Abstract / Synopsis
Creativity, informal reasoning and dynamic exchange of ideas form the pulsating heart of mathematical creation. In this approach, the concept of a mathematical object surpasses conventional boundaries of formal presentation, as they also encompass the intention to prove, significant creative stages within the proving, and the overall experience of prover's journey, which may involve arguments, debates, discovery insights, aesthetic visualizations, and narrative elements. In this paper we present two conceptual frameworks, namely Argumentation-based Proof-Events Calculus (APEC) and Mathematical RUPAs, in order to provide distinct yet interconnected perspectives on informal thinking, knowledge creation, and proving in mathematics. Following the two perspectives, we explore the nature of mathematical objects, the diverse roles of provers, and the influence of social and pluralistic factors in proving practices. Through this analysis, we aim to create a synthesis, named RUPAPEC, that elucidates how the creative and sociocultural dimensions presented in these two approaches can come together into a harmonious whole by mutually reinforcing each other. This theoretical synthesis embodies an ontological exploration delineating the essence and existence of mathematical objects as dynamic entities shaped by creative cognitive processes and interactive dialogues.
DOI
10.5642/jhummath.ZYAD5948
Recommended Citation
Sofia Almpani, Petros Stefaneas & Mihir Chakraborty, "A Dualistic Interpretation of Mathematical Creation Through Art and Argumentation," Journal of Humanistic Mathematics, Volume 15 Issue 2 (July 2025), pages 237-273. DOI: 10.5642/jhummath.ZYAD5948. Available at: https://scholarship.claremont.edu/jhm/vol15/iss2/11
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