Related papers: Simone Weil, Andr{\'e} Weil, Bourbaki and Pythagor…
In the first attempt to introduce gauge theories in physics, Hermann Weyl, around the 1920s, proposed certain scale transformations to be a fundamental symmetry of nature. Despite the intense use of Weyl symmetry that has been made over the…
Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in…
This note is devoted to a detail concerning the work of Albert Einstein and Peter Bergmann on unified theories of electromagnetism and gravitation in five dimensions. In their paper of 1938, Einstein and Bergmann were among the first to…
Feza G\"ursey was a brilliant physicist who loved symmetries and beautiful mathematical structures such as group theory and division algebras. In this centenary year, I give a brief review of some of his contributions and then zero-in on…
The main goal of this expository article is to survey recent progress on the arithmetic Siegel-Weil formula and its applications. We begin with the classical sum of two squares problem and put it in the context of the Siegel-Weil formula.…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis,…
This article is a transcription of a video of a 1972 lecture by Jean Dieudonn\'e, enhanced with composite still images from the video. The lecture covers the same material as an earlier paper and lecture notes by Dieudonn\'e, but the live…
This paper attributes the sudden emergence of mathematical probability and statistics in the second half of the seventeenth century to Calvin's Reformed theology. Calvin accommodated Epicurean chance with Stoic determinism and synthesised…
The Pythagorean Theorem is one of the oldest, more famous and more useful theorems of Mathematics, and possibly the one that has had the most impact in the evolution of this and other sciences. In this article, we look at it from different…
These are expanded notes for a short series of lectures, presented at the University of Luxembourg in 2017, giving an introduction to some of the ideas of supersymmetry and supergeometry. In particular, we start from some motivating facts…
Part 1 : For more than two millennia, ever since Euclid's geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time,…
In a recent paper Carot et al. considered carefully the definition of cylindrical symmetry as a specialisation of the case of axial symmetry. One of their propositions states that if there is a second Killing vector, which together with the…
A cycle is algebraically trivial if it can be exhibited as the difference of two fibers in a family of cycles parameterized by a smooth scheme. Over an algebraically closed field, it is a result of Weil that it suffices to consider families…
Given two non-zero integers $a$ and $b$ there exist integers $m$ and $n$ for which $am-bn =(a,b)$. An increasing number of mathematicians have been calling this `B\'ezout's identity', some encouraged by finding "identit\'e de B\'ezout" in…
In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincar\'e and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has…
Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)--to Klein. We will see that they are not rivalling but are tied (by…