9780821821244

Mathematics Unbound

by ;
  • ISBN13:

    9780821821244

  • ISBN10:

    0821821245

  • Format: Hardcover
  • Copyright: 2002-06-01
  • Publisher: Amer Mathematical Society

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Summary

Although today's mathematical research community takes its international character very much for granted, this ''global nature'' is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom thegoal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians andmathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interestedin the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.

Table of Contents

Acknowledgments xiii
List of Contributors
xv
Photograph and Figure Credits xxi
The Evolution of an International Mathematical Research Community, 1800-1945: An Overview and an Agenda
1
Karen Hunger Parshall
Adrian C. Rice
Introduction
1(1)
Internationalization, Internationalism, Transnationalism, Supranationalism, Multinationalism, Denationalization,...: What's in a Word`?
2(3)
The Timeframe: 1800-1945
5(1)
The Internationalization of a Mathematical Research Community, 1800-1945: A First Vintage
6(5)
A Second Vintage and Beyond
11(3)
References
14(3)
The End of Dominance: The Diffusion of French Mathematics Elsewhere, 1820-1870
17(44)
Ivor Grattan-Guinness
Multinationalism vs. Internationalism
17(1)
French Dominance
18(2)
Translating the French
20(4)
Declin?
24(1)
Case Study 1: Real-Variable Analysis
25(2)
Case Study 2: Complex-Variable Analysis
27(1)
Case Study 3: From Energy Mechanics to Energetics
28(2)
Case Study 4: Celestial Mechanics, Especially Perturbations
30(2)
Case Study 5: The Influence of Gauss
32(1)
Concluding Remarks
33(1)
References
34(5)
Appendix
39(6)
Spanish Initiatives to Bring Mathematics in Spain into the International Mainstream
45
Elena Ausejo
Mariano Hormigon
The International Mainstream: A Problem of Definition
45(1)
The Enlightenment
46(2)
The Nineteenth Century
48(3)
The Role of Individuals in History
51(2)
The First Third of the Twentieth Century
53(4)
Conclusion
57(1)
References
58(3)
International Mathematical Contributions to British Scientific Journals, 1800-1900
61(28)
Sloan Evans Despeaux
Introduction
61(1)
Foreign Mathematics in British General Science Journals
62(4)
British Specialized Science Journals as a Venue for Foreign Mathematics
66(3)
Changes in Foreign Participation through the Nineteenth Century
69(7)
A Geographical Profile of the Publication Community
76(3)
Society Involvement and Personal Influence: Factors in Foreign Participation
79(4)
Conclusions
83(1)
References
83(6)
International Participation in Liouville's Journal de mathematiques pures et appliquees
89(16)
Jesper Lutzen
Introduction
89(1)
The National Enterprise
89(2)
Foreign Contributions to Liouville's Journal
91(2)
Countering the Sense of French Self sufficiency
93(2)
International Inspirations for Liouville's Work: Mechanics
95(2)
International Inspirations for Liouville's Work: Potential Theory
97(1)
International Inspirations for Liouville's Work: Differential Geometry
98(2)
Conclusion
100(1)
References
101(4)
The Effects of War on France's International Role in Mathematics 1870-1914
105(18)
Helene Gispert
Introduction
105(1)
The Creation of a National Mathematical Society: Nationalism and Professionalization
106(4)
Structuralization of the SMF: Establishing an Academic Center
110(1)
A Non-academic Periphery: Actors in and Values of the AFAS
111(4)
Foreign Contributions to the Journals of the SMF and the AFAS
115(2)
Center and Periphery: From National Contexts to the International Scale
117(2)
Conclusion
119(1)
References
120(3)
Charles Hermite and German Mathematics in France
123(16)
Thomas Archibald
Introduction
123(1)
Hermite and German Mathematical Values
124(2)
Hermite's Critique of Radicalism
126(2)
The Promotion of Franco-German Relations in Mathematics
128(3)
Bringing German Mathematics to French Students: A Thankless Task
131(2)
German Mathematics and the French Mathematical Research Community
133(2)
Concluding Remarks
135(1)
References
136(3)
Gosta Mittag-Leffler and the Foundation and Administration of Acta Mathematica
139(26)
June E. Barrow-Green
Introduction
139(9)
The Founding of Acta Mathematica
148(1)
Poincare, Cantor, Kovalevskaya, and Acta Mathematica
148(7)
Acta Mathematica Volumes 1-20
155(3)
Conclusion
158(3)
References
161(4)
An Episode in the Evolution of a Mathematical Community: The Case of Cesare Arzela at Bologna
165(14)
Laura Martini
The Bolognese Context
165(1)
Galois Theory in the European Curriculum
166(3)
Arzela's Sources for the Lectures
169(1)
The Ruffini-Abel Theorem
170(5)
Conclusions
175(1)
References
175(3)
Appendix
178(1)
The First International Mathematical Community: The Circolo matematico di Palermo
179(22)
Aldo Brigaglia
Introduction
179(1)
