Related papers: Edward Nelson (1932-2014)
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…
In this note, we take another look at some arithmetic identities of N.J. Fine associated with divisor functions. We connect these functions with indefinite quadratic forms using a result due to Andrews. As a consequence, arithmetic theorems…
We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is…
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, Leibniz, Euler, Cauchy and other giants of infinitesimal…
We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in Banach algebras, from a paper by Skandalis and the author…
One of the "deepest" theorems in mathematics is Endre Szemer\'edi's theorem about the inevitability of arithmetical progressions. Here we try to nibble at it, by doing "finite" analogs. This is already interesting for its own sake, but we…
This is the introductory paper to the special issue of Topology and Its Applications entirely dedicated to the theory of continuous selections of multivalued mappings. Since the pioneering work of Ernest Michael from 1956 can rightfully be…
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…
This is a short obituary of Saunders Mac Lane (1909--2005).
This biographical account of the life and work of David Kendall includes details of his personal and professional activities. Kendall is probably best known for his work in applied probability, especially queueing theory, and in stochastic…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
The mathematical achievements of Harry Kesten since the mid-1950s have revolutionized probability theory as a subject in its own right and in its associations with aspects of algebra, analysis, geometry, and statistical physics. Through his…
This is a short overview of the origins of distribution theory as well as the life of Sergei Sobolev (1908--1989) and his contribution to the formation of the modern outlook of mathematics.
This article is a personal overview of the work of Dennis Sullivan who was awarded the 2022 Abel prize. It was commissioned by the Bulletin of the (Indian) Mathematics Consortium, and it will appear there.
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
The article is dedicated to thye memory of a distinguished mathematician Professor Misha Shubin
Ernest Henley's contributions to understanding isospin symmetry and the experimental and theoretical progress that followed are reviewed. Many experimentalists and theorists worked to bring Ernest's early vision of the subject to fruition.…
Complete infinite multisum sets are eventually linear. After 30 years of sitting in a file cabinet, the proof (thanks to James H. Schmerl) is brought from darkness into light.
An exposition of smooth infinitesimal analysis, which is a way to do calculus with nilsquare infinitesimals, is given.