Vedic Theorems based on Vedic Mathematics Sutras

Abstract

This paper explores the formalization of ancient Vedic Mathematics Sutras as mathematical theorems. Vedic Mathematics, a collection of mental calculation techniques derived from ancient Indian texts, offers intuitive and efficient methods for a variety of mathematical operations. These sutras, traditionally expressed in a succinct and aphoristic style, are reinterpreted here using the rigorous language of modern mathematics. We begin by presenting a comprehensive overview of the primary Vedic Sutras, highlighting their historical significance and practical applications. Each sutra is then translated into a formal theorem, complete with precise definitions, conditions, and domains of applicability. Following this, we provide detailed proofs for each theorem, demonstrating their validity and reliability within the framework of contemporary mathematical logic. Through this formalization process, we aim to bridge the gap between ancient mathematical wisdom and modern theoretical foundations, showcasing the timeless utility of Vedic techniques. Additionally, we discuss the implications of these theorems for modern computational methods and educational practices, suggesting potential areas for further research and application. By rigorously defining and proving these Vedic Theorems, this paper not only preserves the rich heritage of Vedic Mathematics but also enhances its accessibility and relevance to present-day mathematicians, educators, and students