Related papers: Friendly views on Claude Chevalley
We further explore the notion of Ulam words considered by Bade, Cui, Labelle, and Li, giving some lower bounds on how many there are of a given length. Gaps between words and words of special type also reveal remarkable structure. By…
An early phase of theoretical high energy physics in Israel specifically that connected with Yuval Ne'eman and a small group of my classmates, myself, and several others who worked around him after his return to Israel on the "Eight-fold…
Some mathematical properties of the Erd\"os number and its formal equivalents are shown. An informetric equivalent is presented: the Rousseau number. This contribution honors Ronald Rousseau for his 73th birthday.
Following earlier work by Michel Bitbol and Laura de La Tremblaye which examines QBism from the perspective of phenomenology, this short paper explores points of contact between QBism and Maurice Merleau-Ponty's essay The intertwining--the…
Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.
The author describes some of his experiences as a mathematician cooperating with diabetes specialists.
Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian…
A portrait of Kurt Goedel with emphasis on his work on relativity theory and idealistic philosophy.
This article is an extended version of the article published by EDP Sciences at the occasion of the 150 years of the ``Soci\'et\'e Fran\c{c}aise de Physique'' (in French)
Determining all rational points on a curve of genus at least 2 can be difficult. Chabauty's method (1941) is to intersect, for a prime number p, in the p-adic Lie group of p-adic points of the jacobian, the closure of the Mordell-Weil group…
In the century since Einstein's anno mirabilis of 1905, our concept of the Universe has expanded from Kapteyn's flattened disk of stars only 10 kpc across to an observed horizon about 30 Gpc across that is only a tiny fraction of an…
I discuss Ren{\'e} Thom's approach to philosophy based on his mathematical background. At the same time, I will highlight his connection with Aristotle, his criticism of the modern view of science as a predictive process, his ideas on…
Ideas about a duality between gauge fields and strings have been around for many decades. During the last ten years, these ideas have taken a much more concrete mathematical form. String descriptions of the strongly coupled dynamics of…
This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the…
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide…
The aim of this article has been to put together various aspects of the personality of the Italian mathematician Francesco Severi: the mathematical, the political, the institutional, academic and philosophical one. We tried in particular to…
The form and function of a collaborative assessment known as a "Buddy Quiz" is presented. The assessment is conducted in three successive phases over a contiguous 45- to 60-minute class period. A portion of each Quiz is completed in…
The goal of this paper is to review the advances that were made during the last few decades in the study of the entropy, and in particular the entropy method, for Kac's many particle system.
Ce m\'emoire r\'ealis\'e \`a l'IUFM de Cr\'eteil en 1998 sous la direction d'Evelyne Barbin \'etudie l'histoire du d\'ebut du calcul des probabilit\'es. Sources: correspondance entre Pascal et Fermat, et Trait\'e du triangle arithm\'etique…