Aryabhata (476-550 CE) is most known ancient mathematician-astronomers from the golden age of Indian mathematics and astronomy. His most famous works are the Aryabhatiya (499 CE, when he was 23 years old) and the Arya-siddhanta.
The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry. It also contains quadratic equations, continued fractions, sums-of-power series and a table of sines. He wrote different verses to calculate position of moon and planets. He also discovered some simple instruments for astronomical measurements.
His most known work includes, discovery of place value system and zero, approximate value of pi (accurate to five significant figures) and solution of quadratic equation. In astronomy, he correctly insisted that the earth rotates about its axis daily and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the then-prevailing view that the sky rotated. He also treated the planet's orbits as elliptical rather than circular. Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes and 30 seconds (365.25858 days) is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days). Solar and lunar eclipses were also scientifically explained by Aryabhata.
Aryabhata-The Indian Mathematical Genius
Aryabhata a Gupta Astronomer
(This video is made by armatures but it underlines some of the important discovery of Aryabhata)