Logical Foundations of Vedic Mathematics: A Nyāya–Vaiśeṣika Perspective

Abstract

This paper presents a philosophical reflection on Vedic Mathematics through the framework of Indian logic, particularly the Nyāya and Vaiśeṣika systems[2][5]. While Vedic Mathematics is widely recognized for its computational efficiency and mental calculation techniques, this study highlights its deeper epistemological and logical foundations[6]. By analyzing key concepts such as pramāṇa (means of valid knowledge), Nyāya’s five-step syllogism, and Vaiśeṣika’s categorization, the paper demonstrates that Vedic sutras are not merely heuristic shortcuts but condensed expressions of systematic reasoning[2][3][5]. The work further explores how these logical principles manifest in commonly used sutras like Urdhva-Tiryakbhyam, Nikhilam, and Ekādhikena Pūrvena, revealing their alignment with inference, analogy, and perceptual cognition[6]. Additionally, the study situates Vedic Mathematics within contemporary contexts such as cognitive science, artificial intelligence, and pedagogy, emphasizing its relevance in modern knowledge systems[7][2]. Ultimately, the paper argues that Vedic Mathematics represents a synthesis of intuition and formal logic, deeply rooted in Indian philosophical traditions, and offers significant potential for interdisciplinary research[1][4].