34 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Bar-Ilan UniversityIL6 papers
- Russian University of TransportRU6 papers
- Northern Arizona UniversityUS4 papers
- Uniwersytet Komisji Edukacji Narodowej w KrakowiePL4 papers
- Institute of MathematicsPL2 papers
- Novosibirsk State UniversityRU2 papers
- Sobolev Institute of MathematicsRU2 papers
- University of the Basque CountryES2 papers
- Lviv UniversityUA1 paper
6 papers
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…
Is Leibnizian calculus embeddable in first order logic?
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +4
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus o…
Small oscillations of the pendulum, Euler's method, and adequality
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1
Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well…
Controversies in the foundations of analysis: Comments on Schubring's Conflicts
Piotr Blaszczyk, Vladimir Kanovei, Mikhail Katz +1
Foundations of Science recently published a rebuttal to a portion of our essay it published two years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his…
Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
Vladimir Kanovei, Mikhail G. Katz, Thomas Mormann
We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but t…