Dynamic Platonism: Mathematics, Gesture, and Philosophy

Abstract

This paper explores the concept of Dynamic Platonism as a transformative framework for understanding mathematical ontology and practice. Moving beyond traditional ontological Platonism, which posits eternal, unchanging mathematical Forms, Dynamic Platonism emphasizes the fluid, historically situated, and diagrammatically enacted nature of mathematical idealities. Drawing from the work of Lautman, Cavaillès, and contemporary models such as TSK, the authors highlight how mathematical objects are dynamically constituted through gestures, diagrams, and formal processes that evolve within specific contexts. This approach reconciles invariance with change, viewing mathematical truths as partial invariants embedded in a flux of history and embodied activity.