DEVELOPMENTS OF MATHEMATICS AND ASTROLOGY IN ANCIENT INDIA: TEXTUAL TRANSMISSION, ASTRONOMICAL CALCULATIONS, LEGACY, AND INTERNATIONAL IMPACT

Abstract

The development of mathematics and astrology in ancient India represents one of the most remarkable intellectual traditions in human history. Rooted in the Vedic period, this tradition covers more than three millennia, showing a continuous evolution of numerical, geometric, astronomical, and predictive sciences. Early mathematical ideas emerged with the ŚulbaSūtras, which presented advanced geometric principles, namely the Pythagorean theorem, methods of constructing altars, properties of similar figures, and rules for transforming geometric shapes. These works, though ritualistic in intention, lay the bedrock for later advances in algebra, mensuration, and trigonometry. Subsequent mathematicians, including Baudhayana, Āpastamba, Pingala, Aryabhata, Brahmagupta, Bhaskaracharya, Mahaviracharya, and Varahamihira, substantially expanded this knowledge system. Their contributions developed the decimal place-value system, the invention and codification of zero, the development of algebraic methods, trigonometric functions, combinatorics, iterative techniques, and early ideas related to calculus, especially by the Kerala School. Texts like Vedāṅga Jyotiṣa, Surya Siddhanta, Aryabhatiya, Brahmasphutasiddhanta, and Siddhanta Shiromani laid down regular astronomical patterns for the motions of planets, eclipses, calendrical calculations, and timekeeping. Scholars like Aryabhata and Brahmagupta made use of mathematical precision to determine the rotation of Earth, distances of the planets, and periodicity in the heavens, while Varahamihira combined astronomical observations with predictive astrology, as seen in BṛhatSaṃhitā and BṛhatJātaka. In due course, astrology branched out into Horā or predictive astrology, Gaṇita or astronomical computation, and Saṃhitā or mundane astrology, under the influence of contacts with Greek, Persian, and finally regional schools. Taken together, these developments highlight a profoundly interconnected knowledge system in which mathematics, astronomy, and astrology enriched one another. Above all, the innovations of ancient India most notably zero, trigonometry, algebra, and sophisticated astronomical models shaped its own cultural and scientific practices and contributed profoundly to global scientific progress.