Brahmagupta

Brahmagupta was born in 598 AD into an orthodox Shaivite Hindu family. His father’s name was Jishnugupta. It is generally believed that he was born in Ujjain. Not much is known about his early life.

As a young man he studied astronomy extensively. He was well-read in the five traditional siddhanthas on Indian astronomy, and also studied the work of other ancient astronomers such as Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin and Vishnuchandra.

Brahmagupta became an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during his era.

He is believed to have lived and worked in Bhinmal in present day Rajasthan, India, for a few years. The city was a center of learning for mathematics and astronomy, and he flourished as an astronomer in the intellectual atmosphere of the city.

At the age of 30, he composed the theoretical treatise ‘Brāhmasphuṭasiddhānta’ ("Correctly established doctrine of Brahma") in 628 AD. The work is thought to be a revised version of the received siddhanta of the Brahmapaksha school, incorporated with some of his own new material. Primarily a book of astronomy, it also contains several chapters on mathematics.

Brahmagupta is credited to have given the most accurate of the early calculations of the length of the solar year. He initially estimated it to be at 365 days, 6 hours, 5 minutes, and 19 seconds which is remarkably close to the actual value of 365 days, 5 hours, 48 minutes, and about 45 seconds.

He later revised his estimate and proposed a length of 365 days, 6 hours, 12 minutes, and 36 seconds. His work was very significant considering the fact that he had no telescope or scientific equipment to help him arrive at his conclusions. He is believed to have relied primarily on Aryabhata’s findings to arrive at his own conclusions.

In addition to astronomy, his book also contained various chapters on mathematics. Through this book, he laid the foundations of the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms) and bija-ganita (“mathematics of seeds,” or equations).

Brahmagupta’s treatise ‘Brāhmasphuṭasiddhānta’ is one of the first mathematical books to provide concrete ideas on positive numbers, negative numbers, and zero. The text also elaborated on the methods of solving linear and quadratic equations, rules for summing series, and a method for computing square roots. It also contained the first clear description of the quadratic formula (the solution of the quadratic equation).