 3 Green, George, 61 imaginary elements in, 16 9 Green, Rufus, 23 8 projective, 6 Gregory, Olinthus, 59 , 62 George II, 15 0 Grenzkreistheorem, 184 , 18 5 Gergonne, Joseph-Diez, 6 Griffin, William , 61 Annates de Mathimatiques pures et ap- Group theory, 93, 253, 292, 368, 372, 375 pligu^es, 6 Group theory and the classification of crys- German idealism, 24 tallographic structures, 311, 322 German neohumanism, 24 Grundformen, 102 , 105 , 10 6 492 SUBJECT INDEX

Grundlagen der Geometrie, 369, 379, 382, Henry, Joseph, 40, 41, 72, 73, 91 417 Hermite, Charles , 92, 123 , 183 , 319 , 326 , 329, 347, 349 Haar, Alfred, 440 Herschel, Si r John, 7, 63 Habilitationsschrift, 198 Herz, Norbert, 310 Habilitationsvortrag, 35 1 Hesse, Otto, 26, 28, 103 , 157 , 170 , 406 Hadamard, Jacques, 414, 443 Hessel, Johann Friedrich Christian, 322 Hall of Manufactures and Liberal Arts, 302 Hestenes, Magnus R., 396 , 446 Hall, Arthur Graham, 236 Heyne, Christian Gottlob, 15 0 Hall, G. Stanley , 177 , 201, 273, 287, 289 Higher plan e curves , 110 , 112 , 286 , 367 , Haller, Albrecht von, 15 0 368 Halphen, Georges, 12 3 Hilbert's 15t h problem, 19 4 Halsted, Georg e Bruce , 78 , 84 , 97 , 107 , Hilbert's 16t h problem, 340 113, 117 , 130 , 132 , 194 , 328 , Hilbert, David , 110 , 111 , 150 , 152 , 154 , 384, 434 181, 190 , 232 , 240 , 313 , 315 , Hamilton, Si r William Rowan , 18 , 30-32, 326, 328 , 333 , 335 , 340 , 344 , 47, 50 , 13 6 348, 369 , 379 , 382 , 383 , 387 , Hancock, Harris , 292, 293, 364, 365, 371, 389, 390 , 393 , 394 , 396 , 410 , 420 414,417,440,444,451-453 Hardy, G . H., 447 Lecture o n "Mathematica l Problems" , Harkness, James, 241, 416 Paris, 1900 , 442 Harnack's theorem, 34 0 school, 442 Harnack, Axel, 340 views o n the foundations o f geometry , Harper, Willia m Rainey , 276-279 , 282 - 345 285, 289 , 290 , 293 , 294 , 304 , Hildebrandt, Theophil Henry, 436 305, 363-365 , 367 , 368 , 370 , Hill's equation, 39 , 46 372, 403 Hill, Georg e William , 35 , 38-40 , 46 , 93 , Harrison, Carter, 359 293, 312 , 320 , 357 , 414 , 415 , Harvard University, 3 , 7, 8, 12 , 15-21, 35, 428, 429, 433, 446, 453 145, 187 , 196 , 197 , 203 , 204 , Hitchcock, F . L, 265 207, 212 , 234 , 237 , 262-264 , Hitler, Adolf, 452 267, 272 , 279 , 286 , 307 , 355 , Hobart College, 14 5 359, 365 , 384 , 386 , 390 , 406 , Hodge, W . V. D., 449 410, 412 , 416 , 429 , 432 , 434 - Hoffman, Banesh , 448 439,442,444-447,451 Hohenzollerns, 15 5 mathematics at, 14 7 Holder, Otto, 192 , 322, 377 Observatory, 3 5 Holgate, Thomas F., 408, 409 Haseman, Charles, 440 Hollabird, William, 297 Haskell, Melle n Woodman , 196 , 197 , 199 , Hollis, Evans, 45 207-209, 223 , 241 , 255 , 258 , Hooker, Joseph, 73, 75 264, 266, 343, 410 Hopkins, Johns, 53, 54, 57, 275 Hassler, Ferdinan d Rudolph , 13 , 33 , 34 , Hough, George W., 31 0 44, 428 Humboldt, Alexander von, 15 1 Hathaway, Arthu r Safford , 97 , 121 , 129 , Humboldt, Whilhelm von, 24 269, 271, 409 Hunt, Richard Morris, 297, 360 Haupt, Paul, 14 1 Huntington, Edwar d Vermilye, 386, 451 Haverford College, 406, 413, 433, 434 Hurwitz, Adolf , 152 , 183 , 185 , 313 , 326 , Hawkins, Hugh, 14 4 328, 344, 348 Hayden, Sophie, 303 Hutchinson, John Irwin, 367, 371, 393, 420, Hayes, Alice, 240 425 Hecke, Erich, 440 Huxley, Thomas, 81 Hedrick, Ear l Raymond, 410, 440, 442 , 16 6 Heffter, Lothar , 329 Hypercomplex numbe r systems, 315 Heller, N. B. , 367, 371,42 2 Hyperelliptic function theory, 320, 368, 394 Hellinger, Ernst , 440 Hypergeometric or Gaussian differential equa- Helmholtz, Heinrich, 31 0 tion, 343 Helmholtz, Hermann von, 27, 31, 198, 306, 351, 352 , 359 Icosahedral equation, 173 , 220, 349 Hendrick, Joe l E., 85 Icosahedral group, 172 , 17 3 SUBJECT INDEX 493

