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- Institute for Information Transmission ProblemsRU14 papers
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6 papers · 1 filter
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…
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…
Euler's lute and Edwards' oud
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1
In a piece published in 1981, H. M. Edwards touts the benefits of reading the masters. A quarter-century later, Edwards takes seriously his own advice by publishing an encomium on…