From 500 BCE to 500 CE
No one disputes the fact that the writing of the Āryabhaṭīya in 499 CE marked a decisive turning point in the story of mathematics in India. Within its four chapters are to be found ideas and techniques of such originality and power as to have set the course, like a latter-day As. t.ādhyāyī, for the enterprise of mathematics and astronomy for a long time to come. The best known of Aryabhata’s mathematical achievements are the invention of plane trigonometry and, within it, the setting up and the approximate solution of the 2nd order difference equation for the functions sine and cosine, but there are also other ‘gems’, a term which he himself uses. From the historical perspective, as significant as these innovations was the fact that mathematics found a new driving force in astronomy.
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