Related papers: Edward Nelson (1932-2014)
From 1929 to his death in 1944, A. Eddington worked on developing a highly ambitious theory of fundamental physics that covered everything in the physical world, from the tiny electron to the universe at large. His unfinished theory…
This is a survey of some of Erd\H os's work on bases in additive number theory.
A homage to the life and mathematics of John K. S. McKay. Obituary for the Bulletin of the London Mathematical Society.
About global and local algebraic integrability of ovals. A contribution to clarify Newton results and relative comments on his work done by Arnol'd and Pourciau. A possibile application to air damper sections computation is offered, as…
The contributions of Emmy Noether to particle physics fall into two categories. One is given under the rubric of Noether's theorem, and the other may be described as her important contributions to modern mathematics. These are discussed…
This is a brief overview of some turning points in the history of infinitesimals.
We give a survey of the use of infinitesimals within mathematical analysis to rigorously deal with the delta-function from physics, and more generally, with distributions in the sense of L. Schwartz. We use the framework of nonstandard…
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career…
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, including the approaches of Simeon-Denis Poisson,…
A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The developed approach has a pronounced applied character and is based on the principle `The…
We give an introduction to vertex algebras using elementary forward difference methods originally due to Isaac Newton.
This article is a brief Retrospective on the life and work of Robert W. Zwanzig, who formulated nonequilibrium statistical mechanics and who passed away in May of this year.
In 1938 E. T. Bell introduced "The Iterated Exponential Integers". He proved that these numbers may be expressed by polynomials with rational coefficients. However, Bell gave no formulas for any of the coefficients except the trivial one,…
Infinitesimals have seen ups and downs in their tumultuous history. In the 18th century, d'Alembert set the tone by describing infinitesimals as chimeras. Some adversaries of infinitesimals, including Moigno and Connes, picked up on the…
It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context. The aim of this text is to show the converse is the case and invite the reader to…
We discuss the scientific contributions of Edsger Wybe Dijkstra, his opinions and his legacy.
Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings…
Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on the intelligibility of the continuum reveals challenging…
A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy's sentiment that a null sequence "becomes" an infinitesimal. We…
A look back at Kenneth Wilson's contributions to theoretical physics, with some reminiscences of the professor I encountered at Cornell during the 1980s.