“The adoration of the sun, of the planets, and of the stars, in common with the worship of the elements, had a principal place in their religious observances enjoined by the Vedas; and they were led constantly by piety to watch the heavenly bodies. They were particularly conversant with the most splendid of the primary planets, the period of Jupiter being introduced by them, in conjunction with those of the sun and moon, into the regulation of their calendar, sacred and civil, in the form of the celebrated cycle of sixty years." H.T. Colebrooke, 1817.

The first Hindu writer on algebra and astronomy in the purāṇic age was Āryabhaṭa. He was born in Pātalīputra, in 476 CE, and is the author of the Āryabhaṭīya, consisting of the Gītikāpāda, the Gaṇitapāda, the Kālakriyāpāda, and the Golapāda. At the time, Pāṭaliputra in Magadha was a renowned ancient seat of learning that housed the famous University of Nālandā, which likely had an astronomical observatory. Āryabhaṭa was born the very year that the Gupta king Buddhagupta assumed power at Pāṭaliputra. More precisely, 3600 years of the Kali era came to an end on Sunday, 21 March 499 CE, at mean noon at Laṅkā or Ujjayinī, at the moment of the mean Sun's entry into the sign Aries (madhyama-meṣa-saṃkrānti). His birth is accordingly placed at meṣa-saṃkrānti, 21 March 476 CE. 

In his magnum opus, the pioneering  astronomer boldly maintains the theory of the revolution of the earth on its own axis, and the true cause of solar and lunar eclipses. “As a person in a vessel, while moving forward," says Āryabhaṭa, “sees an immovable object moving backward, in the same manner do the stars, though immovable, seem to move daily."  His other work, the Āryabhaṭa-siddhānta, survives only through citations in later literature. Varāhamihira, who followed Āryabhaṭa, distinguishes between the two by the system of day-reckoning employed: one begins the day at midnight at Laṅkā, the other at sunrise — both attributed to Āryabhaṭa.

The Āryabhaṭīya of Āryabhaṭa is a highly concise and technically dense treatise comprising 121 verses that integrate mathematical and astronomical knowledge within a rigorously structured framework. Composed in an aphoristic style—often omitting grammatical elements such as case endings—it presupposes interpretive engagement through commentary traditions.

The text is organized into four pādas (sections), each addressing a distinct domain. The Gītikāpāda establishes foundational cosmological and astronomical constants, including large temporal cycles, units of measurement, planetary revolutions, orbital parameters, and trigonometric data such as sine differences. The Gaṇitapāda presents a systematic treatment of mathematical techniques, encompassing geometry, arithmetic progressions, interest calculations, and both determinate and indeterminate equations, alongside algorithms for root extraction and sine table construction.

The Kālakriyāpāda focuses on temporal computation and planetary kinematics, detailing calendrical divisions, types of time reckoning, and computational procedures for deriving true planetary positions using models such as epicycles and eccentric circles. Finally, the Golapāda advances into spherical astronomy, explicating the geometry of the celestial sphere, observational perspectives from different terrestrial latitudes, and methods for predicting eclipses and planetary visibility.

Taken together, the work exemplifies a synthesis of theoretical abstraction and computational utility, reflecting the sophistication of early Indian scientific thought in both mathematics and astronomy. Āryabhaṭa also developed an original alphanumeric notation system to encode large numbers within metrical verse, enabling compact representation of complex astronomical data and distinct from the later kaṭapayādi system. He also provided a highly accurate approximation of π as 3.1416 (expressed as the ratio 62,832:20,000), surpassing earlier estimates such as that of Ptolemy. Notably, Āryabhaṭa explicitly characterized this value as an approximation (āsanna), reflecting a clear awareness of mathematical precision and epistemic limitation.

Āryabhaṭa also formulated a planetary theory grounded in four core assumptions: an initial conjunction of all celestial bodies at the beginning of the current yuga, geocentric circular motion of mean planets, the use of eccentric and epicyclic models (manda and śīghra) to determine true planetary positions, and uniform linear motion within respective orbits. His epicyclic framework is considered methodologically distinct from that of Ptolemy, suggesting independent development. He introduced significant computational innovations by reducing the number of corrective factors required for inferior planets and refining the calculation of planetary distances through a geometric mean approach. Additionally, Āryabhaṭa provided the first accurate method for determining celestial latitudes of both superior and inferior planets. His adoption of a circle radius of 3,438 arc-minutes—effectively aligning with radian measure—marked an important advancement in simplifying trigonometric calculations and influenced subsequent Indian astronomical practice.

Āryabhaṭa’s Āryabhaṭīya, distinguished by its brevity, precision of astronomical constants, and methodological innovations, emerged as a canonical text that defined the trajectory of Indian astronomy. It gave rise to the Āryabhaṭa School (Āryabhaṭīya-pakṣa), whose adherents venerated him as Bhagavān and Prabhu, and whose intellectual lineage was consolidated by figures such as Bhaskara I through influential commentarial and exegetical works. The text’s authority persisted across centuries, shaping scholarly discourse from Brahmagupta to later commentators like Pṛthūdaka and Bhaṭṭotpala, and remaining central to astronomical study—particularly in South India and especially in Kerala—until the advent of modern Western astronomy. Its enduring impact is evident in the widespread tradition of citation, the proliferation of commentaries and derivative treatises, and its foundational role in regional calendrical systems. Within the Indian Knowledge Systems (IKS), Āryabhaṭa thus stands not merely as an innovator, but as the progenitor of a sustained and authoritative scientific tradition.

References: 

Kripa Shankar Shukla’s Introduction to the critical edition of the Āryabhaṭīya, Indian National Science Academy, New Delhi, 1976.

A History of Civilisation in Ancient India Based on Sanskrit Literature (Volume 2) by Romesh Chunder Dutt, 1893 https://www.google.co.in/books/edition/A_History_of_Civilisation_in_Ancient_Ind/XPi9D3HYIOEC?hl=en&gbpv=0