Mathematics under Gupta Empire
In the realm of arithmetic the most important achievement was the discovery of the decimal system of notation. It was based upon the principle of the place value of the first nine numbers and the use of the zero. Geometry attained great heights and many theorems relating to circles and triangles are mentioned. The most famous work in mathematics was that of Aryabhatta, the Aryabhattiyam which was written in 499 A.D. the work deals with arithmetic, geometry and algebra. Trigonometry was also being cultivated during this time. Indians took the lead over the Greeks as far as mathematics is considered.
Astronomy under Gupta Empire
Astronomy made great progress during the age. Varahamihira and Aryabhatta were the major astronomers. Aryabhatta pointed out that eclipses were caused by the moon coming within the earth`s shadow or between the earth. He utilized trigonometry in astronomy. He worked out accurate formulas to measure two consecutive days. He had also obtained correct equation for the planet`s orbit. Aryabhatta was much more advanced than the European astronomers. Most probably he began composing his work Panchasiddhahtika in 505 A.D. He discusses in this work the principles of the five astronomical schools, which were considered as the most authoritative one in his time. Of these five schools the RomakaSiddhanta clearly betrays Western influence. This is expected to happen as a result of active trade contacts between the Roman Empire and the Gupta Empire. The Surya Siddhanta is the most important and complete astronomical work of the period. It seems that Greek astronomy served as the basis