Brahmagupta

About Brahmagupta

Brahmagupta (597–668 CE) was an Indian mathematician and astronomer who wrote two important works on Mathematics and Astronomy: the Brāhmasphuṭasiddhānta (Extensive Treatise of Brahma) (628), a theoretical treatise, and the Khaṇḍakhādyaka, a more practical text. There are reasons to believe that Brahmagupta originated from Bhinmal.

Brahmagupta was the first to give rules to compute with zero. The texts composed by Brahmagupta were composed in elliptic verse, as was common practice in Indian mathematics, and consequently has a poetic ring to it. As no proofs are given, it is not known how Brahmagupta's mathematics was derived.

Life and work

In the Brāhmasphuṭasiddhānta verses 7 and 8 of chapter XXIV state that Brahmagupta composed this text at the age of thirty in Śaka 550 (= 628 CE) during the reign of King Vyāghramukha, we can thus gather that he was born in 598. Commentators refer to him as a great scholar from Bhinmal, a city in the state of Rajasthan of Northwest India. In ancient times Bhillamala was the seat of power of the Gurjars. His father was Jisnugupta. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacharya, that is, the teacher from Bhillamala. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672. The Brahmasphutasiddhanta (Extensive Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta.

Although Brahmagupta was familiar with the works of astronomers following the tradition of Aryabhatiya, it is not known if he was familiar with the work of Bhaskara I, a contemporary. Brahmagupta had a plethora of criticism directed towards the work of rival astronomers, and in his Brahmasphutasiddhanta is found one of the earliest attested schisms among Indian mathematicians. The division was primarily about the application of mathematics to the physical world, rather than about the mathematics itself. In Brahmagupta's case, the disagreements stemmed largely from the choice of astronomical parameters and theories. Critiques of rival theories appear throughout the first ten astronomical chapters and the eleventh chapter is entirely devoted to criticism of these theories, although no criticisms appear in the twelfth and eighteenth chapters.