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In his 2014 book, Giovanni Ferraro writes at beginning of chapter 1, section 1 on page 7: Capitolo I Esempi e metodi dimostrativi Introduzione In The Calculus as Algebraic Analysis, Craig Fraser, r …

Some aspects of Euler's work were formalized in terms of modern infinitesimal theories by Laugwitz, McKinzie, Tuckey, and others. Referring to the latter, G. Ferraro claims that "one can see in operat …

This is a reference request prompted by some intriguing comments made by Felix Klein. In 1908, Felix Klein formulated a criterion of what it would take for a theory of infinitesimals to be successfu …

This question does NOT concern the RIGOR, or lack thereof, of the early calculus. Rather the question is of its CONSISTENCY. George Berkeley wrote in 1734 with reference to the early calculus that s …

Hilbert's lecture at the ICM in Paris in 1900 presented 10 of the famous 23 open problems. It is well known that the idea of the lecture came from Hermann Minkowski. Hilbert was at Göttingen at the ti …

Recently two formerly unknown articles by Errett Bishop (1928-1983) were posted online by Martín Escardó. One is entitled "A general language", deals with constructive type theory, and is 28 pages lon …

Lagrange is famous for his attempt to found analysis algebraically using power series expansions, an approach that, as we know today, is limited to analytic functions. Lagrange is also known as the in …

Concerning the structure of the learner's mind, psychologist Piaget claimed that There exists, as a function of the development of intelligence as a whole, a spontaneous and gradual construction of e …

It is well known among historians of Fermat that, while his technique of adequality prepared the ground for the general framework later developed by Leibniz and Newton, Fermat himself gave very little …

This pdf by David Joyce notes that in paragraph 66 of his famous essay, Dedekind claims to prove the existence of an infinite set. The proof exploits the assumption that there exists a set $S$ of all …

Fermat had a friend at Toulouse named Lalouvère. Lalouvère was censor, jesuit, and mathematician (in alphabetical order). Antonella Romano writes on page 512 of her book La Contre-Réforme Mathémat …

The invention of intrinsic differential geometry is usually attributed to Gauss in the context of his theorema egregium but the notion of the curvature of an embedded surface existed before. Who was t …

The original impetus for Sophus Lie's work was apparently to streamline the solution of certain problems of variational type such as those treated in the work of Euler and Lagrange. This presumably i …

Can one justify Leibniz's formalism in a suitable algebraic or topological context? We have published some papers recently where we argue that Leibniz's formalism for the calculus wasn't inconsisten …

Cauchy proved a sum theorem for series of continuous functions in 1821, and published another article on the subject in 1853. Michael Segre, writing in Archive for History of Exact Sciences, claimed …