Biography

Aryabhatta (CE 476–550) is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (CE 499 at age of 23 years) and Arya-Siddhanta. Aryabhata introduced the number Zero. He is presumed to have discovered the value of pi, and proved that it is irrational.Though Aryabhata's year of birth is clearly mentioned in Aryabhatiya, exact location of his place of birth remains a matter of contention amongst the scholars. Some believe he was born in the region lying between Narmada and Godavari, which was known as Ashmaka and they identify Ashmaka with central India including Maharashtra and Madhya Pradesh, though early Buddhist texts describe Ashmaka as being further south, dakshinapath or the Deccan, while other texts describe the Ashmakas as having fought Alexander, which would put them further north.

However, it is fairly certain that at some point, he went to Kusumapura for higher studies, and that he lived here for some time. Bhāskara I (CE 629) identifies Kusumapura as Pataliputra (modern Patna). He lived there in the dying years of the Gupta empire, the time which is known as the golden age of India, when it was already under Hun attack in the Northeast, during the reign of Buddhagupta and some of the smaller kings before Vishnugupta.

Arayabhata uses Sri Lanka as reference for his astronomical systems and mention Sri Lanka on numerous occasions in Aryabhatiya. According to Florian Cajori, Aryabhata's mathematics was much closer to Sri Lankan mathematics than Indian mathematics.


 Works

Aryabhata 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 Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary Varahamihira, as well as through later mathematicians and commentators including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta, and uses the midnight-day-reckoning, as opposed to sunrise in Aryabhatiya. This also contained a description of several astronomical instruments, the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.

A third text that may have survived in Arabic translation is the Al ntf or Al-nanf, which claims to be a translation of Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the ninth c., it is mentioned by the Persian scholar and chronicler of India, Abū Rayhān al-Bīrūnī.



Aryabhatiya

 Direct details of Aryabhata's work are therefore known only from the Aryabhatiya. The name Aryabhatiya is due to later commentators, Aryabhata himself may not have given it a name; it is referred by his disciple Bhaskara I as Ashmakatantra or the treatise from the Ashmaka. It is also occasionally referred to as Arya-shatas-aShTa, lit., Aryabhata's 108, which is the number of verses in the text. It is written in the very terse style typical of the sutra literature, where each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The entire text consists of 108 verses, plus an introductory 13, the whole being divided into four pAdas or chapters:

1.Gitikapada: (13 verses) large units of time - kalpa, manvantra, yuga, which present a cosmology that differs from earlier texts such as Lagadha's Vedanga Jyotisha(ca. 1st c. BCE). Also includes the table of sines (jya), given in a single verse. For the planetary revolutions during a mahayuga, the number of 4.32mn years is given.

2.Ganitapada (33 verses), covering mensuration (kShetra vyAvahAra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations (kuTTaka)

3.Kalakriyapada (25 verses) : different units of time and method of determination of positions of planets for a given day. Calculations concerning the intercalary month (adhikamAsa), kShaya-tithis. Presents a seven-day week, with names for days of week.

4.Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of day and night, rising of zodiacal signs on horizon etc.
In addition, some versions cite a few colophons added at the end, extolling the virtues of the work, etc.

The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, ca. 600) and by Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465).