The Ontology and Epistemology of Mathematics in Indian Tradition: From Ganita to Modern Abstraction

This paper undertakes a foundational exploration of the nature of mathematics from both historical and philosophical perspectives, with a primary focus on the Indian intellectual tradition. It traces the evolution of mathematical thought from ancient Vedic texts such as the ´Sulba S¯utras, through the formal grammar of P¯an. ini, to modern abstract mathematics including group theory, automata, and topology. The investigation is rooted in the dual inquiries of ontology and epistemology, examining what it means for mathematics to be and how mathematical knowledge is constructed and validated. Particular emphasis is placed on the Indian concepts of gan. ita (mathematics), ´s¯unya (zero), and ´s¯unyat¯a (emptiness), and their correspondence with Western notions such as the Cartesian dualism, the set-theoretic empty set, and symbolic logic. The paper explores the recursive cosmological cycles found in Indian time theory, mathematical cosmology, and ritual geometry, showing how these ideas anticipated or paralleled developments in modern mathematics, including measure theory, combinatorics, and fractals. With detailed references to logical systems (Ny¯aya), sacred architecture (v¯astu-´s¯astra), cyclic time constructs (kalpas and yugas), and formal structures in linguistic grammar (As.t. ¯adhy¯ay¯ı), the paper argues for a view of mathematics as both a sacred science and a system of abstract formalism. Across these investigations, mathematical structures are treated not merely as tools for calculation but as profound reflections of metaphysical principles, visualizable through mandalas, yantras, and cosmological diagrams. This study invites a reassessment of how different cultures have understood and visualized mathematics as an expression of cosmic and cognitive order.