历史与综述
Mathematicians have long been fascinated by the resolution of algebraic and Diophantine equations in search of integer or rational solutions. This article presents a list of thirty-three open problems in number theory, posed in the 13th…
This is about algebras of complex $n\times n$ matrices. Do these algebras look similar for all large $n$? This paper is intended for general audience.
We study poker hand rankings in the partially generalised setting of a deck with $r$ ranks, rather than the typical 13 ranks. We provide the hand rankings for all $r$ and observe some interesting phenomena such as the smallest $r$ such that…
We report on the process of taking an early 2000's mathematical library, the Small Phylogenetic Trees, and transforming it into a FAIR, modern, and sustainable repository for data from algebraic phylogenetics. This process is based on a…
The Dutch scientist Christiaan Huygens refined Archimedes' celebrated geometrical computation of $\pi$ to its highest point. Yet the rich content of his beautiful treatise \emph{De circuli magnitudine inventa} (1654) has apparently never…
In this paper, we highlight the influence of Arab/Islamic civilization in the field of the history of astronomy on European historians. We also aim to elucidate the stance of Orientalists toward the study of Arab sciences and to clarify…
In this paper, we examine the asymptotic behavior of the longest increasing subsequence (LIS) in a uniformly random permutation of $n$ elements. We rely on the Robinson--Schensted--Knuth correspondence, Young tableaux, and key classical…
The mathematisation of the socio-economic sphere, where mathematics actively constructs social reality, presents a challenge for studies on ethics in mathematics and its education. While existing scholarship on ethics in mathematics offers…
We give a concise historical background to Montmort's matching problem and its modern variants such as the hat-check problem, then develop a unified counting framework for fixed-point-free allocations. Using elementary recurrence and…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
2023 year marks the hundredth birth anniversary of prominent Russian mathematician and thinker Igor Rostislavovich Shafarevich (1923-2017). The article presents a selection of quotations from various works of him, devoted to the future of…
In this paper, we study the Pulsar Sequence, an integer sequence derived from Latin-square-based Pulsar puzzles introduced by the Cracking the Cryptic YouTube channel. A Pulsar puzzle consists of two interlocked spirals of circled and…
This article offers a motivating travel guide towards the Jordan normal form, one of the highlights in courses on linear algebra or advanced mathematics. Its itinerary is characterized by a focus on core geometric aspects and the avoidance…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…
September 7, 2025 marked the 80th anniversary of the birth of Oleg Marichev. Marichev is known mathematician which has developed many of Mathematica's algorithms for the calculation of definite and indefinite integrals and hypergeometric…
This manifesto has been written as a practical tool and aid for anyone carrying out, managing or influencing mathematical work. It provides insight into how to undertake and develop mathematically-powered products and services in a safe and…
Starting from Greg Moore's description about Physical Mathematics, a framework is proposed in order to understand it, based on Gilles Ch\^atelet's philosophy. It will be argued that Ch\^atelet's ideas of inverting, splitting, augmenting and…
We present a modern reconstruction of the classical formula, first derived by medieval Arab astronomers, that describes the trajectory of the tip of a gnomon's shadow during the day as a function of latitude, solar declination, and gnomon…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…