Related papers: BourbOulipo. Relazioni tra Oulipo e Bourbaki
The apparently trifling unexpected hanging paradox has generated an enormous philosophical literature. We introduce the mathematician to this literature, paying special attention to aspects that involve nontrivial mathematics. This xxx…
Based on Plato's Timaeus, we present some reflections on music, cosmology and mathematics and their mutual influence.The article is dedicated to the composer Walter Zimmermann. The final version of this article will appear in the volume…
These notes are an exposition of Galois Theory from the original Lagrangian and Galoisian point of view. A particular effort was made here to better understand the connection between Lagrange's purely combinatorial approach and Galois…
In a recent article, Khrennikov claims that a particular theorem about agreement between quantum measurement results poses a problem for the interpretation of quantum mechanics known as QBism. Considering the basic setup of that theorem in…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
Supersymmetry is a theme with many facets that has dominated much of high energy physics over the past decades. In this contribution I present a very personal perspective on these developments, which has also been shaped in an important way…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time.…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…
We give an overview and conceptual discussion of some of our results on contextuality and non-locality. We focus in particular on connections with the work of Itamar Pitowsky on correlation polytopes, Bell inequalities, and Boole's…
The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other…
The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished…
In this paper we discuss the impact of the last Landau paper on physics and mathematics to date and make some predictions about its likely impact on sciences in new millennium.
In the article "The Tale of Two Queens and Two Towering Figures" published in CNJ in 2012 (CNJ vol. 57 No. 5, pp. 304-315), we discussed the contributions of Copernicus and Newton to coin minting and monetary reforms, as well as the…
We recall Labatie's effective method of solving polynomial equations with two unknowns by using the Euclidean algorithm.
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
We survey a range of models of opinion exchange. From the introduction: "The exchange of opinions between individuals is a fundamental social interaction... Moreover, many models in this field are an excellent playground for mathematicians,…
In this article I compare two interpretations of quantum mechanics (QM) that draw inspiration from phenomenology: the London-Bauer-French interpretation (hereafter LBF) as articulated by Steven French, and QBism. I give special attention to…
We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1),…