Inflection point s of a cubic curve, 342 mathematics fellowships , 78 , 79 Ingold, Louis, 426 organizational plan , 5 7 Institut de France, 5 , 6 Studies in Historical and Political Sci- Institute fo r Advance d Stud y (IAS) , 447 , ence, 88 452 Johnson, Reverdy, 74 , 86 International Congress of Mathematicians, Jones, George William, 269, 271 Zurich, 1896 , 327 Jordan, Camille , 106 , 163 , 172 , 375, 377- International Mathematical Congress, Chicago 379 (IMCC), 1893, 242, 294-296, 305, Jordan, David Starr , 1 6 327, 331 , 344 , 358 , 363 , 377 , Jordan, Herber t Edwin , 424 378, 393, 398, 402, 407, 430 Journal de I'Ecole poly technique, 6 Proceedings of the, 360 Journal fur die reine und angewandte Math- Publication of , 41 4 ematik, 116 , 15 9 International Mathematical Congress, Hei- Journal of Physiology, 88 delberg, 1904 , 309 International Mathematical Congress, Rome, Karman, Theodor von, 453 1908, 387 Kaestner, Abraham, 15 0 Intuition Kansas State College, 367, 432, 449 geometrical, 34 6 Kelland, Philip, 62 naive, 345 Kellogg, Oliver Dimon, 440, 442, 446 refined, 34 5 Kempe, A. B., 93 Invariance of genus, 15 9 Kenyon College, 11 3 Invariant, 67 , 10 1 Key, Thomas, 6 4 Invariant theory , 69-71 , 93 , 99, 100 , 104 , Kiepert, Ludwig , 16 3 105, 110 , 117 , 131 , 286 , 367 , Killing, Wilhelm, 217 , 234 368 Kirchhoff, Gustav , 28, 156 , 198 , 232, 347 symbolic method of , 10 6 Kirwan, Robert, 9 syzygies, 68 Klein, Anna (ne e Hegel), 243, 246 Irreducible covariants, 102-104 , 10 8 Klein, Christia n Felix , 31 , 90 , 110 , 113 , 138-143, 146 , 147 , 154 , 170 , Jackson Park, 298 , 300, 303 189-191, 199 , 200, 264-266, 271, Jackson, Dunham, 44 4 273, 274 , 286 , 287 , 293 , 294 , Jacobi function, 319 , 320 296, 304 , 330 , 331 , 357 , 370 , Jacobi, Carl Gustav Jacob, 26, 27, 69, 152, 371, 378 , 379 , 390 , 393 , 394 , 157, 177 , 309, 319, 396 400-402, 405 , 406 , 415 , 417 , Jacobian modula r equation, 32 4 430, 431 , 433 , 434 , 437-440 , Jacoby, Harold, 26 7 443,451 James, William J., 27 , 208 his view s o n mathematica l proclivitie s Jeans, James, 439 of differen t ethni c groups, 34 6 Jefferson, Thomas , 13 , 33, 63 lecture courses, 187, 190, 199, 202, 207- Jenney, William LeBaron , 29 7 209, 211 , 214 , 220 , 221 , 228, Horticultural Building , 30 3 354 Johns Hopkins University, The, 28, 33, 40, positivism, 34 6 49, 53 , 54 , 57 , 72 , 75 , 80 , 83, private seminars, 19 9 84,88,90-92,94,99, 131 , 133, protocol books, 19 1 138, 140 , 143 , 145 , 146 , 148 , seminars, 191 , 192, 197 , 199 , 209, 213, 187, 189 , 191 , 200 , 201 , 213, 220, 223,228,247, 37 1 218, 240 , 261-263 , 270 , 272 , Uber Riemanns Theorie der algebrais- 274, 275 , 277 , 279 , 285 , 287 , chen Funktionen und ihrer Inte- 292, 293 , 334 , 365 , 366 , 369 , grate, 228 370, 375 , 410 , 412 , 416 , 417 , Vorlesungen uber das Ikosaeder, 186 , 197, 429, 430 , 432 , 435 , 436 , 439 , 201, 203 , 228 , 230 , 322 , 349 , 445, 448 368 Johns Hopkins University Circulars, 86 , Klein-Poincare correspondence , 18 3 87 Kleinian era in American mathematics, 18 9 mathematical logi c at, 13 0 Kline, J, R., 45 0 Mathematical Seminary, 79, 86, 87, 109, Kneser, Adolf , 394 , 395 117 Kneser, Hellmuth , 44 0 mathematics at, 14 7 Koebe, Paul, 181 , 186 494 SUBJECT INDEX

