67 citations · 818 across the 113 of their papers we have counts for
6 papers · 1 filter
Leibniz's well-founded fictions and their interpretations
Jacques Bair, Piotr Blaszczyk, Robert Ely +2
Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contras…
A footnote to The crisis in contemporary mathematics
Boris Katz, Mikhail G. Katz, Sam Sanders
We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the…
Klein vs Mehrtens: restoring the reputation of a great modern
Jacques Bair, Piotr Błaszczyk, Peter Heinig +3
Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Kl…
Monotone subsequence via ultrapower
Piotr Blaszczyk, Vladimir Kanovei, Mikhail G. Katz +1
An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus p…
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…
Fermat's dilemma: Why did he keep mum on infinitesimals? and the European theological context
Jacques Bair, Mikhail G. Katz, David Sherry
The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparent…