Brahmagupta (598 - 668 CE) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brahmasphutasiddhanta (dated 628), a the- oretical treatise, and the Khandakhadyaka (dated 665), a more practical text.
Brahmagupta was the first to give rules to compute with zero. The texts composed by Brahmagupta were in elliptic verse in Sanskrit, as was common practice in Indian mathematics.
Brahmagupta was born in 598 CE according to his own state- ment. He lived in Bhillamala in Gurjaradesa (modern Bhinmal in Rajasthan, India) during the reign of the Chavda dynasty ruler, Vyagrahamukha. He was the son of Jishnugupta and was a Hindu by religion, in particular, a Shaivite. He lived and worked there for a good part of his life. Prithudaka Svamin, a later com- mentator, called him Bhillamalacharya, the teacher from Bhilla- mala.
In the year 628, at the age of 30, he composed the Brahmas- phutasiddhanta which is believed to be a revised version of the received Siddhanta of the Brahmapaksha school of astronomy. Scholars state that he incorporated a great deal of originality into his revision, adding a considerable amount of new material.
The book consists of 24 chapters with 1008 verses in the arya metre (A meter used in Sanskrit, Prakrit and Marathi verses). A good deal of it is astronomy, but it also contains key chapters on mathematics, including algebra, geometry, trigonometry and algorithmics, which are believed to contain new insights due to Brahmagupta himself.
Brahmagupta gave the solution of the general linear equa- tion in chapter eighteen of Brahmasphutasiddhänta. He fur- ther gave two equivalent solutions to the general quadratic equation and indeterminate equations. He also worked on the formula for cyclic quadrilaterals and many more import- ant mathematical concepts.
In chapter twelve of his Brahmasphutasiddhanta, Brahmagupta provides a formula useful for generating Pythagorean triples: 12.39. "The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey."
In chapter seven of his Brähmasphutasiddhanta, entitled Lunar Crescent, Brahmagupta rebuts the idea that the Moon is far- ther from the Earth than the Sun. He does this by explaining the illumination of the Moon by the Sun. He also explored the lon- gitudes of the planets, diurnal rotation, lunar and solar eclips- es, risings and settings, the moon's crescent and conjunctions of the planets in his treatise Khandakhadyaka
Later, Brahmagupta moved to Ujjain, Avanti, a major centre for astronomy in central India. At the age of 67, he composed his next well-known work Khanda-khadyaka, a practical manual of Indian astronomy in the karana category meant to be used by students.
Brahmagupta died in 668 CE, and he is presumed to have died in Ujjain.
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