Physical Sciences and Mathematics Commons^™

Mathematics As Creative Structure: A Review Of Marcus Du Sautoy’S Blueprints, Sangeetha Balakrishnan, Latha R

Journal of Humanistic Mathematics

Marcus du Sautoy’s Blueprints: How Mathematics Shapes Creativity (2025) makes a provocative claim that creativity emerges not in opposition to constraint, but through it. Working through nine mathematical “blueprints” — symmetry, randomness, the Fibonacci sequence, among others — du Sautoy traces recurring structural patterns across artistic practice, natural phenomena, and mathematical thought. The argument is ambitious and persuasive. In this review we consider what the book adds to longstanding conversations about the relationship between scientific and humanistic ways of knowing, and reflect on what it means to reframe mathematics as an imaginative and exploratory enterprise rather than a purely technical …

The Logic Of Leaves: Mathematical Poems And Graphs, Ksawery Tomczak

Journal of Humanistic Mathematics

This collection explores the intersection of mathematics and poetry through six original works that blend formal rigor with lyrical expression. Each poem draws from a distinct mathematical concept—proof, set theory, combinatorics, graph theory, and cardinality—reframing it through metaphoric and aesthetic lenses. From the lyrical contemplation of infinite sets to the emotive longing of a graph in love, the verses reveal the emotional resonance and philosophical depth embedded in mathematical thought. The collection culminates in a visual piece rendered in \LaTeX and TikZ, illustrating all integer partitions of the number five as a branching tree, accompanied by a poem that sings …

College Algebra: A Key Element To Degree Completion, Christopher Charlie Jett, Gregory Downing

Journal of Humanistic Mathematics

College Algebra is often under scrutiny because it serves as a critical gateway to graduation for students enrolled in our nation’s undergraduate degree programs. In this paper, we problematize the authority typically ascribed to this course and discuss meeting students’ discipline-specific needs in core mathematics courses such as it. To help facilitate college student success with respect to mathematics course requirements, we recommend that educational constituents and leaders expand dual-enrollment opportunities, infuse culturally relevant practices, and leverage other core mathematics courses as alternatives to College Algebra. In doing so, we add to the ongoing conversation about addressing this issue in …

An Essay On Teaching And Learning Mathematics: Through The Lens Of Artificial Intelligence, Music, And Sports, James Diederich

Journal of Humanistic Mathematics

This essay is aimed at a wide audience: anyone who has engaged in learning or teaching math. It provides a unique perspective drawn from a mathematician’s interests in working with K-12 teachers, familiarity with artificial intelligence (AI), and amateur pursuits of learning to play an instrument and of learning a difficult sport. While I delve into these topics, no special background is needed in the slightest. In particular, I draw lessons from some failures in AI that reflect on why the conventional procedural approach to teaching and learning math fails many students. I also provide insight into how we learn …

Graduate Student Reflections On Mentoring Undergraduate Researchers In Mathematics, Melissa Beerbower, Jillian Cervantes, Pamela E. Harris, Kimberly J. Harry, Matt Mcclinton, Gabriella Pinter

Journal of Humanistic Mathematics

This is an interview with four graduate students who for the first time mentored undergraduate students during a summer research program. The interviewees present their lessons learned in mentoring and advice to other graduate students looking to mentor students.

The Urysohn Lemma: Munkres Variation, Irida Altman

Journal of Humanistic Mathematics

There is a tradition of Mathematics contributing to the understanding of Music. This article sets out to contribute in the other direction. It uses musical sensibilities to feel its way through a piece of mathematics called the Urysohn Lemma, suggesting the presence of rhythmic, melodic, and harmonic elements within standard proving practices of contemporary Western mathematics. This article employs a literary-philosophical technique of viewing a text in one discipline (mathematics) through the conceptual lens of another (music). As such, this article reports on no experiments—reading the article is the experiment. Each reader performs it for themselves.

