Organizer: Zachery Keisler, Saluda High School, Saluda, SC; Organizer's Email: zkeisler@saludaschools.org
While traditional history of mathematics courses extensively covers ancient Greek geometry and the calculus contributions of Newton and Leibniz, they often overlook significant mathematical developments from other cultures and pioneering work by underrepresented mathematicians. The ancient Babylonians’ foundational role in trigonometry and Graciela Beatriz Salicrup López’s pioneering work in categorical topology during the late 1970s and early 1980s exemplify the rich mathematical heritage beyond Western Europe. This second annual special session on the unspoken history of mathematics continues to illuminate the contributions of diverse cultures and historical figures typically absent from conventional curricula. Participants will engage with presentations celebrating overlooked mathematical traditions and innovators while collaborating to develop curriculum units and projects that expand history of mathematics courses. This session invites faculty and educators committed to helping students understand the diverse, interconnected, and truly global nature of mathematical development.
In 1834, a Scottish engineer named John Scott Russell witnessed something he did not expect: a single wave rolling down a narrow canal without changing its shape. Intrigued, he chased it on horseback and later described it as a “wave of translation.” At a time when waves were thought to quickly spread out and disappear, Russell’s moving bump of water seemed almost impossible. His observation raised a lasting question: how can a wave travel long distances without breaking apart? Decades later, this mystery found a mathematical explanation. In the late nineteenth century, Diederik Korteweg and Gustav de Vries wrote down an equation for shallow water waves that allowed such stable traveling waves to exist. Their equation showed that two competing effects, one that tries to spread the wave out and one that tries to steepen it, can balance perfectly. The story did not end there. Over the twentieth century, mathematicians and physicists refined these ideas, searching for better ways to describe water waves and other wave phenomena. Important insights were provided by Gerald Whitham, who emphasized how simple wave patterns can slowly change as they move. The journey continues into the 1990s with a new chapter written by Roberto Camassa and Darryl Holm. Their Camassa–Holm equation predicts solitary waves with sharp crests, called “peakons,” revealing that even stranger wave shapes can arise from the same shallow water setting that inspired Russell’s canal experiment. This talk follows the path from a man on horseback chasing a wave to modern mathematical equations, illustrating how a simple physical curiosity grew into a rich theory of solitary waves and nonlinear equations.
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The humanistic approach to any aspect of mathematics adds a refreshing dimension. It is especially pertinent from the pedagogical angle. The session on the Unspoken History of Mathematics is a perfect platform to raise such questions and generate new lines of thinking. For the sake of simplicity, I have defined bricks and blocks of mathematics as a set in the complement of a set of hard core theorems, propositions, lemmas, corollaries, definitions, problems etc. In this paper, I explain bricks and blocks by taking the example of the most celebrated theorem, Fermat’s Last Theorem (FLT). After more than 350 years, its proof was ultimately put to rest in 1994 by Andrew Wiles (b.1953 - ). The nuts and bolts or bricks and blocks of FLT, with a focus on Wiles, are his wife and children, schools and colleges he attended, institutions he worked, his students, classmates, neighbors, friends, colleagues, supervisors, and any tangible factors. They are generally invisible, unheard, and unspoken!
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From two distinct areas at opposite ends of North America, Mayan and Katovik numerals share a great deal of similarities in both design and function. While Katovik numerals were only recently created in 1994, it served a purpose to its community that previously had difficulty in expressing how they had been doing math. The Mayans on the other hand had been able to calculate an accurate calendar and track cycles of the moon and the sun. Both of these systems are a form of body-counting, where they are a base 20 system, sub-base 5. These were meant to represent all of our fingers and our toes. The main difference between these two systems, is that the Mayan numerals are a near perfect system, where they changed how a place value worked in order to work with their records more accurately. Ultimately despite the difference in geography and involvement in the modern era, both of these cultures created reliable systems that help understand the world around us.
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Throughout history, conquering powers have sought to suppress culture as a means of control. This talk will explore underground universities as sites of intellectual resistance, focusing on clandestine efforts in occupied Poland during the Second World War. Although higher education was directly targeted by Nazi policy, Polish scholars organized secret courses, exams, publications, and degree programs, often at great personal risk. Using education itself as an act of defiance, these faculty members and students contributed to sustaining national identity and many would go on to shape postwar intellectual life.
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In this talk, I will describe a project based assessment created for an abstract algebra course that centers the mathematical work of women algebraists highlighted in the Association for Women in Mathematics (AWM) EvenQuads playing card project. Rather than presenting algebra as a finished body of results, this assignment invited students to explore topics such as geometric group theory, elliptic curve groups, and tropical algebra through the work of mathematicians whose contributions are often absent from traditional undergraduate coursework. Students completed individualized structured problem sets connected to each honoree’s research area, developed a short biography, and gave a presentation linking the mathematics to the mathematician’s contributions. I will discuss the goals of the assignment, share examples of the algebraic tasks designed for the project, and reflect on how integrating these mathematicians into assessment broadens the historical narrative students encounter in upper level mathematics.
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In this talk, we’ll trace the development of mathematics in Latin America, using precise examples to anchor a broader story. We’ll start with the Mayans' vigesimal positional numeral system—remarkable for its early and systematic use of zero—which enabled sophisticated calendrical calculations and astronomical observations. Fast forward to the present, and we encounter the work of Carolina Araujo in birational geometry, particularly her contributions to the theory of Fano manifolds and rational curves within Mori theory. These cases serve as guideposts for a deeper discussion spanning Indigenous mathematical traditions, the influence of colonial-era education, and the emergence of active research communities in Mexico, Brazil, and Argentina. By sharing these stories, we’ll see how Latin American mathematics has been shaped by creativity, exchange, and resilience, and why its contributions matter in today’s global mathematical landscape.
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Mathematics, at its heart, is African. Unfortunately, much of ancient African traditions and customs have been lost due to colonization and slavery, including their knowledge and practice of mathematics. However, artifacts uncovered by archeologists confirm the understanding of math principles by African artisans. African art holds the secret behind the history of mathematics in Africa. With a focus on Sona sand drawings, this presentation will explore the beauty of mathematics that can be pulled from the ancient customs of the Tchokwe people of Angola. By exploring the work of Paulus Gerdes, a mathematician known for his work with the Tchokwe people, a discussion of mirror curves and symmetry arises from the analysis of the Sona sand drawings. He takes the patterns created by these curves to make what he coins as Lunda-designs. In this presentation, you will learn how to create your own Lunda-design and learn why they are mathematically beautiful.
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