Aryabhata, also called Aryabhata I or Aryabhata the Elder, an astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. He is also known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name. He flourished in Kusumapura—near Pataliputra (Patna), then the capital of the Gupta dynasty—where he composed at least two works, Aryabhatiya (c. 499) and the now lost Aryabhatta Siddhanta.
Aryabhatta Siddhanta circulated mainly in the northwest of India and, through the Sāsānian dynasty (224–651) of Iran, had a profound influence on the development of Islamic astronomy. Its contents are preserved to some extent in the works of Varahamihira (flourished c. 550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. It is one of the earliest astronomical works to assign the start of each day to midnight.
Aryabhatiya was particularly popular in South India, where numerous mathematicians over the ensuing millennium wrote commentaries. The work was written in verse couplets and deals with mathematics and astronomy. Following an introduction that contains astronomical tables and Aryabhata’s system of phonemic number notation in which numbers are represented by a consonant-vowel monosyllable, the work is divided into three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola (“Sphere”).
In Ganita Aryabhata names the first 10 decimal places and gives algorithms for obtaining square and cubic roots, using the decimal number system. Then he treats geometric measurements—employing 62,832/20,000 (= 3.1416) for π, very close to the actual value 3.14159—and develops properties of similar right-angled triangles and of two intersecting circles. Using the Pythagorean theorem, he obtained one of the two methods for constructing his table of sines. He also realised that second-order sine difference is proportional to sine. Mathematical series, quadratic equations, compound interest (involving a quadratic equation), proportions (ratios), and the solution of various linear equations are among the arithmetic and algebraic topics included. Aryabhata’s general solution for linear indeterminate equations, which Bhaskara I called kuttakara (“pulverizer”), consisted of breaking the problem down into new problems with successively smaller coefficients—essentially the Euclidean algorithm and related to the method of continued fractions.
With Kala-kriya Aryabhata turned to astronomy—in particular, treating planetary motion along the ecliptic. The topics include definitions of various units of time, eccentric and epicyclic models of planetary motion (see Hipparchus for earlier Greek models), planetary longitude corrections for different terrestrial locations, and a theory of “lords of the hours and days” (an astrological concept used for determining propitious times for action).
Aryabhatiya ends with spherical astronomy in Gola, where he applied plane trigonometry to spherical geometry by projecting points and lines on the surface of a sphere onto appropriate planes. Topics include prediction of solar and lunar eclipses and an explicit statement that the apparent westward motion of the stars is due to the spherical Earth’s rotation about its axis. Aryabhata also correctly ascribed the luminosity of the Moon and planets to reflected sunlight.
The Indian government named its first satellite Aryabhata (launched 1975) in his honour.

His pure mathematics discusses topics such as determination of square and cube roots, geometrical figures with their properties and mensuration, arithmetric progression problems on the shadow of the gnomon, quadratic equations, linear and indeterminate equations. Aryabhata calculated the value of pi (π) to the fourth decimal digit and was likely aware that pi (π) is an irrational number, around 1300 years before Lambert proved the same. Aryabhata’s sine table and his work on trignometry were extremely influential on the Islamic Golden Age; his works were translated into Arabic and influenced Al-Khwarizmi and Al-Zarqali. In his spherical astronomy, he applied plane trigonometry to spherical geometry and gave calculations on solar, lunar eclipses. He discovered that the apparent westward motion of stars is due to the spherical Earth’s rotation about its own axis. Aryabhata also correctly discovered that the luminosity of the Moon and other planets is due to reflected sunlight. For his explicit mention of the relativity of motion, he also qualifies as a major early physicist
A verse mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was near Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.[12] Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.