Seventh Century

628 Ancient Indian mathematician and astronomer Brahmagupta completes the Brāhmasphuṭasiddhānta, a text on mathematical astronomy explaining the role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations.
629 - 645 The famous Chinese traveler Hiuen Tsang visited India during Emperor Harshawardhana's reign. But his kingdom disintegrated into small states even as Hunas invaded. It was a period when the Deccan and the south became powerful.
500 – 750 Empires of Chalukyas (543 – 753), Pallavas (275 – 897) & Pandya (200 BC – 1300) – all southern India - flourished.