Prime Numbers Are Written On Your Hand: You Simply Have Not Been Counting Correctly, Nona Servais Kamdem Simo, Awa Traore

Journal of Humanistic Mathematics

Prime numbers have resisted systematic description for over two millennia. We propose that part of the difficulty may lie in an insufficiently attentive examination of one’s own hands. In particular, we assign the natural numbers to the joints of the human hand according to a cyclic traversal protocol, and make a handful of observations which can naturally be translated into number-theoretic properties of prime numbers. We show that these properties lead us to natural activation thresholds of a unified three-phase sieve algorithm — the resulting framework provides, for the first time, a zone-based partition of the admissible space with explicit …

Developing A Learner-Centered Teaching Routine, Hyeeun Jang

Journal of Humanistic Mathematics

This paper shares my story of developing, from Fall 2022 to Spring 2025, a learner-centered teaching routine for my undergraduate mathematics courses. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a short end-of-class exit check, at times supported by quick visuals in Mathematica and, when useful, Python. Instead of relying on extended traditional lectures, the routine emphasizes collaborative problem solving and invites students to articulate and check their reasoning together. I used this routine mainly in my elementary statistics classes, but also in calculus and linear algebra. The evidence I …

Numbers, Patterns, And Memories: Early Experiences Of Mathematicians And Mathematics Education Researchers, Constantinos Xenofontos

Journal of Humanistic Mathematics

This paper offers a reflective analysis of early mathematical experiences shared by fifty-six mathematicians and mathematics education researchers, including my own, as part of Cambridge Mathematics’ “Seven Questions with . . . ” interview series. Drawing on thematic analysis, I identify five key patterns across participants’ recollections: the context of early mathematical engagement, the influence of significant others, emotional responses, shifts in mathematical thinking, and mathematics as a social or competitive experience. Many accounts emphasise informal, everyday encounters with mathematics—often preceding formal education—as central to developing interest and confidence in the subject. The findings challenge the notion of innate mathematical …

Preparing Undergraduates To Philosophize With Children About Mathematics, Lawrence M. Lesser

Journal of Humanistic Mathematics

This paper shares my reflections and insights from preparing and facilitating a session in a weeklong inaugural study away program for undergraduate students (especially philoophy majors). My session was a vehicle for helping these students experience or visualize how the program’s Philosophy for Children (P4C) approach could be applied to exploring and discussing mathematics with children.

The Dynamics Of Vincent Van Gogh, Monica Morales Hernandez

Journal of Humanistic Mathematics

This article explores the interplay between Vincent van Gogh’s distinctive artistic style and principles of fluid dynamics, particularly through metaphorical comparisons. Van Gogh’s swirling, turbulent brushstrokes in works such as The Starry Night and Wheatfield with Crows evoke the chaotic and dynamic behaviors found in fluid motion, like vortices and turbulence. Although there is no documented scientific influence from fluid dynamics on van Gogh’s art, the parallels between his emotive, flowing techniques and the mathematical principles governing fluid behavior offer a unique lens to appreciate both his artistic innovation and the science of fluid dynamics.

Mathematicians Against The Tide, Nicola Ciccoli

Journal of Humanistic Mathematics

Mathematicians in popular culture are often depicted as people obsessed by their studies but with little connection to society, poor social skills, mental issues and narrow interests, and more generally a dull life. Adding to these explicit stereotypes, subtler and more implicit ones also abound, regarding mathematicians’ gender, ethnicity, age; they are all supposed to be white middle-aged men. In this paper I describe a project aimed at disrupting such stereotypes that culminated in a book containing short comics and biographies of twentieth-century mathematicians that were, with respect to the perceived image of mathematicians, against the tide.

Waiting For The Magic: A Historical And Mathematical Study Of Queues In Disney Theme Parks, Nina E. Becket

Journal of Humanistic Mathematics

This paper, written as part of an honors research project in high school, provides an introduction to the line and queuing systems at Disney theme parks. We begin with a brief history of Disney World and its creators. We then introduce the basics of queuing theory and queuing notation. Finally, we examine modern line systems at Disney (as of 2023) and the future of its different queue systems.

An Exploration Of Mathematical And Musical Connections, Jeffrey Pair, Egypt Pannell, Dani Rodriguez, Jerico Sarmiento

Journal of Humanistic Mathematics

In this paper, we present an introduction to some of the mathematical principles underlying music and mathematically develop a connection between the twelve musical notes and the group of integers modulo twelve. Our discussion touches on the simple mathematical ratios used to calculate consonant musical tones on the length of a string, the frequencies of tones and the method by which the twelfth root of two provides the foundation of equal temperament tuning, some algebraic connections to musical concepts like the euphonious circle of fifths, and a curious connection to twin primes.

