The Aryabhatiya is a Sanskrit astronomical and mathematical treatise composed by the Indian mathematician and astronomer Aryabhata (476-550 CE). Written in 499 CE when Aryabhata was approximately 23 years old, it is one of the earliest surviving works of Indian classical astronomy and among the most influential scientific texts of the ancient world. The text is composed in verse form and covers arithmetic, algebra, plane and spherical trigonometry, and a model of planetary motion. It served as a foundational reference for later Indian astronomical schools and was translated into Arabic during the Islamic Golden Age, contributing to the transmission of Indian mathematics to the wider world.

The Aryabhatiya is organized into four sections (padas): the Gitikapada, a brief introductory section stating cosmological parameters; the Ganitapada, covering mathematics including place-value notation, square and cube roots, series, and the approximation of pi (π ≈ 3.1416); the Kalakriyapada, addressing time-reckoning and planetary models; and the Golapada, treating the celestial sphere, eclipses, and the geometry of celestial phenomena. The mathematical sections introduce what is now recognized as an early treatment of indeterminate equations (kuttaka), a method later developed into what Western mathematics calls the Euclidean algorithm applied to linear Diophantine equations.

The Aryabhatiya presents a geocentric model of the solar system in which the Earth rotates on its axis - a position that distinguished Aryabhata from many of his contemporaries and successors in the Indian tradition. His model accounts for the apparent motion of the stars as a consequence of terrestrial rotation rather than stellar movement. Aryabhata calculated the length of the sidereal year as approximately 365 days, 6 hours, 12 minutes, and 30 seconds, a figure close to modern measurements. He also provided calculations for the distances and diameters of the planets, and offered a correct geometric explanation of solar and lunar eclipses as caused by shadows rather than by supernatural agency. The relationship between elements that some scholars read as proto-heliocentric and later models such as the Tychonic system has been a subject of comparative historiography in the history of astronomy.

The Aryabhatiya was commented upon extensively by later Indian scholars, most notably Bhaskara I (c. 629 CE) and Nilakantha Somayaji (c. 1500 CE). Arabic translations, produced during the 8th and 9th centuries, introduced its mathematical and astronomical methods to Islamic scholars, who in turn influenced European medieval science. The Kerala school of astronomy and mathematics, active from the 14th through 16th centuries, built substantially on Aryabhata's framework, developing infinite series expansions for trigonometric functions that predate similar discoveries in European mathematics.

There is broad consensus among historians of science and mathematicians that the Aryabhatiya represents a significant and original contribution to pre-modern mathematics and astronomy. Scholarly debate continues regarding the extent of Aryabhata's originality versus his synthesis of earlier Indian traditions, and regarding whether certain passages imply a partially heliocentric model or remain strictly geocentric. See Aryabhatiya - History of Science Consensus.

• Geocentric interpretation: Most historians read the Aryabhatiya as operating within a geocentric framework, with Earth's axial rotation as a kinematic device rather than a cosmological commitment. See Geocentric Interpretation Viewpoint.
• Proto-heliocentric interpretation: A minority of scholars argue that certain passages, particularly those relating planetary periods to solar motion, imply a partially sun-centered model anticipating later developments. See Proto-Heliocentric Interpretation Viewpoint.
• Transmission and influence debate: Historians disagree about the directness of the Aryabhatiya's influence on Islamic and subsequently European astronomy, with some emphasizing independent parallel development. See Transmission and Influence Debate Viewpoint.

• Aryabhatiya - History
• Aryabhatiya - Debate
• Aryabhatiya - History of Science Consensus
• Aryabhata
• Indian Mathematics
• Tychonic System
• History of Astronomy
• Transmission of Knowledge - Islamic Golden Age

1. Aryabhata. Aryabhatiya. Ed. and trans. Walter Eugene Clark. Chicago: University of Chicago Press, 1930.
2. Kim Plofker. Mathematics in India. Princeton: Princeton University Press, 2009. pp. 111-149.
3. David Pingree. “Aryabhata.” Dictionary of Scientific Biography, vol. 1. New York: Scribner, 1970. pp. 308-309.
4. Takao Hayashi. “Aryabhata's Rule and Table for Sine-Differences.” Historia Mathematica 17 (1990): 105-153.
5. George Ifrah. The Universal History of Numbers. New York: Wiley, 2000. pp. 447-452.