Kohlstedt, Sall y Gregory, 41 Levy, Maurice, 318 Koniggratz Lichtenberg, Geor g Christoph, 15 0 1866, 15 5 Lie's general theory of contact transforma- Konigsberger, Leo , 26, 28, 240 tions, 33 7 Kovalevskaya, Sofia , 28, 240 Lie's -to-sphere transformation, 165 , 336 Kowalewski, Gerhard , 238 Lie's theory of continuous groups, 323, 325, Krause, Martin, 329 337 Kronecker, Leopold, 27, 152, 161, 163, 166, Lie, Sophus, 142 , 144 , 148 , 161 , 163, 165, 177, 190 , 194 , 199 , 208 , 217 , 167, 190 , 208 , 210 , 217 , 218 , 224, 230, 282, 349 234, 236-239 , 315 , 323 , 336 , Krupp, Alfred, 304 337, 346 , 350 , 351 , 353 , 369 , armory exhibit, 30 3 379, 430 Krupp, Friedrich, 30 4 Lindemann, Ferdinand, 347 Kummer surface, 165 , 337, 341 Line complexes, 156 , 159 , 341 Kummer's theor y o f idea l numbers , 348 , Line coordinates, 15 6 349 Line geometry , 156 , 159 , 161 , 164 , 165 , Kummer, Erns t Eduard, 161 , 190, 368 368 Kundt, August, 27, 19 8 Pluckerian, 163 , 336 Linear differential equations , 368, 406 Laboratory method of teaching, 418 Liouville, Joseph, 27 Lacroix, Silvestre, 7-9, 13 , 50, 64 Lipschitz, Rudolf, 155 , 15 9 Ladd, Christine (later Christine Ladd-Franklin), Little Egypt, 300 83-86, 97 , 116 , 121 , 129 , 132 , Lobachevsky, N., 163 , 166 , 350 133,214,240,242-244 Loewy, Alfred, 39 9 Ladies' and Gentleman's Diary or United Lombard College, Illinois, 1 6 States Almanac, 5 1 London Mathematical Society, 46, 267, 404 Lagrange's problem, 396 Louisiana State University, 45 0 Lagrange's theory of partial differential equa- Lovering, Joseph, 45 tions, 33 7 Lovett, Edga r O., 236-238, 36 9 Lagrange, Joseph-Louis, 1 , 38, 310 , 312 Micanique analytique, 6 7 Lutzen, Jesper, 295 Lame equation, 212 Lame, Gabriel, 212 MacCullagh, James, 50 Land-grant universities, 264 Macfarlane, Alexander , 328 , 329 Landau, Edmund, 333, 440 MacKinnon, Annie, 249, 257 Laplace, Pierre S., 4, 9, 38, 50, 310 MacLane, Saunders, 446 Mecanique celeste, 12 Maclay, J., 268 Lasker, Emanuel, 220 MacMahon, Perc y Alexander, 93, 12 5 Laue, Max von, 323 Macmillan & Co., 403, 404 Law of quadratic reciprocity, 9 3 Maddison, Isabel, 249, 257 Lawrence Scientific School , 18-21 , 35 , 47, Maltby, Margaret , 244, 249 50, 269 Mangoldt, Hans, 396 Lazzaroni, 40, 41 , 182 , 18 5 Lebesgue, Henri, 38 7 Marietta College, 14 5 Lefschetz, Solomon , 434, 449-451 Marrat, William, 42 Legendre, Adrian-Marie, 8, 13, 17, 64, 121, Martin, Artemas, 328 319 Martin, Henry Newell, 5 8 Lehmer, Derrick Norman, 423 Maschke's theorem, 399 Lehr- und Lernfreiheit, 24 , 150 , 19 0 Maschke, Heinrich, 197-200, 202, 203, 222, Leibniz, Gottfried Wilhelm, 17 5 241, 255 , 259 , 290 , 293 , 304 , , 27 , 76 , 175 , 187 , 191 , 307-309, 324 , 326 , 329 , 331 , 192, 203 , 208 , 211 , 234 , 235 , 349, 354 , 361 , 363 , 364 , 366 , 237,238,240,369,381,430 368, 369 , 371 , 373 , 375 , 396 , Mathematics Seminar, 176 , 18 5 399-401,408,420,426,436 Lemoine, Emile , 330 lecture courses, 368 Lennes, Nels Johann, 384, 423 mathematical interests , 393, 398 Lerch, Matyas, 328 teaching style, 370 Lesezimmer, 209 Mason, Charles Max, 414, 440, 442, 444 Leverrier, Urbain, 18 , 50 SUBJECT INDEX 495