Impact Of Covid-19 Pandemic On Mathematics Achievement And Problem-Solving Ability: Insights From Secondary Schools In India, Laishram Nirtish Singh, Anand Jyoti Sanasam, Jocyline Thokchom, Ningombam Cha Cogent, Laisom Sharmeswar Singh

Journal of Humanistic Mathematics

The COVID-19 pandemic disrupted students’ engagement with mathematics. This study aims to contribute to our understanding of the extent of this disrupting by examining differences in mathematics achievement and problem-solving ability between adjacent cohorts who learned Class 8 under different schooling conditions in India: Group A (pandemic-exposed Class 8 cohort) and Group B (post-reopening Class 8 cohort). Using a descriptive design in a natural setting, we selected a stratified sample of 1,200 students from Class 9 and Class 10 across 21 secondary schools in Manipur, India. The sample was stratified by gender, family type, school type, and locality to ensure …

"Math Is Like A Rollercoaster": Exploring Math Similes And Metaphors, Carmen M. Latterell, Janelle L. Wilson

Journal of Humanistic Mathematics

In this article we explore the metaphors and similes that pre-service elementary teachers use to describe mathematics. Employing qualitative content analysis, we separately coded the metaphors and similes into conceptual categories and analyzed themes that emerged. This grounded theory approach led to the creation of seven categories of metaphors and similes and three overarching themes. Math was viewed as a journey, a puzzle, a personal experience, a creative process, an algorithm, infinite, and an embodied process. Pre-service elementary teachers viewed mathematics as a process that takes effort. Overall, mathematics is a positive experience for them. In addition, mathematics involves fitting …

Cultivating Mathematics Teacher Educators’ Hearts, Critical Consciousness, And Professional Praxis Through Book Study, Mary Raygoza, Missy D. Cosby, Sheila Orr, Barbara King, Justin T. Burris, Siddhi Soni

Journal of Humanistic Mathematics

At a time when executive orders and state legislation are attempting to ban practices promoting equity, belonging, and social justice from education, specifically STEM education, in the United States, mathematics teacher educators (MTEs) remain committed to humanizing mathematics teaching and learning practices and seek opportunities to learn how to adhere to their convictions while preparing mathematics teachers for the classroom. This paper offers reflections and considerations for how the authors engaged interested MTEs to shift or strengthen their individual and collective professional praxis through a book study. Specifically, we examine the design (the what) and process (the how) of a …

Piracy, Terrorism, And The Law: Differential Equations In Hostage Situations, Gabriel Hallevy

Journal of Humanistic Mathematics

Pirates have taken the crew of an American ship hostage. They promise to release the hostages only if another pirate who is held in an American prison for commission of piracy crimes against American citizens, is released. Should the U.S. government enter into negotiations with them? Should they send armed forces and risk the hostages? Should they release the prisoner immediately and unconditionally? The article models and analyzes possible policies regarding sensitive situations involving hostages and other related risks using differential equations. The solutions are surprisingly simple, but not necessarily intuitive. Our analysis aims to demonstrate how powerful mathematics is …

Grationality, With A Spoon, L. Jeneva Clark

Journal of Humanistic Mathematics

I introduced grationality at a 2025 sectional meeting of the Mathematical Association of America to install a handle on a concept akin to rationality of numbers, but in a geometric context. More specifically, we define a nice n-gon to be a regular n-gon with side lengths that are natural numbers; then a number n is grational if and only if there exists a nice n-gon such that its area equals the sum of areas of n congruent nice n-gons. In this paper I offer several examples of grational and non-grational numbers, followed by theorems about how the grationality of a …

The Set Card Game And Partitions Into Maximal Caps: A Partial Difference Sets Approach, John Polhill

Journal of Humanistic Mathematics

More specifically, we revisit the problem of determining the maximum number of cards that can be dealt in the SET® card game without any matches, which is well known to be equivalent to the problem of determining the size of a maximal cap in the affine space AG(4,3). We present a new approach to the problem by using partial difference sets, a method that is equivalent to using strongly regular graphs with a regular automorphism group. The paper includes several possible avenues for future investigations on how partial difference sets might be used in related problems.

A Method For Folding Origami Rectilinear Polygon Extrusions, Everett L. Jin

Journal of Humanistic Mathematics

We present a method for generating crease patterns for folding any rectilinear polygon extrusion with a specified uniform minimum edge-to-edge distance, using a rectangular sheet of paper. We demonstrate that the resulting models are efficient and watertight. In addition, they achieve optimal efficiency, meaning they attain the smallest possible scale factor from the original sheet of paper to the folded rectilinear polygon extrusion. Finally, we provide a code implementation of the method. Our study not only facilitates crease pattern design for origami artists but also offers an innovative, art-driven pedagogical tool for inspiring interest in mathematics.

Manipulating Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Technological Behaviour Of Pellets Containing Dried Green Crop, Christian Furll

IGC Proceedings (1977-2023)

Pelleted dried green crop presents essential advantages compared to chaff and meal as processing forms. Normally, the solidity of the pellets does not exceed the values required by animal feeding. Abrasion resulting from turnover processes is at present too high, particularly for the discharge of bins. Belt conveyors, vibrating conveyors, and bucket elevators are suitable to convey pellets. Storage of pellets over long periods has to be done by respecting prescribed climate conditions. Zones with excessive portion of abraded par­ticles in the storing pile are a preferred cause for self-heating. Slit-type dosing units as well as dosing units equipped with …

Results Of Comparative Investigations Into The Chevving And Ruminating Activities Of The Dairy Cow Fed Dried Forage From Grass And Leguminous Crops, B Piatkowski, S Nagel

IGC Proceedings (1977-2023)

The chewing and ruminating activities were studied of dairy cows fed grass, alfalfa, and straw of different physical forms. An electronic­ally controlled measuring device was applied. When feeding 8 kg of grass hay (32 % crude fibre in dry matter), the ruminating time was 5: 24 and 1 :49 hours (20,712 and 6,982 ruminat­ing movements) for chopped and ground + pelleted forages, respectively. It declined from 1 : 49 to 0: 0 l hours (from 6,929 to 70 move­ments) when hot-air dried alfalfa (23 % crude fibre) was fed in chopped and ground + pelleted forms, respectively. The ruminating time …

Feed Efficiency In Dairy Cows Of Roughages Preserved And Treated In Different Ways, M Zausch, E Boldt

IGC Proceedings (1977-2023)

Trials were conducted with dairy cows to investigate the feed efficiency of grass-clover mixture (wilted silage, silage made of fresh material with addition of foDTiic acid, artifi­cially dried forage, pellets with varying portions of straw). The results obtained allow to draw the following conclusions:

As regards dry matter intake, digestibility, and feed efficiency, grass-dover for wilted silage should be wilted to give a OM content not exceeding 40 %.

Pelleting artificially dried grass-clover mix­ture and its use in mixed rations together with other separately pelleted components should be avoided.

The best feed efficiency is reached when dried grass-clover is converted …

The Influence Of Dried And Ensiled Grass On Rumen Fermen­Tation, J Voigt, B Piatkowski

IGC Proceedings (1977-2023)

Rumen-fistulated cows were used to study the influence of the forage preservation technique on rumen fermentation and holdup time of the feed in the rumen. Cocksfoot (Dactylis glomerata) preserved as wilted silage or dried green crop was fed in the following variants: wilted silage alone; wilted silage + sugar beet + protein supplement; dried green crop alone; dried green crop + sugar beet + protein supplement. As compared with dried green crop, the shares of true protein and sugar in wilted silage were reduced from 9.8 • to 6.4 '.'I􀉧 and from 7.7 to 1.8 %in DM, respectively. In comparison …

Changes In Feeding Value Of Preserved Grass And Legumes By The Action Of High Temperatures, R Prym, F Weissbach

IGC Proceedings (1977-2023)

High temperatures acting on grass and legumes during preservation and storage, cause nutrient digestibility to deteriorate. Protein digestibility is likely to be most strongly affected. Digest­ibility measurements were performed on sheep to estimate the extent of heat damage suffered by dried green forage and silages. Various laboratory methods were applied for record­ing. such damage. The detennination of the acid-detergent insoluble crude protein portion proved a very suitable approach.

Growth And Nitrogen Retention Of Lambs Fed Alfalfa Dehy­Drated At Different Temperatures, H K. Goering

IGC Proceedings (1977-2023)

Alfalfa was dried at four temperatures ranging from 60 to 180 °C in two experiments to evaluate the effect on composition, diet di­gestibility, and growth by lambs. In Experi­ment I, the alfalfa was supplemented with 0.6 % salt and pelleted. In Experiment 2, alfalfa was supplemented with 24.4 % starch, 18.5% straw, 6% cane molasses, 0.5% sodium phosphate, and 0.6 % salt so that total nitrogen intake was not in excess of the protein require­ment for growth of the lambs. Cell wall, acid­detergent fiber, lignin, acid-detergent insoluble nitrogen, and pepsin insoluble nitrogen in­creased in the alfalfa dried at 180 °C. …

Non-Mechanical Field Losses In Wilting Grasses As Influenced By Different Factors, G Rucker, O Knabe

IGC Proceedings (1977-2023)

When wilting grasses, non-mechanical field losses of different extent may occur. The main factors influencing the extent of losses were: water content at cutting time, drying rate, temperature, amount of rain, swath den­sity, and content of water-soluble carbohy­drates in the crop.