### Mathematics and Astronomy

In the scientific field, Brahmagupta is the most outstanding figure in this period. He made a number of seminal contributions in mathematics. He was the first mathematician in the world to recognize negative numbers, which he presented as ‘debts’ in contrast to positive numbers, which he called ‘fortunes’. In many other ways he was ahead of the mathematicians of the time. For instance, one of his methods for proving Pythagoras’ theorem remained unknown to the western world till the seventeenth century. Astronomy was closely linked to mathematics, the word for the mathematician – *ganaka *– being also the term for the astronomer. Like his equally eminent predecessor Aryabhata, Brahmagupta was thus an astronomer also. He headed a major observatory, and grappled with such questions as lunar and solar eclipses, conjunctions of the moving planets with each other as well as with fixed stars, etc.

The *Surya Siddhanta*, which provided the basis of medieval astronomy in India from the fifth century onwards by replacing the Vedanga astronomy, continued to undergo gradual changes; it was its later version, one that evolved between 628 and 960 CE that was to gain immense popularity. In Tamil region, an old system of astronomical calculations by means of certain numerical schemes continued as a parallel tradition, as distinct from the trigonometrical tradition of the *Surya Siddhanta*. Apart from Brahmagupta, Bhaskara I, who was a contemporary of Brahmagupta and a disciple of the great Aryabhata, and Lalla (748 CE) were the leading astronomers of our times.

### Medicine

In medicine, Vagbhata claimed, or was claimed, to have become the leading authority for his age, rendering superfluous the previous masters. There are two Vagbhatas, the first of whom wrote a treatise called the *Ashtanga-sangraha*, and who flourished in the seventh century just before the visit of the Chinese pilgrim Yijing. Scholars place the other Vagbhata, the author of *Ashtanga-hrdaya-samhita*, about a century later. Both were Buddhists, and thus bear witness to the close links of Buddhism with the medical tradition; medicine was avidly studied in the monasteries of Nalanda and Vikramashila.