This is a survey of several approaches to the framework for working with infinitesimals and
infinite numbers, originally developed by Abraham Robinson in the 1960s, and their …

In the history of infinitesimal calculus, we trace innovation from Leibniz to Cauchy and
reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores …

What was Leibniz's take on ''impossible''numbers? Gottfried Wilhelm Leibniz (1646–1716)
described imaginary roots, negative numbers, and infinitesimals as useful fictions. But did he …

We apply Benacerraf's distinction between mathematical ontology and mathematical
practice (or the structures mathematicians use in practice) to examine contrasting …

We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss,
Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal …

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified
propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the …

In a piece published in 1981, HM Edwards touts the benefits of reading the masters. A
quarter-century later, Edwards takes seriously his own advice by publishing an encomium …

Abstract The Mathematical Intelligencer recently published a note by Y. Sergeyev that
challenges both mathematics and intelligence. We examine Sergeyev's claims concerning …

This collection of various texts on Karl Marx and Mathematics is the revised and extended
second edition of the Special Supplement to Karl Marx, Mathematical Manuscripts (1994; …

Abstract We examine Paul Halmos' comments on category theory, Dedekind cuts, devil
worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory …