34 citations · 88 across the 17 of their papers we have counts for
17 papers
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…
Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow
Tiziana Bascelli, Emanuele Bottazzi, Frederik Herzberg +6
Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Th…
Is mathematical history written by the victors?
Jacques Bair, Piotr Blaszczyk, Robert Ely +9
We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leib…
Almost equal: Method of adequality from Diophantus to Fermat and beyond
Mikhail G. Katz, David M. Schaps, Steven Shnider
We analyze some of the main approaches in the literature to the method of `adequality' with which Fermat approached the problems of the calculus, as well as its source in the paris…
Relative systoles of relative-essential 2-complexes
Karin U. Katz, Mikhail G. Katz, Stephane Sabourau +2
We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely pre…
Cayley 4-form, comass, and triality isomorphisms
Mikhail G. Katz, Steven Shnider
Following an idea of Dadok, Harvey and Lawson, we apply the triality property of SO(8) to study the comass of certain self-dual 4-forms on R^8. In particular, we prove that the Cay…