Writing the History of Mathematics: Its Historical Development / Edition 1

by Joseph W. Dauben, Christoph J. Scriba

Overview

As an historiographic monograph, this book offers a detailed survey of the professional evolution and significance of an entire discipline devoted to the history of science. It provides both an intellectual and a social history of the development of the subject from the first such effort written by the ancient Greek author Eudemus in the Fourth Century BC, to the founding of the international journal, Historia Mathematica, by Kenneth O. May in the early 1970s.

Product Details

ISBN-13:	9783764361679
Publisher:	Birkhäuser Basel
Publication date:	11/11/2002
Series:	Science Networks. Historical Studies , #27
Edition description:	Softcover reprint of the original 1st ed. 2002
Pages:	689
Product dimensions:	7.01(w) x 10.00(h) x 0.39(d)

Table of Contents

I Countries.- 1 France.- 1.1 Introduction.- 1.2 Changing Appreciation of the Ancients, from the Renaissance to the Seventeenth Century.- 1.3 History of the Progress of the Human Mind (in the Enlightenment).- 1.3.1 Fontenelle, the Initiator of a Tradition.- 1.3.2 The Historical Dimension of the Encyclopedia Project.- 1.3.3 Montucla’s Monumental Work.- 1.4 Historiography in Revolutionary Times.- 1.5 The Reform of Society Through the Sciences: Positivism.- 1.6 Oriental Studies and the History of Mathematics in the Nineteenth Century.- 1.6.1 Collaboration Between Scientists and Orientalists.- 1.6.2 Academic Controversies on the History of Arabic Mathematics.- 1.6.3 François Woepcke’s Research.- 1.7 The History of Mathematics by Mathematicians: Chasles and his Successors.- 1.8 The Spread of Historical Work in Journals and the Broadening of the Subjects Treated.- 1.9 The History of Mathematics in Relation to the General History of Science: Paul Tannery.- 1.10 Nationalist Tendencies.- 1.11 Philosopher-Scientists of the Twentieth Century.- 1.12 The History of Mathematics and the Institutionalization of the History of Science Between the Two World Wars.- 1.13 The Historical Epistemology of Gaston Bachelard.- 1.14 Towards an Autonomous History of Mathematics After the Second World War.- 1.15 The Centre Alexandre Koyré and Research on the History of Mathematics.- 1.16 History According to Bourbaki.- 1.17 Further Developments.- 1.18 Conclusion.- 2 Benelux.- 2.1 Geographical and Political Considerations.- 2.2 Humanist-Inspired Return to the Sources.- 2.3 Catalogues of Mathematicians.- 2.4 The Eighteenth Century.- 2.5 Historiography of Mathematics in the Kingdom of the Netherlands 1815–1830.- 2.6 Historiography of Mathematics in Belgium after 1830.- 2.7 Historiography of Mathematics in the Netherlands after 1830.- 2.8 Amateurs and Professionals, Journals and Societies.- 2.9 Conclusion.- 3 Italy.- 3.1 Introduction.- 3.2 The Rediscovery of Classical Mathematics.- 3.3 Interlude: Contributions of the Jesuits.- 3.4 The History of Mathematics in the Enlightenment.- 3.5 History as a Research Topic for Mathematicians.- 3.5.1 Pietro Cossali.- 3.5.2 Gregorio Fontana.- 3.5.3 Giovanni B. Venturi and Pietro Franchini.- 3.5.4 The Influence of Lagrange.- 3.5.5 Guglielmo Libri.- 3.6 The Risorgimento and the Search for Italian Forerunners.- 3.7 Boncompagni’s “Bullettino” and Its Influence.- 3.8 The History of Mathematics in the Early Twentieth Century.- 3.8.1 The School of Peano in Turin.- 3.8.2 The School of Enriques in Bologna.- 3.9 Second Interlude: Galileo and Leonardo.- 3.10 The Emergence of Professional Historians.- 3.10.1 GinoLoria.- 3.10.2 Ettore Bortolotti.- 3.11 Enriques and the Institute for the History of Science in Rome.- 3.12 After World War II.- 3.13 Conclusion.- 4 Switzerland.- 4.1 Introduction.- 4.2 Humanism and Enlightenment.- 4.3 The Contribution of the “Naturforschende Gesellschaften”.- 4.4 The Major Editions.- 4.5 Further Developments.- 4.6 Conclusion.- 5 Germany.- 5.1 Introduction.- 5.2 The Beginnings.- 5.2.1 The First Glimmer: Regiomontanus and Some Successors.- 5.2.2 Two Extremes: Leibniz and Wolff.- 5.2.3 Three Additional Eighteenth-Century German Authors.- 5.2.4 Mathematician, Bibliographer and Epigrammatist: Kästner.- 5.3 First Half of the Nineteenth Century.- 5.3.1 Prom Watch-Maker to Professor of Technology: Poppe.- 5.3.2 Handbooks and History: Klügel and Mollweide.- 5.3.3 Opposite Twins? Nesselmann and Arneth.- 5.4 From 1850 up to World War I.- 5.4.1 The “Philologists”: Editions of Texts.- 5.4.2 Hermann Hankel and Moritz Cantor: First Comprehensive Studies.- 5.4.3 Günther and Braunmühl: On the Way to Professionalism.- 5.4.4 Felix Klein and His “Vorlesungen.” Editions of “Collected Works”.- 5.5 Between the Wars.- 5.5.1 More Studies on Arabic Mathematics.- 5.5.2 Toeplitz, Neugebauer, and Bessel-Hagen: The “Kiel-Göttingen-Bonn Group”.- 5.5.3 Wieleitner, Tropfke, and Their Successors Vogel and Hofmann.- 5.6 History of Mathematics Under the Third Reich.- 5.7 The German Democratic Republic.- 5.8 The Federal Republic of Germany.- 5.9 History of Mathematics in a Reunited Germany.- 5.10 Conclusion.- 6 Scandinavia.- 6.1 Introduction.- 6.2 Early Publications on the History of Mathematics.- 6.3 National Interests.- 6.4 Professional History of Mathematics.- 6.5 Eneström’s Scientific History of Mathematics.- 6.6 Zeuthen’s Historical Mathematics.- 6.7 Text Editions.- 6.8 After Eneström and Zeuthen.- 6.9 Conclusion.- 7 The British Isles.- 7.1 Introduction.- 7.2 Prior to the Early Twentieth Century.- 7.3 Studies of Special Topics.- 7.4 Largely Historians of Newton.- 7.5 Some Cambridge Historians.- 7.6 The Royal Society Catalogue of Scientific Papers.- 7.7 Historians of Greek Mathematics.- 7.8 General Writing to the First World War.- 7.9 Pearson and the History of Statistics.- 7.10 Between the Wars.- 7.11 After the Second World War.- 7.12 Conclusion.- 8 Russia and the U.S.S.R..- 8.1 Introduction.- 8.2 History of Mathematics Before 1917 179 The First Post-Revolutionary Years: Formation of the Soviet School.- 8.3 Research Schools After World War II.- 8.4 Dominant Postwar Research Themes and Publication Formats.- 8.5 Social Dimensions of the History of Mathematics After World War II.- 8.6 Conclusion.- 9 Poland.- 9.1 Early Developments.- 9.2 Twentieth-Century Contributions.- 9.3 Conclusion.- 10 Bohemian Countries.- 10.1 Introduction.- 10.2 Beginnings.- 10.3 History of Mathematics 1750–1850.- 10.4 The Mid-19th Through the Mid-20th Century.- 10.5 History of Mathematics in Czechoslovakia Since 1945.- 10.6 Conclusion.- 11 Austria.- 11.1 Introduction.- 11.2 Regiomontanus and Tannstetter.- 11.3 Decline and Revival.- 11.4 The “Encyklopädie”.- 11.5 Recent Developments.- 11.6 Conclusion.- 12 Greece.- 12.1 The Classical and Hellenistic Periods.- 12.2 The Byzantine Period.- 12.3 Voulgaris and the Athonian Academy.- 12.4 The Ionian Academy.- 12.5 The Greek National State (1822 to the Present).- 12.6 Conclusion.- 13 Spain.- 13.1 Introduction.- 13.2 Polemics With Respect to Sixteenth-Century Spanish Mathematicians.- 13.3 Mathematics in the Liberal State.- 13.4 Conclusion.- 14 Portugal.- 14.1 Introduction.- 14.2 The Beginnings: Garção Skier.- 14.3 The Second Half of the Nineteenth Century: Francisco de Castro Freire.- 14.4 The Golden Age of Portuguese Historiography of Mathematics: 1900–1940.- 14.5 The Modern Period: 1940–1970.- 14.6 Conclusion.- 15 The Americas.- 15.1 Introduction.- 15.2 South America.- 15.2.1 Historiographical Remarks.- 15.2.2 Conquest and Early Colonial Times.- 15.2.3 The Established Colonies.- 15.2.4 Independent Countries.- 15.2.5 The Twentieth Century.