Krakow: Copernicus.īorovik, A., & Katz, M. Controversies in the foundations of analysis: Comments on Schubring’s conflicts. Foundations of Science, 18(1), 43–74.īłaszczyk, P., Kanovei, V., Katz, M., & Sherry, D. Ten misconceptions from the history of analysis and their debunking. Studia ad Didacticum Mathematicae V, 129–142. Annales Academiae Paedagogicae Cracoviensis. A note on Otto Hölder’s treatise Die Axiome der Quantität und die Lehre vom Mass. The analyst, a discourse addressed to an infidel mathematician.īłaszczyk, P. Numerosities of labelled sets: A new way of counting. The Philosophical Review, 74, 47–73.īenci, V., & Di Nasso, M. Cambridge: Cambridge University Press.īenacerraf, P. A primer of infinitesimal analysis (2nd ed.).
#MATH INFINITESIMALS ARCHIVE#
Archive for History Exact Sciences, 4, 1–144.īell, J. HOPOS: The Journal of the International Society for the History of Philosophy of Science, 6(1), 117–147.īeckmann, F. Leibniz vs Ishiguro: Closing a quarter-century of syncategoremania. Notices of the American Mathematical Society, 61(8), 848–864.īascelli, T., Błaszczyk, P., Kanovei, V., Katz, K., Katz, M., Schaps, D. Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow. Is mathematical history written by the victors? Notices of the American Mathematical Society, 60(7), 886–904.īascelli, T., Bottazzi, E., Herzberg, F., Kanovei, V., Katz, K., Katz, M., et al. Berlin and New York: de Gruyter.īair, J., Błaszczyk, P., Ely, R., Henry, V., Kanovei, V., Katz, K., Katz, M., Kutateladze, S., McGaffey, T., Schaps, D., Sherry, D. In Ursula Goldenbaum & Douglas Jesseph (Eds.), Infinitesimal differences: Controversies between Leibniz and his contemporaries (pp. Leery Bedfellows: Newton and Leibniz on the status of infinitesimals. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves.Īrthur, R. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. The Leibnizian law of continuity similarly finds echoes in Euler. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. We apply Benacerraf’s distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others.
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