RUME 28
2026
Alexandria, Virginia
The Case for Complexity Theory and Formal Science to Study the Structure of Mathematics
Page: 964
Mathematical structure refers to the characteristics, topology, and relationships within and between mathematical concepts invariant to external contexts and interpretations which instantiate the concept. Research on mathematical structure is typically guided by the post-positivist and interpretivist research paradigms, which respectively emphasize the impact of human observations and interpretations on mathematical concepts, both of which are external to the intrinsic structure of mathematical concepts. This report proposes a shift to complexity theory, a research paradigm standard to modern physics and engineering which emphasizes physically necessary mathematical principles over observation and interpretation, to faithfully study structure intrinsic to mathematics itself. I propose the Tornado Theory as a theoretical framework emerging from the tenets of complexity theory and current mathematics education literature which could guide future research on mathematical structure. Finally, potential analytical techniques for the Tornado Theory based on network- and information-theoretic principles are introduced.