An Attempt to Derive Mathematical Theorems from Vedic Sub-Sutras

The Vedas are the most ancient knowledge reservoir of Hindu philosophy. Bharati Krishna Tirtha Ji developed Vedic mathematics after eight years of intensive study of the Vedas. He extracted mathematical concepts from the Vedas and developed Vedic mathematics, which consists of sixteen sutras and thirteen sub-sutras. This paper investigates the translation of ancient Vedic Mathematics sub-sutras into formal mathematical theorems. Vedic Mathematics, celebrated for its intuitive and effective mental calculation methods, is reexamined through the lens of contemporary mathematics. The analysis begins with summarizing significant Vedic sub-sutras, highlighting their historical significance and practical uses. Each sub-sutra is rephrased into a formal theorem with clear definitions, criteria, and applicable domains. Where appropriate, detailed proofs are included, showcasing the validity of the established theorems within modern mathematical reasoning. This research aims to connect ancient mathematical knowledge with modern theory, illustrating the relevance of Vedic methods for today’s mathematicians, educators, and learners, while also proposing future research opportunities.