Selected Title s i n This Serie s 23 Kare n Hunge r Parshal l an d Adria n C . Rice , Editors , Mathematic s unbound : Th e evolution o f a n internationa l mathematica l researc h community , 1800-1945 , 200 2 22 Bruc e C . Bernd t an d Rober t A . Rankin , Editors , Ramanujan : Essay s an d surveys , 2001 21 Arman d Borel , Essay s i n the histor y o f Li e groups an d algebrai c groups , 200 1 20 Kolmogoro v i n perspective, 200 0 19 Herman n Grassmann , Extensio n theory , 200 0 18 Jo e Albree , Davi d C . Arney , an d V . Frederic k Rickey , A station favorabl e t o th e pursuits o f science : Primary material s i n the histor y o f mathematics a t th e Unite d State s Military Academy , 200 0 17 Jacque s Hadamar d (Jerem y J . Gra y an d Ab e Shenitzer , Editors) , Non-Euclidea n geometry i n the theor y o f automorphic functions , 199 9 16 P . G . L . Dirichle t (wit h Supplement s b y R . Dedekind) , Lecture s o n numbe r theory , 1999 15 Charle s W . Curtis , Pioneer s o f representation theory : Frobenius , Burnside , Schur , an d Brauer, 199 9 14 Vladimi r Maz'y a an d Tatyan a Shaposhnikova , Jacque s Hadamard , a universa l mathematician, 199 8 13 Lar s Garding , Mathematic s an d mathematicians : Mathematic s i n Swede n befor e 1950 , 1998 12 Walte r Rudin , Th e wa y I remember it , 199 7 11 Jun e Barrow-Green , Poincar e an d th e thre e bod y problem , 199 7 10 Joh n Stillwell , Source s o f hyperbolic geometry , 199 6 9 Bruc e C . Bernd t an d Rober t A . Rankin , Ramanujan : Letter s an d commentary , 199 5 8 Kare n Hunge r Parshal l an d Davi d E . Rowe , Th e emergenc e o f the America n mathematical researc h community , 1876-1900 : J . J . Sylvester , Feli x Klein , an d E . H . Moore , 1994 7 Hen k J . M . Bos , Lecture s i n the histor y o f mathematics, 199 3 6 Smilk a Zdravkovsk a an d Pete r L . Duren , Editors , Golde n year s o f Mosco w mathematics, 199 3 5 Georg e W . Mackey , Th e scop e an d histor y o f commutative an d noncommutativ e harmonic analysis , 199 2 4 Charle s W . M c Arthur, Operation s analysi s i n the U.S . Army Eight h Ai r Forc e i n Worl d War II , 199 0 3 Pete r L . Dure n e t al. , Editors , A century o f mathematics i n America , par t III , 198 9 2 Pete r L . Dure n e t al. , Editors , A century o f mathematics i n America, par t II , 198 9 1 Pete r L . Dure n e t al. , Editors , A century o f mathematics i n America , par t I , 198 8 This page intentionally left blank MATHEMATICS UNBOUND: The Evolution of an International Mathematical Research Community, 1800-1945 This page intentionally left blank https://doi.org/10.1090/hmath/023 HISTORY OF MATHEMATICS Volum e 23 MATHEMATICS UNBOUND: The Evolution of an International Mathematical Research Community, 1800-1945 Karen Hunger Parshall Adrian C. Rice Editors America n Mathematica l Societ y Londo n Mathematica l Societ y Editorial Boar d American Mathematica l Societ y Londo n Mathematica l Societ y George E . Andrew s Davi d Fowler , Chai r Joseph W . Daube n Jerem y J . Gra y Karen Parshall , Chai r To m Korne r Michael I . Rose n Pete r Neuman n 2000 Mathematics Subject Classification. Primar y 01A55 , 01A60 , 01A70 , 01A72 , 01A73 , 01A74, 01A80 . A complet e listin g o f photograph an d figur e credit s appear s o n pag e xxi . Library o f Congres s Cataloging-in-Publicatio n Dat a Mathematics unboun d : th e evolutio n o f a n internationa l mathematica l researc h community , 1800-1945 / Kare n Hunge r Parshall , Adria n C . Rice , editors . p. cm . — (Histor y o f mathematics, ISS N 0899-242 8 ; v. 23 ) Includes bibliographica l reference s an d index . ISBN 0-8218-2124- 5 (acid-fre e paper ) 1. Mathematics—Research—History—19t h century . 2 . Mathematics—Research—History — 20th century . 3 . Mathematics—History—19t h century . 4 . Mathematics—History—20t h cen - tury. I . Parshall, Karen Hunger, 1955 - II . Rice, Adrian C . (Adrian Clifford) , 1970 - III . Series. QA11.2.M28 200 2 510'.72~dc21 2002022744 Copying an d reprinting . Individua l reader s o f thi s publication , an d nonprofi t librarie s acting fo r them , ar e permitted t o mak e fai r us e o f the material , suc h a s to cop y a chapter fo r us e in teachin g o r research . Permissio n i s grante d t o quot e brie f passage s fro m thi s publicatio n i n reviews, provide d th e customar y acknowledgmen t o f the sourc e i s given . Republication, systemati c copying , or multiple reproduction o f any material i n this publicatio n is permitte d onl y unde r licens e fro m th e America n Mathematica l Society . Request s fo r suc h permission shoul d b e addressed t o the Acquisitions Department , America n Mathematica l Society , 201 Charle s Street , Providence , Rhod e Islan d 02904-2294 , USA . Request s ca n als o b e mad e b y e-mail t o reprint-permissionOams.org . © 200 2 by the America n Mathematica l Society . Al l rights reserved . Printed i n the Unite d State s o f America . The America n Mathematica l Societ y retain s al l right s except thos e grante d t o the Unite d State s Government . @ Th e pape r use d i n thi s boo k i s acid-free an d fall s withi n th e guideline s established t o ensur e permanenc e an d durability . The Londo n Mathematica l Societ y i s incorporated unde r Roya l Charte r and i s registered wit h th e Charit y Commissioners . Visit th e AM S hom e pag e a t URL : http://www.ams.org / 10 9 8 7 6 5 4 3 2 1 0 7 06 0 5 0 4 03 0 2 Contents Acknowledgments xii i List o f Contributors x v Photograph an d Figur e Credit s xx i Chapter 1 . Th e Evolutio n o f a n Internationa l Mathematica l Researc h Community, 1800-1945 : A n Overvie w an d a n Agend a KAREN HUNGE R PARSHAL L AN D ADRIA N C . RIC E 1 Introduction 1 Internationalization, Internationalism , Transnationahsm , Supranationahsm , Multinationalism, Denationalization , .. : What's i n a Word? 2 The Timeframe : 1800-194 5 5 The Internationalizatio n o f a Mathematica l Researc h Community , 1800-1945: A First Vintag e 6 A Second Vintag e an d Beyon d 1 1 References 1 4 Chapter 2 . Th e En d o f Dominance : Th e Diffusio n o f Frenc h Mathematic s Elsewhere, 1820-187 0 IVOR GRATTAN-GUINNES S 1 7 Multinationalism vs . Internationalism 1 7 French Dominanc e 1 8 Translating th e Frenc h 2 0 Declinl 2 4 Case Study 1 : Real-Variabl e Analysi s 2 5 Case Study 2 : Complex-Variabl e Analysi s 2 7 Case Study 3 : Fro m Energ y Mechanic s to Energetics 2 8 Case Stud y 4 : Celestia l Mechanics , Especiall y Perturbation s 3 0 Case Study 5 : Th e Influenc e o f Gauss 3 2 Concluding Remark s 3 3 References 3 4 Appendix 3 9 Chapter 3 . Spanis h Initiative s t o Brin g Mathematic s i n Spai n int o th e International Mainstrea m ELENA AUSEJ O AN D MARIAN O HORMIGO N 4 5 The International Mainstream : A Problem o f Definition 4 5 The Enlightenmen t 4 6 The Nineteenth Centur y 4 8 The Rol e o f Individuals i n History 5 1 viii CONTENT S The Firs t Thir d o f the Twentiet h Centur y 5 3 Conclusion 5 7 References 5 8 Chapter 4 . Internationa l Mathematica l Contribution s t o Britis h Scientifi c Journals, 1800-190 0 SLOAN EVAN S DESPEAU X 6 1 Introduction 6 1 Foreign Mathematic s i n Britis h Genera l Scienc e Journal s 6 2 British Specialize d Scienc e Journal s a s a Venu e fo r Foreig n Mathematic s 6 6 Changes i n Foreig n Participatio n throug h th e Nineteent h Centur y 6 9 A Geographica l Profil e o f the Publicatio n Communit y 7 6 Society Involvement an d Persona l Influence : Factor s i n Foreign Participation 7 9 Conclusions 8 3 References 8 3 Chapter 5 . Internationa l Participation i n Liouville's Journal de mathematiques pures et appliquees JESPER LUTZE N 8 9 Introduction 8 9 The Nationa l Enterpris e 8 9 Foreign Contribution s t o Liouville' s Journal 9 1 Countering th e Sens e o f Frenc h Self-sufficienc y 9 3 International Inspiration s fo r Liouville' s Work : Mechanic s 9 5 International Inspiration s fo r Liouville' s Work : Potentia l Theor y 9 7 International Inspiration s fo r Liouville' s Work : Differentia l Geometr y 9 8 Conclusion 10 0 References 10 1 Chapter 6 .