Śūnya, Khaṃ, and Lopaḥ: Textual and Conceptual Perspectives of Zero in Indian Traditions

Abstract

In Indian intellectual traditions, śūnya developed across Vedic literature, Sanskrit grammar, and classical mathematics, acquiring meanings associated with absence, non-manifestation, numerical representation, and equilibrium. This study examines the concept through a textual and comparative analysis of selected Sanskrit sources, including the Ṛgveda, Yajurveda, Pāṇini’s Aṣṭādhyāyī, Āryabhaṭa’s Āryabhaṭīya, Brahmagupta’s Brahmasphuṭasiddhānta, and Bhāskarācārya’s Bījagaṇitam. Particular attention is given to the terms khaṃ, lopaḥ, adarśana, abhāva, and śūnya and their respective textual contexts. In Indian mathematics, śūnya is examined through its treatment as a numerical state, including Brahmagupta’s formulation of the sum of equal positive (dhana) and negative (ṛṇa) quantities. In Pāṇinian grammar, lopaḥ is examined as non-appearance within a rule-governed linguistic system. By bringing these textual traditions into comparative dialogue while maintaining their historical distinctions, the study explores śūnya as a multi-layered concept involving numerical representation, functional non-manifestation, and equilibrium.

Keywords

• Sanskrit
• Zero
• Interpretation
• Synonym