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

Research output: Contribution to journalComment/debate

29 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 languageEnglish
Pages (from-to)848-864
Number of pages17
JournalNotices of the American Mathematical Society
Volume61
Issue number8
DOIs
StatePublished - Sep 2014

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