历史与综述
We outline the development of the research group of Harmonic Analysis in Italy and the personality of its founder, Alessandro Fig\`a-Talamanca.
The literature on ethics and sustainability in mathematics and its education is increasingly complex and fragmented, potentially leading to communication breakdowns between different scholarly traditions. To address this, the paper…
This is the story of the first Fields Medal awarded to Lars Ahlfors. It was smuggled out of Finland in 1944, pawned in Sweden during World War II, and returned to Helsinki in 2004. This article is based on an interview with Ahlfors' second…
This paper identifies several different interconnected challenges preventing the move towards more ethical and sustainable mathematics education: the entrenched belief in mathematical neutrality, the difficulty of simultaneously reforming…
The aim of this survey is to outline the state of the art in research on a class of linearized polynomials with coefficients over finite fields, known as scattered polynomials. These have been studied in several contexts, such as in [A.…
In this note, we list many equivalent constructions of the tangent polar graph $NO^+(6,2)$.
In this article, we provide a new elementary proof of the Basel problem.
We revisit the classic 'guess my number' game and extend it from its familiar binary form to representations in any integer base. For each base we derive formulas for the number of cards needed to identify a given integer and, conversely,…
A classic three-jug puzzle asks, given three jugs $A$, $B$, and $C$ with fixed maximum capacities, with jug $A$ filled with wine to its maximum capacity, whether is it possible to divide the wine into two halves by pouring it from one jug…
Working with letters that represent unknown constants, i.e., parameters, has been historically challenging for students. This is an important skill for their success in many future quantitative settings, and yet it appears this topic is…
In 1986, composer Wendy Carlos introduced three unusual musical scales she called alpha, beta and gamma, equal temperament-inspired scales that de-emphasize the octave as the primary interval in favor of the major and minor thirds and the…
To conduct a didactic analysis of the current modality of study of real numbers in the Bachelor's Degree in Mathematics, we rely on the notion of didactic paradigm and employ a novel research methodology within the framework of the…
We present the problems and solutions to the 63rd Annual International Mathematical Olympiad.
This note presents a brief account of the School of Mathematical Physics of the National Group of Mathematical Physics of the Istituto Nazionale di Alta Matematica (INdAM), written on the occasion of its 50th anniversary.
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Checkered patterns are characterized by their square structure and the use of only two distinct colors. These colors are typically represented by two types of numerical sets: {1,0} and {1,-1}. Matrices based on {1,0} may seem identical to…
In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from…
Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another…