Authors:Sarah Glaz et al. Abstract: The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Included as background is a brief discussion on the history and mathematics involved, and a reflection on several landmark locations and some of the relevant imagery appearing in the poem and the collage. PubDate: Wed, 01 Feb 2023 19:20:30 PST

Authors:Vijay Fafat Abstract: How would the Bible written about a Mathematical God start, describing the Creation of Mathematics and Logic' How would Rigveda's "Nasadiya sukta" read if it were describing the Void before mathematics was "born"' Here is an attempt at a partial answer, one which takes the original Genesis chapter and the Nasadiya sukta and makes suitable changes to create a fairly consistent, if somewhat anachronistic narrative (with the slight mixing up of Bertrand Russell and Lobachevsky / Bolyai attributable to "Babelogic"), along with a new ending to the Beginning... PubDate: Wed, 01 Feb 2023 19:20:29 PST

Authors:Audrey Nasar Abstract: "Astor Place Barber" is a short story about a math professor and a barber. It plays with the logical concept of a paradox via the Barber's Paradox, which, made famous by Bertrand Russell, tells the story of a barber who both shaves himself and does not shave himself. PubDate: Wed, 01 Feb 2023 19:20:29 PST

Authors:Scott W. Williams Abstract: This poem describes the still unsolved 1937 conjecture of Lloyd Collatz: Do repeated applications of the algorithm described yield the number 1' PubDate: Wed, 01 Feb 2023 19:20:28 PST

Authors:Virgilio A. Rivas Abstract: This short poem is inspired by Robert Langlands, recipient of the 2018 Abel Prize. The poem tries to sum up in poetic language, as brief but substantial as it can be, the philosophical and rhetorical connotation of his contributions to mathematics, from automorphic forms to number theory, and the famous Langlands programme, among others. Also partly inspired by Edward Frenkel's tribute to Langlands, the book Love and Mathematics, the poem seeks to capture the philosophical beauty of mathematics that privileges the importance of 'functions' over 'passions', consistent with Langlands' purely mathematical side. PubDate: Wed, 01 Feb 2023 19:20:27 PST

Authors:Kim Regnier Jongerius Abstract: Inspired by the song "Memories" from the musical Cats, this work describes some of the frustrations and joys inherent in mathematical work. PubDate: Wed, 01 Feb 2023 19:20:27 PST

Authors:Joël A. Doat Abstract: This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides' liar paradox. PubDate: Wed, 01 Feb 2023 19:20:25 PST

Abstract: In our July 2022 issue, we announced an open call for poetry about mathematical constants other than pi. And you delivered. This folder contains five eclectic poems celebrating those constants beyond the half-circle, written by Robin Chapman, John Donoghue, Kevin Farey, Lawrence M. Lesser, and E. R. Lutken.Enjoy! PubDate: Wed, 01 Feb 2023 19:20:25 PST

Authors:Judith V. Grabiner Abstract: In his book Algebra the Beautiful, G. Darnell Williams has undertaken a challenging job – to show the importance, deep structure, intellectual connections, and sheer beauty of classroom algebra. This review describes some of the questions the book raises, the historical and cultural context it provides, and the intellectual apparatus it deploys. PubDate: Wed, 01 Feb 2023 19:20:24 PST

Authors:Maohua Le et al. Abstract: In this article, dictated by Maohua Le and arranged by Yongzhong Hu, Professor Le briefly recounts his legendary experience of self-study mathematics, which reflects the life experiences of his generation of Chinese people. PubDate: Wed, 01 Feb 2023 19:20:23 PST

Authors:Sarah Voss Abstract: Drawing from one of my recent sermons, I chart the path of mathaphor (metaphor drawn from mathematics) as a literary tool. Following a short history of the concept, I detail contemporary author Colum McCann’s significant use of a geometric term to unveil and encourage compassion. PubDate: Wed, 01 Feb 2023 19:20:22 PST

Authors:Kien H. Lim et al. Abstract: Mathematics can be intellectually demanding, engaging, and fulfilling. Learning mathematical concepts adequately warrants an environment where students can err without penalty, shame, or hurtful consequences. Teaching mathematics efficaciously depends on the trusting relationship between the teacher and the students. We advocate blending mathematics teaching with kindness because it benefits the teacher, the students, and society. Kindness, niceness, caring, and benevolence are interrelated but not synonymous. We outline four progressive levels of kindness: conditional, superficial, optimal, and genuine. Blending mathematics teaching and kindness effectively requires the teacher to decenter from their own perspectives and adopt the student’s perspective as the student struggles through a challenging math problem. The efficacy of blending teaching and kindness depends on the teacher’s inner cultivation of benevolence. In one’s journey towards teaching with genuine kindness, one would need self-knowledge, unwavering commitment, continual practice, collegial support, spiritual guidance, and mindful awareness. PubDate: Wed, 01 Feb 2023 19:20:21 PST

Authors:Richard Delaware Abstract: This is a proof, in poetic form, of a bit of real analysis, more specifically involving the topology of accumulation points, that exploits the human optical phenomenon of figure-ground perception. Sometimes it is not a change in content, but a snap shift in point of view that yields a proof. PubDate: Wed, 01 Feb 2023 19:20:21 PST

