67 citations · 151 across the 6 of their papers we have counts for
6 papers · 1 filter
When does a hyperbola meet its asymptote? Bounded infinities, fictions, and contradictions in Leibniz
Mikhail G. Katz, David Sherry, Monica Ugaglia
In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of…
Leibniz on bodies and infinities: rerum natura and mathematical fictions
Mikhail G. Katz, Karl Kuhlemann, David Sherry +1
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpret…
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…
A non-standard analysis of a cultural icon: The case of Paul Halmos
Piotr Blaszczyk, Alexandre Borovik, Vladimir Kanovei +4
We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his p…
Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
Mikhail G. Katz, David Sherry
Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's h…
Ten Misconceptions from the History of Analysis and Their Debunking
Piotr Blaszczyk, Mikhail G. Katz, David Sherry
The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesi…