Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Tiziana Bascelli; Emanuele Bottazzi; Frederik Herzberg; Vladimir Kanovei; Karin U. Katz; Mikhail G. Katz; Tahl Nowik; David Sherry; Steven Shnider

doi:10.1090/noti1149

Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Tiziana Bascelli
, Emanuele Bottazzi
, Frederik Herzberg
, Vladimir Kanovei
, Karin U. Katz
, Mikhail G. Katz
, Tahl Nowik
, David Sherry
, Steven Shnider

Department of Mathematics

History and philosophy of science
University of Trento
Bielefeld University
Russian University of Transport
Northern Arizona University

Research output: Contribution to journal › Comment/debate

32 Scopus citations

Abstract

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.

Original language	English
Pages (from-to)	848-864
Number of pages	17
Journal	Notices of the American Mathematical Society
Volume	61
Issue number	8
DOIs	https://doi.org/10.1090/noti1149
State	Published - Sep 2014

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AU - Nowik, Tahl

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Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

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