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In November 2014 Alexander Grothendieck passed away at the age of 86. There is no doubt that he was one of the greatest and most innovative mathematicians of the 20th century. After a bitter childhood, his meteoric ascent started in the…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
The notion of Poisson manifold with compatible pseudo-metric was introduced by the author in [1]. In this paper, we introduce a new class of Lie algebras which we call a pseudo-Rieamannian Lie algebras. The two notions are strongly related:…
Children can take many paths to become scientists. But they undoubtedly include the following steps Play, play and play; Observe; Ask (themselves). In this paper I will talk about some of my experiences teaching girls and boys, teenagers…
We review the work of Dominic Welsh (1938-2023), tracing his remarkable influence through his theorems, expository writing, students, and interactions. He was particularly adept at bringing different fields together and fostering the…
Mikhail Lomonosov (1711-1765) was the eminent Russian polymath and a towering figure of the European Enlightenment. This English translation of Mikhail Lomonosov seminal work "Oration on the Origin of Light " draws from its original Russian…
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an…
The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and…
This paper is intended both an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past twenty years. It is…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
Students entering engineering in universities of applied sciences were tested to see whether they understood easy Science problems within the first week of the first semester. The test comprised of mathematics and physics questions in both…
Th\'eophile De Donder, a Belgian mathematician born in Brussels, elaborated two important ideas that created a bridge between thermodynamics and chemical kinetics. He invented the concept of the degree of advancement of a reaction, and, in…
In this article, we present new comments to the article On Kant's First Insight Into The Problem of Space Dimensionality and Its Physical Foundations. In particular, we discuss how the space concept is designed in the first writing of Kant.…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
We describe the early evolution of theories with fermion-boson symmetry
A noncommutative (NC) version of Poisson geometry was initiated by Van den Bergh by introducing at the level of associative algebras the formalism of double Poisson brackets. Their key property is to induce (standard) Poisson brackets under…
Should teachers concentrate on critical thinking, estimation, measurement, and graphing rather than college-clone algorithmic physics in grades K--12? Thus far physics education research offers little substantive guidance. Mathematics…
Lectures presented at the VI Mexican School of Particles and Fields, Villahermosa, 3-7 October, 1994. Contents: 1. Introduction 2. The Symmetry Group Approach to the Quantum Mechanics of Identical Particles 3. How Come Anyons? 4. The…
Maxwell's demon was born in 1867 and still thrives in modern physics. He plays important roles in clarifying the connections between two theories: thermodynamics and information. Here, we present the history of the demon and a variety of…