Aryabhata (476-550 CE) was an Indian mathematician and astronomer who lived and worked during the Gupta period. He is widely regarded as one of the most significant figures in the history of mathematics and astronomy. His principal surviving work, the Aryabhatiya (499 CE), is a compact treatise in verse covering arithmetic, algebra, plane and spherical trigonometry, and astronomy. A second work, the Arya-siddhanta, is known only through references by later scholars and is considered lost. Aryabhata is associated with an astronomical school centered at Kusumapura, identified by most scholars with Pataliputra (modern Patna, Bihar).
The Aryabhatiya is divided into four sections: the Gitikapada (cosmological constants), the Ganitapada (mathematics), the Kalakriyapada (time-reckoning), and the Golapada (spherical astronomy). Among its notable mathematical content are an approximation of π (pi) to four decimal places (3.1416), methods for extracting square and cube roots, a table of sine differences (an early trigonometric innovation), and a general solution method for linear indeterminate equations - a technique later termed the kuttaka (“pulverizer”). In astronomy, Aryabhata proposed that the apparent westward rotation of the stars results from Earth's own axial rotation, a heliocentric-adjacent position that was controversial among his contemporaries and later Indian commentators. He calculated the sidereal rotation of Earth and the lengths of the planetary periods with considerable accuracy relative to modern values. His system used a large astronomical cycle (the kalpa) as a computational base and reconciled observational data with a mathematical framework.
Aryabhata's birth is assigned by scholarly convention to 476 CE on the basis of a statement in the Aryabhatiya itself, in which he gives his age as 23 at the time of composition (499 CE). His place of birth is disputed; candidates include Ashmaka (in the Deccan) and the region around Pataliputra. The identification of “Kusumapura” with Pataliputra is widely accepted but not universally settled.
There is broad scholarly consensus on the authenticity and dating of the Aryabhatiya and on Aryabhata's foundational contributions to Indian mathematics and mathematical astronomy. See Aryabhata - Mathematics Consensus and Aryabhata - Astronomy Consensus.