30 citations · 199 across the 25 of their papers we have counts for
17 papers · 1 filter
What makes a theory of infinitesimals useful? A view by Klein and Fraenkel
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theore…
Cauchy, infinitesimals and ghosts of departed quantifiers
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for t…
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Tiziana Bascelli, Piotr Blaszczyk, Alexandre Borovik +7
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…
Gregory's sixth operation
Tiziana Bascelli, Piotr Blaszczyk, Vladimir Kanovei +6
In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under sc…
Toward a history of mathematics focused on procedures
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +3
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Thei…
Interpreting the infinitesimal mathematics of Leibniz and Euler
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
We apply Benacerraf's distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations…