Mathematics And Astronomy In Ancient India: Contributions Of Aryabhata And Successors

Ancient Indian mathematics and astronomy evolved as part of a tightly linked scholarly tradition wherein numbers, geometry, trigonometry, calendars, and planetary astronomy were practiced and theorized simultaneously rather than as distinct and separate activities. In such an intellectual environment, Aryabhata, whose Aryabhatiya was written around 499 CE, emerged as the pivotal classical scholar. He provided not only mathematical formulas but also geometrical facts, sine values, solutions to indeterminate equations, models for planetary motion, theories of eclipses, and the remarkable proposition that the observed daily rotation of the stars is due to the rotation of the Earth. But what made Aryabhata influential was more than just his own contributions, since other Indian mathematicians and astronomers such as Bhaskara I, Brahmagupta, Lalla, and Bhaskara II preserved, disputed, modified, and elaborated on his teachings, resulting in one of the most impressive pre-modern mathematical astronomical traditions found anywhere in the world. This paper contends that the accomplishments of Aryabhata and the Indian tradition based on his work can be considered an important scholarly tradition in which mathematics worked for astronomy, astronomy inspired mathematics, and the practice of commentary was a powerful force of innovation.