Doctoral Dissertation Research: The Shift from Abstraction to Material and Virtual Models in Mathematical Research and Pedagogy

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IntroductionAt the beginning of the twenty-first century, mathematicians sought tangible experiences with mathematical theories and objects; in turn, they advocated an experiential, embodied, and sensorial mediated approach to mathematical training. Intellectual MeritThrough archival research, in-depth interviews, and participant observation in conferences, classrooms, and labs, this project aims to locate the shift characterized above in its historical and institutional context. Specifically, this project asks what prompted and enabled mathematicians to seek a more embodied and procession understanding of mathematical ideas, and then tracks what this change might entail for the way mathematics is now communicated and taught.To answer the above questions, PhD candidate will examine five case studies starting in the 1960s and leading up to the present: (1) mathematical videos produced in the late 1960s to illustrate otherwise abstract and difficult to imagine mathematical problems; (2) a 1987 drawing manual that called on topologists to draw pictures and illustrate their work; (3) An NSF-funded mathematical research center at the University of Minnesota, established in 1991, that was dedicated to developing visualization programs for mathematicians; (4) the appropriation of fiber arts (such as knitting and crocheting) to investigate the properties of mathematical surfaces; and (5) the emergence over the past two decades of computational origami, which brings the ancient art of origami under the purview of professional mathematics.All five cases represent examples of "mathematical manifestation," which denotes the concrete, demonstrable, exemplary, displayable, and presentable aspects of mathematical research. By focusing on the experiential aspects of mathematical work, this project seeks to bring to the history of mathematics practice-based investigations and theoretical tools developed by science studies scholars, as well as offer a unique theoretical intervention into theories of mathematical practice.Potential Broader ImpactsThis project will contribute to scientific pedagogy by examining a under examined approach to mathematical education, which supplements the axiomatic abstract method by cultivating the experiential, hands-on, and embodied nature of mathematical work. By focusing on the application of computer graphics in mathematics, the project will provide a new perspective from which to understand debates within theMathematical community regarding the application of computer technology to mathematical work.