Mathematical Contents Of Jaina Texts

Summary

This article examines the rich mathematical tradition found within Jain canonical and philosophical texts, especially focusing on the symbolic and structured approach of Digambara Jain scholars. Jain works like the Gommatasāra, Labdhisāra, and Tiloyapaṇṇatti are noted for their algebraic, geometric, and set-theoretical approaches, especially as they pertain to karma theory and cosmology. Key highlights include: i) Symbolic Mathematics: The use of arithmetic, algebraic, and geometric symbolism in texts like the Karṇāṭaka Vṛtti and Labdhisāra highlights a formalized mathematical system. ii) Karma Theory and Cosmology: Jain mathematics models not just abstract theory but concrete cosmological and karmic phenomena using variables like pradeśa (space units), anubhāga (energy levels), sthiti (duration), and prakṛti (configuration). iii) Early Use of Zero & Place Value System: Jain texts demonstrate early understanding and use of zero and advanced number systems. iv) Set Theory & Computation: Concepts like fixed/variable sets, transfinite cardinality, triangular matrices, and symbolic logic mirror elements of modern set theory and computing. Proposals are made for their computational modeling in C++ or Mathematica. v) Mathematical Vocabulary: A large inventory of measurable terms (e.g., parikarma, vargana, rāśi, kalpa, yojana) is discussed, some of which can be structured for computerization or theoretical physics models. vi) Scholarly Contributions: Scholars like Pandit Todaramala, Mahāvīrācārya, and Srīdhara are credited for formalizing Jain mathematics. Srīdhara's possible Jaina background is discussed in detail.