Every summer, the Taylor Mathematics Department participates in FMUS, which is Faculty Mentored Undergraduate Scholarship. Under the supervision of a Taylor faculty member, students research a topic of their field over an eight-week period during the summer.
Sophomores Kate Poorbaugh and Sylvia Huang worked with Dr. Jeremy Case during the summer of 2025. The project involved Napier’s Calculating Machines. John Napier is generally credited with inventing the logarithms in the 1500’s, but he also developed several methods to perform the four arithmetic functions as well as square and cubic roots. He claimed, “Arithmetic has now become a game. Gone is the tedium of calculation.”
Dr. Case created the idea of looking at Napier’s machines while researching a Math History class trip to London and Paris for a future January (maybe 2027). Originally, the idea was planned as a great math education research project comparing our contemporary paper and pencil arithmetic calculations to ancient and historical means. Since Sylvia, a Data Science major, and Kate, a double major in Mathematics and Political Science, Philosophy, and Economics agreed to participate, the project adapted to pursue interests more relevant to their majors. Patent law is one of Kate’s interests so she was particularly curious in whether Napier retained his intellectual property rights.
We looked at primary historical sources. Sylvia and Kate created physical wooden copies of Napier’s “bones” in bases besides base 10. They put together his Promptuary which is able to perform multi-digit multiplication by aligning sheets of paper together.
Mathematical research often goes in ways you did not plan. We discovered another of Napier’s machines, the chessboard-abacus, could be applied to a number system based on the golden ratio. Furthermore, the physical moves became a sort of game in calculating arithmetic operations and square roots. One physical move is like jumping over a peg like the solitaire game involving golf tees you find in Cracker Barrell. It referenced back to Napier’s ideas of arithmetic as a game.
Kate and Sylvia presented their work at an Indiana Undergraduate Math conference at Indiana University-Indianapolis. We also traveled to Ohio State University for the Young Mathematicians Conference July 31-August 1. The two presented their work among other undergraduate math researchers from around the country including Yale, Princeton, Cambridge, and other top institutions. Sylvia and Kate made a great presentation.
Our plans are for Sylvia and Kate to submit their work to an undergraduate research journal in the coming year and present a poster at Taylor’s Homecoming. Their work follows a long line of summer undergraduate research in Taylor’s Math Department.
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