Aryabhatta mentions in the Aryabhatiya that it was composed 3,600 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476.
Aryabhatta provides no information about his place of birth. The only information comes from Bhaskara I, who describes Aryabhatta as asmakiya, “one belonging to the Asmaka country.” During the Buddha’s time, a branch of the Asmaka people settled in the region between the Narmada and Godavari rivers in central India; Aryabhatta is believed to have been born there.
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhaskara I (CE 629), identify Kusumapura as Pataliputra, modern Patna. A verse mentions that Aryabhatta was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhatta might have been the head of the Nalanda university as well. Aryabhatta is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.
Therefore, it would make great sense that this was where he would have invested a great deal of time learning to be a great astronomer. There were not exactly scores of other opportunities for him to take advantage during the classical era as institutions in which to learn astronomy were likely very limited.
Aryabhatta is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.
The Aryabhatiya was a well-constructed work that covered many different facets of mathematics and astronomy. Portions of the work were quoted in other works and this has allowed it to avoid becoming lost. Within the mathematics portion of the work, a great deal was written about high level math topics.
There are 108 verses in the text and the style of writing is very tight and direct. It can be said the work is written in a manner not dissimilar from the sutra literature crafted at the time. Within the work, information is revealed about the table of sines, progressions in geometry and arithmetic, the relationship of time, the positions of the planets, and insights into celestial spheres. To a great extent, the work was many years ahead of its time. Both thought-provoking and introspection inducing, anyone interested in the subjects of math and astronomy would find it worth reading.
As with many of the great astronomers in history, Aryabhata promoted the notion the earth spun on its own axis and the sun revolved around the earth and not the other way around. This belief is known as heliocentrism and it was deemed a heresy in most parts of the world until well past the Middle Ages.
Aryabhatta is believed to have died around 550 A.D. He has left an amazing legacy to be sure. A great many modern mathematicians and astronomers look towards his early work for inspiration.