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Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms
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Apr 2017
Tiziana Bascelli
Piotr Blaszczyk
Alexandre Borovik[...]
David Sherry
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weie...
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Interpreting the Infinitesimal Mathematics of Leibniz and Euler
Article
May 2016
Jacques Bair
Piotr Blaszczyk
Robert Ely[...]
Steven Shnider
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 17th and 18th century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass's ghost behind some of the received hi...
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