Tracing the Celestial Legacy through Mathematical and Astronomical Advancement during the Vijayanagar Empire

Santosh Kumar; Siddhant Mishra; Shalini Rana

doi:10.5269/bspm.79809

Santosh Kumar Yadav
Siddhant Mishra Research Scholar, Department of History, Lovely Professional University, Phagwara Punjab https://orcid.org/0009-0004-1200-118X
Shalini Rana https://orcid.org/0000-0002-9297-5221

Résumé

Advances in trigonometry, infinite series, and computational techniques during the late medieval Deccan transformed indigenous mathematical practice and enabled precise astronomical prediction. This study examines the construction of refined sine tables, early calculus-like series expansions, and iterative algorithms for numerical solutions, and observational protocols that underpinned planetary models. Through critical analysis of manuscripts, temple and royal inscriptions, and Sanskrit treatises, I document contributions by mathematicians and astronomers connected with the Vijayanagar sphere such as Madhava, Jyesthadeva, and Nilakantha Somayaji, whose work on trigonometric series, iterative computation, and a quasi-heliocentric planetary model anticipated later methodological shifts. The paper situates these technical advances within institutional contexts of patronage, scholarly networks, and mathematical pedagogy, demonstrating how courtly support fostered practical computation for calendrical, navigational, and ritual needs. Comparative perspectives with contemporaneous Chinese and European practices reveal convergent moves toward empirical measurement and analytic approximation, while underscoring distinct conceptual frameworks. By foregrounding mathematical methods first, the study reorients narratives about the Vijayanagar period from artistic achievements to scientific agency, arguing that its mathematical-astronomical legacy constitutes a critical bridge between classical Indian techniques and early modern scientific trajectories. The findings revise scientific historiography and offer novel frameworks for integrating South Asian mathematical practices into global histories of science.

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