ROPES, RITUALS, AND RADICAL MATH: INDIA’S GEOMETRIC REVOLUTION

Abstract

This paper presents a comprehensive theoretical framework that interprets Indian mathematics as a product of ritual-constrained innovation. Grounded on computational analysis of Sanskrit manuscripts, archaeological data from Vedic sites, and altar geometries, the study argues that sacred practices catalyzed crucial developments in geometry, algorithmic reasoning, and proto calculus. It highlights three key transitions: the geometric precision of √2 in the Sulbasutra (c. 800–400 BCE); Aryabhata’s transformation of altar logic into recursive algorithms and sine functions (499 CE); andthe Kerala School’s derivation of infinite series for π and sine, grounded in spiritual concepts of convergence and preceding European calculus by more than two centuries. The proposed “ritual-seed model,” show sacred limitations fostered mathematical abstractions through embodied material activities, recursive altar approach, and sacralized rectification. Textual analysis, which tracks Sanskrit works through Arabic translations (e.g., Arjabhar, 770 CE) and Jesuit documents (Codex Vaticanus 459) reinforces the model’s global significance. India is repositioned as a generative hub challenging Eurocentric narrative while encouraging decolonial re-assessment of the ritualistic foundations of mathematical reasoning.