历史与综述
Diamond open access journals charge neither readers nor authors. Despite long-standing support for this ideal within mathematics, relatively few such journals exist. This article documents the Association for Mathematical Research's…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
Born from years of teaching undergraduate and graduate algebra courses at Chongqing University, this text is designed to introduce Galois theory while minimizing prerequisites. It seeks to reconnect the abstract machinery of modern algeba:…
We use contemporary mathematical notation to describe the method for determining the age of the ecclesiastical moon as mandated by pope Gregory XIII and elaborated in the book of Christopher Clavius \emph{Romani calendarii explicatio}. The…
This paper is an introductory and informal exposition on the topology of polygonal meshes. We begin with a broad overview of topological notions and discuss how homeomorphisms, homotopy, and homology can be used to characterise topology. We…
In this article we discuss the proof in the short unpublished paper appeared in the 3rd volume of Godel's Collected Works entitled "On undecidable sentences" (*1931?), which provides an introduction to Godel's 1931 ideas regarding the…
This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proportional systems, long associated with natural growth and…
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments…
The ceiling of the Buttery in All Souls College, Oxford, designed by the English Baroque architect Nicholas Hawksmoor, has a vaulted form on an oval base. It is coffered with an array of approximately square sunken lacunaria, whose sizes…
The book is a unique phenomenon in Russian geometry education. It was first published in 1892; there have been more than 40 revised editions, and dozens of millions of copies (by these parameters, it is trailing only Euclid's Elements). Our…
Vincenzo Galilei and Constantijn Huygens were both humanists and eminent musicians, the former from the late Renaissance and the latter from the early Modern era. Their respective sons, Galileo and Christiaan, were scientists whose…
This paper provides a brief write-up showing that for any finite state game, a disjunctive number $x$ will eventually win that game. The proof techniques here are well known and this result follows immediately from folklore results in graph…
A pair of numbers is amicable if each number equals the sum of the proper divisors of the other. This paper after exploring the history and evolution of amicable numbers, introduces a novel characterization of amicable pairs whose greatest…
The rapid adoption of generative artificial intelligence (AI) tools in higher education is transforming how students engage with undergraduate mathematics, raising concerns about learning and assessment validity. This study examines the…
This is an expanded version of the Maskit memorial tribute that appeared in the August 2025 issue of the Notices of the AMS.
We address certain structural innovations in the music of Claudio Monteverdi, which defined the pivotal transition from the Renaissance prima pratica to the Baroque seconda pratica. To formalize this analysis, we employ Mazzola's…
This is a review (in Italian) on aperiodic tilings of the plane intended for a general audience. First, we recall some basic results about lattices and periodic tilings. Then, we move on to one-dimensional (domino) tilings and Wang tilings.…
Here, we give a self-contained and elementary proof of a minimax theorem due to Fan in a simplified setting that can be taught in an advanced undergraduate course. Our proof follows Nikaido's argument with some simplifications.