- 15.2.6 Current Developments.- 15.2.7 Conclusion.- 15.3 Mexico.- 15.3.1 The Creation and Development of the Royal University.- 15.3.2 After Independence.- 15.3.3 The Emergence of Modern Mathematics in Mexico in the Twentieth Century: The Autonomous National University.- 15.3.4 The Faculty of Sciences.- 15.3.5 The Nightmare: The 1968 Student Movement.- 15.3.6 Conclusion.- 15.4 United States of America.- 15.4.1 Introduction.- 15.4.2 History of Mathematics in the United States: Early Efforts Through World War I.- 15.4.3 Increasing Professionalization: History of Mathematics and History of Science.- 15.4.4 Recent History of Mathematics in the United States.- 15.4.5 Conclusion.- 15.5 Canada.- 15.5.1 Before 1966.- 15.5.2 Kenneth O. May.- 15.5.3 The Situation Today.- 16 Japan.- 16.1 The Prewar Period, 1868-1945: The Flowering of the Study of the History of Japanese Mathematics.- 16.1.1 End? Toshisada and His Successor Mikami Yoshio.- 16.1.2 The Tōhoku School.- 16.2 The Postwar Period, 1945–1986: Beginnings of the Serious Study of the History of Western Mathematics.- 16.3 Conclusion.- 17 China.- 17.1 The Decline of Traditional Chinese Mathematics.- 17.2 Early Authors.- 17.3 The “Qian-Jia School” and Its Successors.- 17.4 The Modern Scholars.- 17.5 Conclusion.- 18 India.- 18.1 Introduction.- 18.2 Beginnings of Indigenous Historiography.- 18.3 Modern Historical Studies and Historiography of Indian Mathematical Sciences.- 18.4 Indian Historians.- 18.5 The Twentieth Century.- 18.6 Conclusion.- 19 Arab Countries, Turkey, and Iran.- 19.1 Introduction.- 19.2 Exchanges with Western Europe.- 19.3 A New Start for Historiography of Science and Mathematics.- 19.4 Diverse Attitudes towards History of Science and Mathematics.- 19.5 Trends in History of Mathematics in Iran and Turkey.- 19.6 The New Institutions.- 19.7 Conclusion.- 20 Postscriptum.- 20.1. The Character of Historiography.- 20.2 George Sarton’s Views.- 20.3 Interrelations.- 20.4 On the History of Historiography.- 20.5 Functions of Historiography.- 20.6 Institutional Factors.- 20.7 History of Mathematics and Mathematics Education.- 20.8 History of Mathematics: Recent Trends.- 20.9 Electronic Resources.- 20.10 The Humanism of Mathematics.- II Portraits and Biographies.- Portraits.- Biographies.- III Abbreviations, Bibliography, and Inde.- Abbreviations.

Editorial Reviews

"This book, a historiographical one, is very useful as a reference.... The book is unique. It should be in all libraries that support graduate level history and philosophy of science and mathematics. Other libraries should consider purchasing it. Individuals familiar with the subject may wish to own it. Beginners should start with histories." —Mathematical Reviews

"It is really a valuable monograph which should be studied by every historian of mathematics." —Zentralblatt Math

"How good is the book? Well, quite good.... The main content of the other half is a collection of brief biographies of many significant historians of mathematics. I am very glad to have these.... Meanwhile, most history fanatics will want to have access to this book. . . . The upshot is that this is a book that should be in any library that tries to have a complete set of historical source material." —MAA Online

"This historiographic monograph is a great step forward, both in restoring this image and in detailing how histories of mathematics have been written.... The value of this book is further enhanced by a glossary of foreign terms and an extensive index. Anyone who is interested in the history of mathematics will enjoy and use this work.... Highly recommended." —CHOICE

"Forty-four authors from many countries contributed. …There is biography section with portraits, as well as an extensive bibliography." —BookNews

From the Publisher