The Circolo matematico di Palermo in the Sicilian Cultural Milieu
179(1)
The Circolo matematico di Palermo in the Italian Mathematical Milieu
180(3)
The Role of Giovan Battista Guccia in the Circolo
183(3)
The Circolo and the Internationalization of Mathematical Research
186(1)
A Decade of Great Development, 1904-1914
187(8)
The Decline
195(3)
Conclusions
198(1)
References
199(2)
Languages for Mathematics and the Language of Mathematics in a World of Nations
201(28)
Jeremy J. Gray
Introduction
201(1)
A World of Nations
201(2)
National Languages
203(2)
International Languages in General
205(1)
International Languages in Particular
206(3)
Language, Meaning, and Mathematics: Calculation and Pasigraphy
209(2)
Is Mathematics a Language?
211(1)
Universal Language and Calculating Language
212(2)
Nineteenth-century Linguistics
214(2)
Language, Meaning, and Mathematics: Significs
216(2)
Language, Meaning, and Mathematics: Hilbert and Husserl
218(3)
Language, Meaning, and Mathematics: Hilbert and Schroder
221(2)
Conclusion
223(1)
References
224(5)
The Emergence of the Japanese Mathematical Community in the Modern Western Style, 1855-1945
229(24)
Chikara Sasaki
Japanese Mathematics from Traditional to Modern
229(1)
Chinese Mathematics and Its Reform in Seventeenth-Century Japan
230(1)
Learning Western Mathematics as Military Science, 1855-1868
231(1)
Educational Reform during the Early Meiji Period, 1868-1877
232(4)
The University of Tokyo and the Tokyo Mathematical Society, 1877-1881
236(1)
The Germanization of the Political System and of Learning, 1881-1945
236(2)
``For the Nation!'' Fujisawa and Mathematical Research at Tokyo
238(5)
The Kyoto University School
243(1)
The Tohoku University School
243(3)
The Other Colleges and Universities
246(1)
Towards Democratization and Internationalization after World War II
246(1)
Conclusion: General Characteristics of Mathematical Studies in Modern Japan
247(2)
References
249(4)
Internationalizing Mathematics East and West: Individuals and Institutions in the Emergence of a Modern Mathematical Community in China
253(34)
Joseph W. Dauben
Introduction
253(1)
Modern Science Emerges in China: The Self-Strengthening Movement
254(2)
The Beijing Tongwen Guan (1861-1862)
256(2)
The Shanghai Tongwen Guan (1863-1864) and the Jiangnan Arsenal (1865)
258(2)
The Fuzhou Shipyard (1866)
260(2)
Educational Reform and the ``Reign of One Hundred Days''
262(1)
Japan as an Early Role Model
263(1)
England: Supporting the Rise of Mathematics in Modern China
264(4)
France: Contributing to the Transmission of Modern Mathematics to China
268(2)
Germany: A Model for Developing Modern Mathematics in China
270(2)
The United States
272(3)
New Institutional Models
275(1)
Universities
276(1)
The Chinese Mathematical Society
277(4)
Conclusion
281(1)
References
282(5)
Chinese-U.S. Mathematical Relations, 1859-1949
287(24)
Yibao Xu
Introduction
287(1)
The Boxer Indemnity and the Modernization of Chinese Mathematics
288(6)
Harvard: An Educational Center for Chinese Mathematicians
294(2)
The Institute for Advanced Study: A Bridge Between the U.S. and China
296(5)
Two Unsuccessful Invitations
301(3)
Conclusion
304(1)
References
305(6)
American Initiatives Toward Internationalization: The Case of Leonard Dickson
311(24)
Della Dumbaugh Fenster
Introduction
311(2)
Dickson in the Emergent Period of American Mathematics
313(5)
Dickson's Research: The International Exchange of Mathematical Ideas
318(5)
Dickson and the Publication of Manuscripts and Book-length Treatises
323(5)
American Mathematics: Unbound
328(1)
References
329(6)
The Effects of Nazi Rule on the International Participation of German Mathematicians: An Overview and Two Case Studies
335(24)
Reinhard Siegmund-Schultze
Introduction
335(1)
Internationalization: A Complex of Factors
336(3)
Germany Immediately after 1933: The Dogma of Antisemitism
339(3)
Case Study 1: German Participation in the Oslo ICM, July 1936
342(3)
Case Study 2: WWII and German International Participation: Harald Geppert and Wilhelm Suss
345(2)
Conclusions
347(2)
References
349(3)
Appendix
352(7)
War, Refugees, and the Creation of an International Mathematical Community
359(22)
Sanford L. Segal
Introduction
359(1)
Before World War I
360(2)
World War I and After
362(6)
Hitler's Germany and Mathematical Refugees
368(3)
The United States: Country of Refuge for Mathematicians
371(4)
Internationalism under American Leadership
375(1)
References
376(5)
The Formation of the International Mathematical Union
381(18)
Olli Lehto
Introduction
381(1)
Background
381(3)
The First International Congresses of Mathematicians
384(1)
World War I and its Aftermath
385(2)
The Birth of the IMU
387(2)
Opposition to the Policy of Exclusion
389(2)
The Dissolution of the IMU
391(1)
Conclusion
392(1)
Epilogue: The New IMU
393(2)
References
395(4)
Index 399

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