Massachusetts Institute of Technology, 214, Mobius transformations, 17 2 217, 233 , 265 , 266 , 355 , 384 , Mobius, August Ferdinand, 175 , 309, 338 445, 447, 451 Modular equations, 174 , 175, 182-184,209, Mathematical Association of America, 419, 230, 324 443 , 17 3 Mathematical astronomy , 38 , 40 Moise, E. E., 450 Mathematical Companion, 51 Molien, Theodor, 192 , 315 Mathematical Correspondent, 43, 51 Monge, Gaspard, 6 , 50 , 336 Mathematical Diary, 44, 51 Monodromy axiom , 35 2 , 99, 13 3 Monthly Scientific Journal, 51 Mathematical Messenger, 5 1 Moore Method, 45 0 Mathematical Miscellany, 44, 45, 51 Moore's doubly-infinit e syste m o f simpl e Mathematical models , 170 , 285, 307, 338, groups, 324 355, 35 8 Moore, Clarence L . E., 265, 447 Mathematical Monthly, 45 Moore, Eliakim Hastings, 23, 202, 222, 254, Mathematical pedagogy , 368 , 415, 418 279, 281 , 282 , 284-286 , 289 , Mathematical research traditions in the United 290, 292-294 , 305 , 306 , 309 , States, 435, 436 313, 324-326 , 330 , 354 , 360 , Mathematical Review, 51 361, 363-366, 369-371, 373, 374, Mathematical Reviews, 392 376-379, 382 , 384 , 386 , 387 , Mathematical Seminary , 11 7 389, 392 , 395 , 399-401 , 404 - Mathematical Tripos, 61, 66, 433 406, 408 , 409 , 412-416 , 418 - Mathematical Visitor, 5 1 420, 423 , 430 , 434-436 , 439 , Mathematics in the federal government: 1776 - 445,446,451 1876, 33 lecture courses, 368 Mathematische Annalen, 142 , 159, 186, 335, mathematical interests , 372, 383 401 teaching style, 369, 370 Mathieu, Emile, 32 5 Moore, Rober t Lee , 382 , 384 , 386 , 393 , Maury, Matthew Fontaine, 3 5 418, 423 , 434 , 436 , 442 , 450 , Maxwell, James Clerk, 31, 317, 433 451 Treatise on Electricity and Magnetism, Moore, Sr., Eliakim Hastings , 281 31, 17 9 Money, Frank, 218 , 406, 416, 433, 435 Mayer's Hotel, 35 6 Morrey, C. B., 447 Mayer, Adolf, 175 , 176 , 186 , 351 Morrill Act, 264, 265, 269 Mayer, Tobias, 15 0 Morris, Charles D'Urban, 5 8 McClintock, Emory , 94 , 355, 413, 415 Morse, Marston, 434 , 444, 446, 447 McCosh, James, 131 , 264 Morse, Samuel F. B., 309 McDonald, John Hector , 393 , 425 Moulton, Francis R., 44 4 McKinney, Thomas Emery , 423 Moutard, Theodore, 164 , 336, 337 McMahon, James, 269, 271 Muhll, Karl von der, 175 , 17 6 McNeish, Harry Franklin, 42 3 Muir, Thomas, 93 McShane, Edward J. "Jimmy", 396 , 446 Miiller, Georg Elias, 240 Messenger of Mathematics, 26 8 Miiller, Johannes (aka Regiomontanus), 17 5 Metric geometry, 16 4 Munchhausen, Gerlac h Adol f von, 15 0 Metz Munich, 17 0 battle sites, 15 5 Meyer, Franz, 323 , 329 Napoleon, Louis, 15 5 Michelson, Albert A. , 289 National Academ y o f Sciences , 41, 42, 45, Midway Plaisance, 30 0 46,48 Miller, George Abram, 203, 235, 238, 239 Proceedings of, 41 Miller, John Anthony, 426 National Researc h Council, 444 Miller, Willard, 21 3 Nautical Almanac, 35, 38, 39, 45, 143, 207, Mineralogical Journal, 42 269, 398, 429 Minimal surfaces , 21 7 Naval Almanac, 14 4 Minkowski space , 352 Naval Observatory, 3 5 Minkowski, Hermann, 190 , 238, 317, 326, Nef, Joh n U. , 289 328, 333 , 352, 440, 442 Netto, Eugen, 328 , 371, 375-377 Mitchell, Oscar Howard , 97 , 121 , 145 Neue Geometrie des Raumes, 156 , 15 9 Mittag-Leffler, Gosta , 46, 183 , 320 Neumann, Carl , 76 , 175 , 17 7 496 SUBJECT INDEX

Neumann, Franz, 26, 50 Partition theory, 99, 116 , 117 , 121 , 125 Neumann, John von, 446 Pascal's theorem, 374 Neumegen, Leopold, 5 9 Pasch, Moritz, 345, 382 New Haven Colloquium lectures, 1906, 387, Patton, Francis, 264 389 Peacock, George , 7 , 62 New York Mathematical Society (late r the Peano, Guiseppe, 38 2 AMS), 42 , 267 , 268 , 355 , 360 , Peckham, Edward L., 407 402-404, 430 Peirce, Benjamin, 8, 12 , 17-21, 32, 33, 35, Bulletin of the (later Bulletin of the AMS), 40, 41 , 44-50 , 65 , 73 , 76 , 80 , 51,268,402,430,431 91,92,94, 112 , 130 , 133,262- New York University, 453 264, 269, 428, 429, 453 Newcomb, Simon , 35 , 38 , 40, 77 , 78 , 89, Peirce, Benjamin Osgood, 19 , 20, 212, 263 90, 92 , 93, 143 , 200, 201, 213, Peirce, Charles Sanders, 19 , 45, 85, 93, 94, 306, 