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Einsteinian physics represents a distinct paradigm shift compared to Newtonian physics. There is worldwide interest in introducing Einsteinian physics concepts early in school curriculum and trials have demonstrated that this is feasible.…
Isaac Newton's book 'Opticks' from the 18th century includes several hypotheses on the structure of matter. Most of the hypotheses were confirmed during the 19th and 20th centuries at the scale of atoms and molecules. Conflicts appear…
Einstein was deeply puzzled by the success of natural science, and thought that we would never be able to explain it. He came to this conclusion on the ground that we cannot extract the basic laws of physics from experience using induction…
In this manuscript, I introduce and describe the work of mathematicians and mathematics educators in the group Transforming Post-Secondary Education in Mathematics (TPSE Math or TPSE, pronounced "tipsy", for short). TPSE aims to coordinate…
The first approach to the history of mathematics in China led by Li Yan (1892--1963) and Qian Baocong (1892--1974) featured discovering {\it what} mathematics had been done in China's past. From the 1970s on, Wu Wen-tsun and others shifted…
The current status of Doubly Special Relativity research program is shortly presented. I dedicate this paper to my teacher and friend Professor Jerzy Lukierski on occasion of his seventieth birthday.
These are lecture notes for the course "Poisson geometry and deformation quantization" given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
In a contribution to the volume {\it A Passion for Physics}, a collection of essays in honor of Geoffrey Chew's sixtieth birthday, I wrote, together with A. Capella, Uday Sukhatme, and Tran Thanh Van {\it The Pomeron Story.} This is a…
The Milanese period in Albert Einstein's life is a key one for the understanding of the development of his scientific questioning. While being a student in Z\"urich from 1896, Einstein returned regularly to Milan to meet his family for the…
In this paper we explore the relationships between Calvino's memos and Mathematics. In the first part, we discuss how Lightness, Quickness, Exactitude, Visibility, Multiplicity are present in the mathematical language, reasoning and in the…
This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.
The evolution of theoretical physics in the XX century differs significantly from that in XVII-XIX centuries. While continuous progress is observed for theoretical physics in XVII-XIX centuries, modern physics contains many questions that…
This paper is about two things: (i) Charles Sanders Peirce (1837-1914) -- an iconoclastic philosopher and polymath who is among the greatest of American minds. (ii) Abductive inference -- a term coined by C. S. Peirce, which he defined as…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
The author thinks that the main ideas or Relativity Theory can be explained to children (around the age of 15 or 16) without complicated calculations, by using very simple arguments of affine geometry. The proposed approach is presented as…
The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
We study in depth a certain permutation statistic that was the subject of a brilliant insight by 12-year-old Noga Alon. Our approach is purely empirical and experimental, yet it is fully rigorous, thereby debunking, yet another time, the…
There are growing uncertainties surrounding the classical model of computation established by G\"odel, Church, Kleene, Turing and others in the 1930s onwards. The mismatch between the Turing machine conception, and the experiences of those…