Abstract
When talking about the status of the history of mathematics, one possible approach would be a summary of what has been published by other historians of mathematics concerning their own field.1 In the light of so many different thoughts and opinions concerning the history of mathematics, I am less interested in summarizing what others have done already than in giving my own account of what constitutes history of mathematics now and possibly in the future. This subjective element is not an expression of disrespect for the work others have done; rather it concedes the many restrictions that every account like this must suffer. I name only two. As a member of what I should call for simplicity’s sake the European culture, my opinions and judgements necessarily depend on this specific cultural back-ground; they might be different, even very different, had I been brought up in China or in India. A second restriction concerns specialization in the history of mathematics as a subject. I have worked for many years on the history of probability theory as a major field of research. Probability theory belongs to applied mathematics. Because my examples for different current forms of the history of mathematics are taken from the history of probability theory, one might well question whether they adequately represent the history of mathematics generally.
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References
Representative and very useful are a series of articles of Christoph J. Scriba on the history of mathematics and its uses in teaching mathematics like Geschichte der Mathematik, in: Überblicke Mathematik 1 (ed. D. Laugwitz), Mannheim 1968, p. 9–33, or The place and function of a’ historical introduction’ in the curriculum of mathematics students, Historia Mathematica 2 (1975), 327–331. An overview concerning the history of modern mathematics is given by Philip Kitcher and William Aspray in their “opinionated introduction„ to William Aspray and Philip Kitcher (eds.): History and Philosophy of Modern Mathematics, University of Minnesota Press, Minneapolis 1990, p. 20–31.
Comp. Ivo Schneider: Hintergrund und Formen der Mathematikgeschichte des 18. Jahrhunderts, which will appear in Archives Internationales d’Histoire des Sciences.
Histoire de l’Académic Royale des Sciences Année 1699, edition printed in Amsterdam 1706, p. 4.
Histoire de l’Académie Royale des Sciences Année 1719, edition printed in Amsterdam 1723, p. 114.
Letter from August 20, 1713 in: [Montmort], Essay d’Analyse, second edition, Paris 1713, p. 399.
Jean Etienne Montucla: Histoire des Mathématiques, two vols., vol.1, Paris 1758, p. IX.
Nouveau plan d’une histoirt de l’esprit humain, printed in the Mercure de France 1745/46.
Voltaire: Essay sur l’Histoire Générale et sur les Moeurs et l’Esprit des Nations depuis Charlemagne jusqu’a nos Jours, Genève 1756.
Jacques-Bénigne Bossuet: Discours sur l’histoire universelle à Monseigneur le Dauphin pour expliquer la suite de la religion et les changements des empires, Paris 1681.
Montucla (note 6), p. V.
Friedrich von Schiller: Was heißt und zu welchem Ende studiert man Universalgeschichte?, Jena 1789.
Abraham Gotthelf Kästner: Geschichte der Mathematik seit der Wiederherstellung der Wissenschaften bis an das Ende des achtzehnten Jahrhunderts, 4 vols., Göttingen 1796–1799.
Moritz Cantor: Vorlesungen über Geschichte der Mathematik, 4 vols., Leipzig 1880–1908.
Isaac Todhunter: A History of the Progress of the Calculus of Variations During the Nineteenth Century, Cambridge 1861; A History of the Mathematical Theory of Probability From the Time of Pascal to That of Laplace, Cambridge 1865; A History of the Mathematical Theories of Attraction and the Figure of the Earth From the Time of Newton to That of Laplace, 2 vols., London 1873; A History of the Theory of Elasticity and of the Strength of Materials From Galilei to the Present Time (ed. by Karl Pearson), 2 vols., Cambridge 1886/1893.
Otto Toeplitz: Das Problem der Universitätsvorlesungen über Infinitesimalrechnung und ihrer Abgrenzung gegenüber der Infinitesimalrechnung an den höheren Schulen, Jahresbericht der Deutschen Mathematiker-Vereinigung 36 (1927), 88–100.
Harold M. Edwards: Galois Theory (= Graduate Texts in Mathematics, vol. 101), New York / Heidelberg / Berlin / Tokyo (Springer) 1984.
Charles Henry Edwards: The historical development of the calculus, New York / Heidelberg / Berlin (Springer) 1979.
Donald Mackenzie: Statistics in Britain, 1865–1930: The Social Construction of Scientific Knowledge, Edinburgh University Press 1981.
Lorraine Daston: Classical Probability in the Enlightenment, Princeton University Press 1988.
Michael Crowe: Ten “Laws„ Concerning Patterns of Change in the History of Mathematics, Historia Mathematica 2 (1975), 161–166, and Herbert Mehrtens: T. S. Kuhn’s Theories and Mathematics: a Discussion Paper on the “New Historiography„ of Mathematics, Historia Mathematica 3 (1976), 297–320.
Thomas Crump: The Anthropology of Numbers, Cambridge Universtity Press 1990.
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Schneider, I. (1992). The History of Mathematics: Aims, Results, and Future Prospects. In: Demidov, S.S., Rowe, D., Folkerts, M., Scriba, C.J. (eds) Amphora. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8599-7_28
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DOI: https://doi.org/10.1007/978-3-0348-8599-7_28
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