356 , 357 , 411 , 412 , 415 , 99, 130-134,315 , 33 4 428, 453 Peirce, James Mills, 20, 76, 196 , 263 Newton, Hubert Anson, 21-23, 27, 28, 45, Pentagonal number theorem, 121-123,125, 262, 281, 373 129 Newton, Isaac, 9, 338, 344 Periodization of American mathematics, 2, Principia, 9 14, 427, 428 Neyman, Jerzy, 453 Permutation groups, 375 Noble, Charle s A., 257, 440, 443 Perott, Joseph de, 274, 321, 329 Noether, Emmy , 15 2 Perry, Herbert M., 97 Noether, Max , 157 , 159 , 161 , 163 , 224 , Pervouchine, T. M., 330 228, 232-234 , 326 , 328 , 335 , Peterson, Julius, 93 375 PfafF, Johann, 16 7 Non-Euclidean geometry , 109 , 111 , 113 , Philadelphia's American Philosophical So- 131, 166 , 382 ciety Non-Euclidean trigonometry, 11 2 Proceedings of 4 5 Nonions, 32 , 13 7 Phillips, H. B., 265 , 282 , 283 , 286 , Physikalisch-technische Reichsanstalt, 30 6 296,331, 354,404-406,43 9 Picard, Emile, 443 Number theory, 292, 366-368 Pick, Georg, 19 2 Pierpont, James, 406, 412, 434, 435 Ohio Northern University, 41 1 Pincherle, Salvatore, 326, 328 Ohio State University, 445 Planck, Max, 444 Oliver, Jame s Edward , 91 , 210, 211 , 213, Plane curve theory, 11 0 214, 217 , 249 , 264 , 269-271 , Platonic solids, 17 2 307, 331, 355 Playfair, John, 3-6, 12 , 15 Olmsted, Frederick Law , 298 Plucker, Julius , 148 , 155 , 156 , 159 , 161 , Operator theory, 38 7 168, 336, 341, 368 Oresme, Nicole, 34 7 Plucker relation, 15 6 Osgood, William Fogg, 196 , 204, 207-209, Plucker's formulas, 227 214, 218 , 223 , 226 , 229 , 230 , Poincare mode l fo r hyperboli c geometry , 232-234, 253 , 259 , 264 , 286 , 184 343, 350 , 390 , 394 , 406 , 407 , Poincare, Henri, 38, 39, 93, 139, 182-186, 413, 416 , 436 , 437 , 440 , 442 , 200, 274 , 312 , 345 , 347 , 414 , 451 434, 446 Lehrbuch der Funktionentheorie, 20 4 Poisson, Simeon-Denis, 6 , 50 Owens, Frederick William, 423 Polytechnical Institute , Brunswick, 15 3 Oxford University, 5 , 293 Poncelet, Victor, 6, 161 , 317 New College, 79 Porter, Noah, 55 Potential theory , 179 , 211, 214, 367, 368 Padarewski, Ignance, 30 0 Prandtl, Ludwig, 440 Page, James M., 235, 238 Prdzisions-undApproximationsmathematik, Palace of Fine Arts, 302 347 Palidini, Bernard , 310 Preceptorial system, 264 Parabolic geometry, 16 6 Prentiss, Robert W., 97 Parker, Col. Franci s W., 276 , 113 , 132 , 145 , 187 , Parshall, Kare n Hunger, 431 194, 203 , 220 , 237 , 262 , 264 , SUBJECT INDE X 497

266, 356 , 357 , 394 , 412 , 429 , symmetric, 342 433, 435 , 438 , 439 , 444 , 445 , Riemann's 0-functions, 22 7 447-451 Riemann's characteristics, 226, 227 mathematics at, 14 7 Riemann, Berahard , 148 , 152-154 , 157 , Principal congruence subgroup T(n), 17 4 159, 161 , 173 , 178 , 182 , 189 , Principle of continuity, 338 , 340 228, 309, 336, 343, 438 Pringsheim, Alfred, 328 Riemann-Helmholtz-Lie space problem, 325, Privatdozent, 198 351 Product Riemannian function theory, 148, 157, 161, cross, 32 321, 335, 358 direct, 32 Ritt, Joseph F., 434, 444 dot, 32 Ritter, Ernst, 243, 247, 271, 350 skew, 32 Roch, Gustav, 224 Professionalization o f mathematics, 2 , 16, Roche, Martin, 297 40,48 Rockefeller Foundation, 442 Projective classificatio n o f Non-Euclidea n Rockefeller, Joh n D., 275, 279 (elliptic , hyperbolic, Rogers, William .Barton, 265 parabolic), 351 Rohn, Karl, 177 , 341 Projective concept of cross-ratios, 163, 166 Rose Polytechnic Institute, 317 Projective geometry , 103 , 104 , 111 , 366 , Rothe, Heinrich August, 16 7 368 Rothrock, David Andrew, 237, 444 Projective , 209 Rowland, Henry, 58 , 89, 90, 92, 93, 213 Prussian