Authors:Manmohan Kaur Abstract: Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of mathematics within and beyond the typical K-16 curriculum. We share practical outreach methods inspired by real, fun mathematics, and our experience with a liberal-arts ‘math for poets’ course which aims to develop math appreciation without losing its rigor or depth. While many of us are not comfortable doing live performances or making fancy videos, we all can use these methods to encourage a more positive mindset about mathematics in our communities. PubDate: Wed, 01 Feb 2023 19:20:20 PST

Authors:Cristina Carr et al. Abstract: We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model. PubDate: Wed, 01 Feb 2023 19:20:19 PST

Authors:Erin Griesenauer Abstract: As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have impacted how I set up my classroom, the assignments that I design, and the topics and content that I cover. PubDate: Wed, 01 Feb 2023 19:20:18 PST

Authors:Szilárd Svitek Abstract: Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number' The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state of balance between positive and negative assets was also given. We now take them for granted, but the history of science shows that it was far from a smooth process, and interesting mistakes about zero still occur in education today. I present a few examples below, and how they have been resolved. PubDate: Wed, 01 Feb 2023 19:20:18 PST

Authors:Osvaldo Marrero Abstract: We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it includes some preliminary work that facilitates the proof; therefore, the theorem can also serve as a nice exercise in induction. Additionally, we use well-known facts from calculus to clarify and enhance what is intrinsically a discrete problem. Making an unexpected but welcome explanatory appearance, the number e is pertinent. PubDate: Wed, 01 Feb 2023 19:20:17 PST

Authors:Toby S C Peres Abstract: This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted, and while many examples exist that clearly show an attempt to disperse mathematical ideas, with Lewis Carroll, OuLiPo and ancient poetry considered, the argument that the sole purpose of the writings was for the sake of mathematical development is not clear-cut. PubDate: Wed, 01 Feb 2023 19:20:16 PST

Authors:Marcio Luis Ferreira Nascimento Abstract: According to European folklore, popularized by a fairy tale, storks are responsible for bringing babies to new parents. This probably came from observation in certain European countries, such as Norway, Netherlands or Germany, that storks nesting on the roofs of households were believed to bring good luck, as the possibility of new births. People love stories, but correlation simply means that there is a relationship between two factors that tells nothing about the direction of said relationship, if any. Another possibility is simple coincidence. Let us say that it’s possible that one factor causes another. It’s also possible that the inverse occurs. And maybe both are being caused by a third. The main point is that there is a fundamental confusion between correlation and causality. A correlation doesn’t prove a cause by itself. During these times of abundant fake news, it is necessary to warn folks of the fallacy of mistaking correlation for causation. PubDate: Wed, 01 Feb 2023 19:20:15 PST

Authors:Wendy Ann Forbes et al. Abstract: Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversation that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful way, sustaining the progress made in mathematics education, all stakeholders should embrace the changing context of our network within the environment and interact through listening. PubDate: Wed, 01 Feb 2023 19:20:15 PST

Authors:Thomas Hillen Abstract: Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three' Here we show that a mathematical classification can be used to identify these scales as representatives of certain scale families. Moreover, the classification reveals another scale family, which is much less known: the harmonic major scale. We find that each scale family contains exactly seven scales, which include the modes (dorian, phrygian,...) and other scales such as the Romanian, Gypsi or Hindu-scales. Besides of giving a complete classification of proper heptatonic scales, we also emphasize the pedagogical potential of these {0,1}-representations of scales, as these can help students to navigate and remember complicated scales. PubDate: Wed, 01 Feb 2023 19:20:14 PST

Authors:Gila Hanna et al. Abstract: This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that students have to learn its command language, in addition to mathematics course content and elementary logic. PubDate: Wed, 01 Feb 2023 19:20:13 PST

Authors:Graziano Gentili et al. Abstract: In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved. PubDate: Wed, 01 Feb 2023 19:20:12 PST

Authors:Valentin A. B. Küchle et al. Abstract: Humanistic geographers distinguish between space and place: “What begins as undifferentiated space becomes place as we get to know it better and endow it with value” (Tuan, 1977, page 6). In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place illuminating for understanding important aspects of students’ learning experiences during the coronavirus pandemic—and possibly beyond. Specifically, after introducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt transition to online education. We conclude by discussing implications of attending to space and place for designers and researchers of (pandemic) online instruction and make connections to how the pandemic and attending to space and place can serve as a catalyst for reshaping undergraduate mathematics education. PubDate: Wed, 01 Feb 2023 19:20:11 PST

Authors:Omid Khatin-Zadeh et al. Abstract: When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely perceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and we may view it as a kind of mathematical metaphor, which is common strategy for solving mathematical problems. This process is a metaphor because, in the sense that a certain representation of a mathematical problem is described in terms of a visual representation of that problem. Furthermore, since a graphical representation is visual, it can be depicted by gestures. Therefore, visual and motor systems can be actively employed to process a given problem and find a solution for it. In this way, mathematical metaphor offers us a way to employ a wider range of cognitive resources to understand mathematics. PubDate: Wed, 01 Feb 2023 19:20:10 PST

Authors:Juan Fernández González et al. Abstract: We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical practice. PubDate: Wed, 01 Feb 2023 19:20:09 PST