Related papers: Edward Nelson (1932-2014)
As is now well known, the generalization of the square of opposition to a hexagon was discovered independently by three philosophers in the early 1950s: Paul Jacoby, Augustin Sesmat, and Robert Blanch\'{e} . Much less well known is the…
Work in progress concerning alternative formalizations of arithmetic.
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
Irving Ezra Segal (1918-1998) has proposed some axioms for mathematical cosmology. These are here re-examined and Segal's redshift formula and energy conservation in the Einstein universe are established in full on their basis. A detailed…
Besides the better-known Nelson's Logic and Paraconsistent Nelson's Logic, in "Negation and separation of concepts in constructive systems" (1959), David Nelson introduced a logic called S with the aim of analyzing the constructive content…
In this paper we revisit the work of E.T. Bell concerning partition polynomials in order to introduce the reciprocal partition polynomials. We give their explicit formulas and apply the result to compute closed formulae for some well-known…
This contribution to the book in honour of J.S. Bell will probably differ from the remaining ones, in particular since only a part of it will be devoted to specific technical arguments. In fact I have considered appropriate to share with…
C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Assuming just a few elementary facts in field theory and the exclusion-inclusion formula, we show how one see the…
Errico Presutti was a leading figure in mathematical physics and an important contributor to rigorous results in statistical mechanics. Due to his strong scientific personality and human qualities, there are many who remember Errico…
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the…
The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and…
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
Infinitesimals are natural products of the human imagination. Their history goes back to the Greek antiquity. Their role in the calculus and analysis has seen dramatic ups and downs. They have stimulated strong opinions and even vitriol.…
This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…
We present an overview of some of Alberto Collino's work which uses the Griffiths infinitesimal invariant of a normal function.
In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of Newton's method. In this paper we reconsider his algorithm in…
The need to describe abrupt changes or response of nonlinear systems to impulsive stimuli is ubiquitous in applications. Also the informal use of infinitesimal and infinite quantities is still a method used to construct idealized but…
We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871-1956).
The knotted solitons introduced by Faddeev and Niemi is presently a subject of great interest in particle and mathematical physics. In this paper we give a condensed matter interpretation of the recent results of Faddeev and Niemi.
John Desmond Bernal (1901-1970) was one of the most eminent scientists in molecular biology, and also regarded as the founding father of the Science of Science. His book The Social Function of Science laid the theoretical foundations for…