Ministry of Culture, 242, 246, 305- Royal Astronomical Society , 434 307,326,361,415 Royal Institution, Liverpool, 61 Pseudo-Euclidean geometry , 353 Royal Military Academy, Woolwich, 59, 70, Purdue University, 416 100 Purkert, Walter, 295 Royal Society of London, 5 , 434 Putnam, Thomas Milton, 424 Ruckkehrschnitttheorem, 18 5 Rudin, Mary Ellen, 450 Quarterly Journal of Pure and Applied Math- Runge, Carl, 440 ematics, %% Ruprecht, Therese, 204 Quartic curves, 340 Russell, Bertrand, 447 Quaternions, 18 , 30-32, 47 , 50 , 136 , 137 , 367 Salmon, George , 85 , 103 , 105 , 107 , 110 , Quintic equations, 173 , 349 163, 167 , 225, 338, 373 Savilian Professorship of Mathematics, Ox- Ranum, Arthur, 424 ford, 135 , 138 , 13 9 , 6 Sawin, Albert M., 328 Redtenbacher, Ferdinand , 31 7 Scheffers, Georg , 46, 315, 324 Rees, John K., 268 Scheibner, Wilhelm, 17 5 Rees, Mina, 446 Schlegel, Victor, 329 Remsen, Ira, 55, 58, 88 Schmidt(-Ott), Friedrich, 242, 308 Rendiconti del Circolo Matematico di Palermo, Schmidt, Erhard , 440 374 Schoenflies, Arthur , 311, 322, 323, 329 Reuleaux, Franz, 317 Scholz, Erhard, 182 , 18 6 Reye, Theodor, 198 , 342 Schottky, F., 224 Rheticus, Joachim, 17 5 Schroeder, Joseph, 208 Ricci-Curbastro, Gregorio, 19 1 Schubert's calculus, 19 4 Rice Institute, 237, 437 Schur, Friedrich, 177 , 186 , 217, 315, 383 Richardson, Henry Hobson, 297 Schur, Issai, 398 Richardson, Roland G. D., 413, 434, 445, Schur, Wilhelm, 251, 252 452 Schwarz s-functions, 22 0 Richelot, Friedrich, 26 Schwarz, Hermann Amandus, 148, 183, 185, Riedler, Alois, 317 198, 199 , 217, 230, 344 Riemann mapping theorem, 437 Schwarzian derivative, 344 Riemann surfaces, 148 , 152, 157, 161, 168, Scott, Charlotte Angas, 241, 242, 249 169, 178 , 180 , 182-184 , 186 , Second Reich, 15 5 214, 226, 232 Sedan projective, 169 , 341, 342 battle sites, 15 5 498 SUBJECT INDEX

See, T. J. J., 421 320, 329, 410 Segre, Corrado, 438 Strong, Nehemiah, 2 Self-conjugate grap h Strong, Theodore, 44, 45 self-conjugate partition , 126 , 12 8 Struik, Dirk, 233, 265, 295, 447 Serre, Jean-Pierre, 209 Studies from the Biological Laboratory, 8 8 Serret, Joseph, 27, 375, 378 Studley, Duane, 270 Servos, John, 416 Study, Eduard, 46, 177, 185, 194, 208, 310, Siegel, Car l Ludwig, 452 315,328, 329,331,438,44 6 Silliman, Benjamin, 15 , 42, 45 Stufentheorie, 35 0 Simson, Robert, 3 Stufentheorie (o r level theory), 17 4 Sinclair, Mar y Emily, 425 Sturm, Charles, 62, 212 Singularities of algebraic curves, 394 Sturm, Rudolf, 34 2 Singularities of complex potential functions, Sturm-Liouville theory , 392 , 437 179, 18 0 Substitution theory, 367 , 368 Skinner, Ernes t Brown, 415, 426 Sullivan, Louis, 297 Slaught, Herber t Ellsworth, 367 , 368 , 371, Sylvester, James Joseph, 31-33, 38, 49, 53, 375,415,418,423 58, 59 , 61 , 62 , 64-76 , 78-80 , Smith, A. W., 426 83-94, 99 , 100 , 103 , 105-108 , Smith, David Eugene , 268, 421 110, 113 , 116-119 , 123 , 125 , Smith, Henry, 135 , 13 9 127, 130 , 132 , 134 , 135 , 137 - Smith, James Archy, 367, 371 141, 143-145 , 147 , 148 , 186 , Smith, Paul A., 450 187, 189 , 191 , 200 , 225 , 253 , Smith, Percy, 250, 434 266, 273 , 285 , 315 , 319 , 334 , Smithsonian Institution, 41 357, 369 , 370 , 379 , 384 , 411, Snow, B. W., 208, 213 413,417,418,430,431,433 Snyder, Virgil , 217 , 218 , 221 , 253 , 257 - dialytic method, 62 259, 271, 355, 433, 435, 447 law of , 69 Society o f Germa n Natural Scientist s an d lecture courses, 79, 105 , 121 , 123 , 124, Physicians, 359 135, 13 8 Sohncke, Leonard, 322 philosophy of mathematics, 81, 82, 106 Sommerfeld, Arnold , 200 students of, 129 , 14 5 Sousa, John Philip, 300 teaching style, 80-82, 371 South Dakota State College, 401 theory of forms, 6 6 Space curves, 19 4 , 43 2 Sphere geometry, 166 , 217, 33 6 Syzygies, 10 4 Spottiswoode, William, 46 St. John' s College, Cambridge, 61, 11 3 Taber, Henry, 134 , 274, 290, 328, 331 Stabler, Edward, 267 Tait, Peter Guthrie, 30 , 31, 77 , 237 Tamarkin, J. D., 392 Stanford, Leland , 272 Tappan, Henry B., 266 Stanley, Anthony D., 22, 262 Tchebycheff, Pafnuty , 34 7 Staudt, Christian von, 163 , 167 , 169 , 334 Technische Hochschule, 170 , 176 , 19 1 Steenrod, Norman, 450 Temple University, 36 7 Steiner, Jacob, 157 , 16 3 Tetrahedral line complexes, 16 4 Steinhaus, Hugo, 440 Thayer, Majo r Sylvanus, 12-1 4 Steinmetz, Charles , 202 Theorie der Transformationsgruppen, 210 , Stern, Moritz Abraham, 15 2 235,336,351 Stieltjes, Thomas, 387 , 28 , 29 Stokes, George Gabriel, 213, 433 Theta functions, 28 6 Stolz, Otto, 16 3 Thibaut, Bernard , 15 2 Stone, M. H., 434, 446 Thomas, James Carey, 85 Stone, Ormond, 94, 281, 405, 411 Thomas, M. Carey, 85 Story, Willia m E. , 76 , 79 , 80 , 85 , 87-89 , Thomas, T. Y., 448 92, 93 , 99, 108 , 110-112 , 129 , Thomas, Theodore, 297 141, 144 , 200 , 213 , 264 , 274 , Thompson, Henr y Dallas , 203 , 208 , 209 , 289,292,313,331,449 223, 255, 258, 264, 356 lecture courses, 109 , 11 2 Thomson, William , Lor d , 29 , 31 , Stringham, , 97, 112, 177, 334 191, 210 , 259 , 264 , 266 , 319 , Three-body problem, 38, 39, 446 SUBJECT INDE X 499

Topology, 264 University o f Illinois , 398 , 416, 432, 435, Townsend, Edga r Jerome, 416, 440 439, 445 Traiti des Substitutions et des Aquations University of Kansas, 439 algtbriques, 163 University of Konigsberger, 26, 28 Transcendence of n, 347 , 145,203,210, 236, Transcendence of e, 34 7 241, 262 , 266 , 377 , 406 , 432 , Transformation groups, 167, 236-238, 323 436, 442, 445, 450 Treatise on Natural Philosophy, 211 , 354 Triple systems, 371, 375, 376, 379 University of Missouri, 443 Tubingen University, 26 University of Montana, 384 Tucker, Albert W., 450 University of Nebraska, 145 , 432, 449 Tukey, John, 450 University of North Carolina, 14 5 Tulane University, 450 University of Paris, 381, 434, 438, 443 Twain, Mark, 223 University o f Pennsylvania , 2 , 262, 355 , Tyler, Harr y Walter , 208-210 , 214 , 217 , 411,432,450 223, 229-234 , 256 , 259 , 265 , University of , 14 5 313,326,331,353,447,451 University of Strassburg , 198 , 386 University o f Texas , 113 , 145 , 381 , 384 , Ueber die Reihenentwicklungen der Poten- 450 tialtheorie, 21 2 University of Turin, 438 Ulrich, Georg, 15 2 University o f Virginia , 63 , 64 , 145 , 236 , Underhill, Anthon y Lispenard, 425 292,405,411,450 United State s Coasta l Survey , 33-35 , 41 , University o f , 145 , 213 , 242 , 116, 130,266,428,42 9 265, 266 , 354 , 409 , 415 , 432 , United States Military Academy, 1 2 445, 450 United States Patent Office, 14 5 University College London, 59, 62 Van Hise, Charles R., 265 University of Berlin, 24, 26, 27, 143 , 152, Van Name, Addison, 28 161, 163 , 187 , 190 , 194 , 198 , Van Velser, Charles A., 97 199, 202 , 208 , 229 , 230 , 240 , Van Vleck , Edwar d Burr , 207 , 213 , 214 , 241, 282 , 292 , 364 , 434 , 436 , 220, 253 , 256 , 258 , 259 , 265 , 440 331, 354 , 406, 410 University of California, 55-57 , 211, 266, Van Vleck, John Hasbrouck, 410 381, 394 , 398 , 432 , 437 , 443 , Van Vleck , Joh n Monroe , 207 , 313 , 331, 445, 447, 453 354, 355 University of Chicago, 241, 242, 246, 254, Varignon, Pierre, 317 261, 275 , 278 , 279 , 283 , 285 , Vassar College, 84, 85, 354 289, 290 , 292 , 293 , 296 , 297 , Veblen, Oswald , 382-384 , 386 , 393 , 414, 300, 327 , 360 , 361 , 363-369 , 423, 434 , 436 , 439 , 442 , 444 , 374, 381 , 383 , 384 , 389 , 390 , 448,449,451,452 393-396, 398 , 401 , 403 , 404 , Vector, 31, 32 406, 410 , 413 , 415 , 429 , 430 , Vector analysis, 30-32 432, 435 , 436 , 438 , 439 , 442 , venia legendi, 19 8 444,445,447,451 Veronese, Guiseppe, 382 Mathematical Club, 363, 370-372, 374, Versailles, 16 5 375, 377 , 398 , 399 , 406 , 415 , Versailles Treaty, 444 420 Veysey, Laurence, 269 mathematics curriculum, 365, 367 Vienna University, 434 Mathematics Department, 23,202,222, Villa Hiigel, 303 237, 279 , 292-294 , 305 , 363 , Voigt, Woldemar, 243, 251, 252 364, 369, 381 Volterra, Vito, 387 mathematics fellowships, 367, 368, 371 von Maier, 244 summer quarter program, 369 Vorlesungshefu 192 , 199 , 209, 231 University of Cincinnati, 36 5 University of Giessen, 26, 15 7 ^-curves, 164 , 323, 352 University of Greifswald, 43 8 Waerden, B. L. van der, 19 4 University of Heidelberg, 26, 28, 156 , 187, Wait, Lucien Augustus, 269, 271 198, 240 Waldo, Clarence, 331,416 Walker, Buz M., 425 500 SUBJECT INDEX

Wallman, Henry, 450 Woods, Frederick Shenstone, 207, 214, 221, Walsh, Joseph L., 233, 446 247, 256-258 , 265 , 354 , 406 , Wangerin, Alfred, 21 2 447 Ward, John, 3 Woodward, Robert, 415 Washburn College, 367 World's Columbian Exposition of 1853 (WCE), Watson, James, 91 New York, 297 Weaver, Warren, 444 World's Columbian Exposition of 188 9 (WCE), Webber, Samuel, 3 Paris, 300 Weber, Heinrich, 153 , 224, 243, 246, 309, World's Columbian Exposition of 1893 (WCE), 313,326,328,368,386 Chicago, 242, 294-296, 359,407, Weber, Wilhelm, 15 1 411 Wedderburn, Josep h H. M. , 47 , 371 , 378, Congresses at the, 303 439 World's Congress Auxiliary, 303 , 310 Weichold, Guido, 93 World's Parliament of , 303, 304 Weierstrass p-function, 17 3 Wranglers, 433 Weierstrass, Karl , 27, 148 , 159 , 161 , 163, Wundt, Wilhelm, 17 6 173, 174 , 177 , 183 , 189 , 190 , 198, 199 , 202 , 229 , 230 , 240 , Yale University , 15 , 16 , 20 , 21 , 23 , 28 , 282, 319 , 320 , 334 , 393-395 , 55,57, 145,250,262,279,281 , 437 355, 365 , 373 , 406 , 429 , 432 , Wellesley College, 244 434, 445, 448 Wesleyan University , 207 , 208 , 213 , 354 , Department of Philosophy and the Arts, 355 21 mathematics at, 14 7 School of Applied Chemistry, 21 Westfall, John Van Etten, 237 School of Engineering , 21 Weyl, Hermann , 152 , 154 , 181 , 186 , 440, Sheffield Scientifi c School , 21 , 24 , 55 , 452 317 Die Idee der Riemannschen Fldche, 181, Young, Gail, 450 186 Young, Jaco b W . A., 292 , 293 , 368 , 371, Weyr, Edouard, 329 375,377,415,420 White City, 298, 360 Young, John Wesley, 439 White, Andrew D., 54, 55, 269 White, Henr y Seely , 157 , 207-209 , 211 , Zeuthen, H. G., 295 , 340 214, 223-226 , 228 , 233 , 253 , Ziwet, Alexander, 210, 259, 266, 331, 333, 255, 256 , 258 , 259 , 274 , 285 , 406, 409 286, 292 , 306 , 313 , 331 , 350 , Zurich, 15 3 354, 360 , 402 , 404-406 , 408 , 422, 430, 433, 440 Whitehead, J. H. C, 44 8 Whitman, C. O., 289 Whitney, Hassler , 447 Whyburn, G. T., 450 Wiener, Norbert, 204, 265, 434, 444, 447, 451 Wilczynski, Erns t Julius, 398, 436 Wilder, R. L., 450 Wilhelm I, 16 5 , 386 Wilson, Norman Richard, 425 Wilson, Woodrow, 264, 439, 444 preceptors, 394 Wiman, A., 401 Winston, Mar y Frances (May) (late r New- son), 241-243 , 246 , 249 , 250 , 252, 257 , 258 , 331 , 354 , 367 , 370, 371, 420 Wirtinger, Wilhelm, 350 Woman's Building, 303