历史与综述
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…
The advent of computers has allowed mathematicians to do increasingly more difficult computations that used to be practically impossible. Peer reviewers will seldom look at any code attached to a math paper, however. In this article, we…
Two mathematical aspects of the centuries-old Japanese sashiko stitching form hitomezashi are discussed: the encoding of designs using words from a binary alphabet, and duality. Traditional hitomezashi designs are analysed using these two…
D-forms have in the past been created from inflexible materials, or considered as abstract mathematical objects. This paper describes a number of realisations of D-forms, and the related pita-forms, in textiles. Examples are given in which…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
This is an essay about the value of mathematical and symbolic reasoning in the age of AI.
It is well known that Charles Hermite kept an intense correspondence with many of the word's leading mathematicians of his time. This paper focuses on Hermite's letters to Francisco Gomes Teixeira, a Portuguese mathematician, who exchanged…
We apply Nancy Cartwright's distinction between theories and basic models to explore the history of rival approaches to modeling a notion of chance for an ideal uniform physical process known as a fair spinner. This process admits both…
We know that the algorithm of Theon of Smyrna (70-135 AD) made it possible to highlight fine frames of $\sqrt2$ by rationals. However, this same algorithm also applies to $\sqrt3$ and makes it possible to find the famous Archimedes…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
The paper deals with some elementary problems about various mean value properties and their connections to harmonic functions and random walks.
We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many…
This article is the first in an occasional series for the Australian Mathematical Society Gazette on diverse aspects and topics of Indigenous mathematical knowledge. This is an important, but neglected, part of the mathematical heritage of…
I describe a puzzle I wrote for the 2018 MIT Mystery Hunt which introduced new types of people in logic puzzles. I discuss the puzzle itself, the solution, and the mathematics behind it.
In 1640 Pierre de Fermat discovered his theorem that if $p$ is prime and $a$ is not divisible by $p$, then $a^{p-1}-1$ is divisible by $p$; or, as we write today, $a^{p-1}\equiv1\pmod{p}$. This is perhaps the first and the most important…
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…
Good problems grab us. They invite us to find patterns, make conjectures, and prove-or perhaps disprove-a conjecture. When I first taught, I saw my work as tantalizing students with structures just beyond their reach, so that I could elicit…
Each time we teach, our students communicate to us. They talk, write, and draw. How do we take in their expressions of self and mathematics? How do we listen? In this column, published in the Fall 2023 AWM Newsletter, I explore different…
Interview with Hyman Bass, whose mathematical life has spanned seven decades.