Aryabhatta was a 5th century mathematician and astronomer who worked in the following areas- the methods of determining square and cube roots, geometrical problems, the progression, problems involving quadratic equations and indeterminate equations of the first degree. The method of solving these equations has been called Kuttaka by later mathematicians. He was the first astronomer to mention that the diurnal motion of the heavens is due to the rotation of the earth about its axis. Other contributions Aryabhatta made towards pure mathematics were his sine tables, his approximation of pi and the expressions that he gave for the sum of squares and the sum of cubes. All his work is documented in the Aryabhatiya.
The seminal contribution of the mathematicians and astronomer Aryabhata I (C. 476 B.C.) must be acknowledged to complete the story of India's scientific achievement. A verse in the Aryabhatiya by Aryabhata tells us the year of his birth in terms of the prevailing calendar. In the modern calendar, the birth year works out as A.D 476, with the Aryabhatiya itself being written in the year A.D 499. The book reflects the level of advancement in astronomy in fifth century India. Aryabhata gives a table of the trigonometric sine function, calling them jya in Sanskrit. The table gives the sines of angles at intervals of 3°45'. The sine tables are needed to work out the geometrical measurements of positions of stars and planets on the celestial sphere. Thus we see that Aryabhata was conversant with the notions of spherical trigonometry. Moreover, at the conceptual level, his awareness of the spherical shape of the Earth and its spin around an axis reflect how advanced he was with respect to his contemporaries. For example, he argues in one verse of the Aryabhatiya that although the stars appear to go westwards, they are in fact fixed and we are observing them from the moving platform of the spinning Earth.
Anulomagatirnausthah pashyatyachalam vilomagam yadvat
Achalani bhani tadvat sampashchimgani lankayam
- aryabhatiya 4.9
In this sloka he gives the analogy of a person going on a boat who sees fixed objects on the land going in the direction opposite to his, and he argues that the fixed stars likewise appear to go westwards because they are viewed from the moving surface of the earth. Here, Aryabhat is pointing to the spin of the earth around its axis from west to east, which gives rise to the apparent motion of the stars in the reverse direction. The analogy is exact and clear. Yet his contemporaries ignored this statement from a respected teacher and scholar like Aryabhat. It is creditable and rewarding to be slightly ahead of your contemporaries, it is much more creditable but not at all rewarding to be way ahead of them. For them they do not understand what you are saying and may ridicule your ideas. This happened to Aryabhata, too. The prevailing geocentric view did not allow one to think of the alternative of a spinning Earth. So Aryabhata's ideas remained buried and were long forgotten by the time the heliocentric view of Nicolous Copernicus (1473-1543).
( J. V. Narlikar, "The Scientific Edge").