Bhaskara II completes the Siddhanta Shiromani

Bhaskara II — the numeral distinguishes him from the 7th-century astronomer Bhaskara I — was also called Bhaskaracharya, ‘Bhaskara the teacher’. In verses of the Siddhanta Shiromani, a work of some 1,450 Sanskrit verses, he states that he was born in the Shaka year 1036 (1114/1115) and composed it at the age of 36 — in Shaka 1072, that is, 1150/1151. He learned mathematics from his father Maheshvara, also an astronomer. He names his home as Vijjadavida in the Sahyadri hills; many scholars identify it with Patan near Chalisgaon in Khandesh, where a local tradition says that he wrote his great work, while others place his birth at Bijapur or Bid. He is said to have headed the astronomical observatory at Ujjain, and in 1207 his grandson Changadeva founded a school for the study of his works under the patronage of the Yadava king Singhana.

The Lilavati, addressed in places to a girl — a legend first recorded by the Mughal poet Faizi in 1587 makes her Bhaskara’s daughter — teaches arithmetic and measurement, including combinations, through problems in verse, building on Brahmagupta and Shridhara; the Bijaganita is the most complete and systematic Indian treatise on algebra, and the two astronomical parts deal with the mathematics of the planets and with the sphere. Bhaskara set out the chakravala, or ‘cyclic’, method of solving indeterminate quadratic equations of the kind now named after Pell, and his treatment of the instantaneous motion of the planets is often cited as anticipating ideas of the differential calculus; he also described a wheel with slanting vessels on its rim meant to turn for ever, one of the earliest designs of a perpetual-motion machine. A little later he wrote another astronomical work, the Karanakutuhala.

The Lilavati was translated into Persian by Faizi at the court of Akbar, and in 1816 John Taylor’s English translation was printed in Bombay.