Writing the History of Mathematics: Its Historical Development

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Joseph W. Dauben
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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 Mathem
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.