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By the grace of God the precious sunken jewel of true knowledge
has been rescued by me, by means of the boat of my own knowl-
edge, from the ocean which consists of true and false knowledge.
He who disparages this universally true science of astronomy, which
formerly was revealed by Svayambhu and is now described by me
in this Aryabhatiya, loses his good deeds and his long life. [Clark,
1980, p. 81]2.6. Brahmagupta. The establishment of research centers for astronomy and
mathematics at Kusumapura and Ujjain produced a succession of good mathe-
maticians and mathematical works for many centuries after Aryabhata I. About a
century after Aryabhata I another Hindu mathematician, Brahmagupta, was born
in the city of Sind, now in Pakistan. He was primarily an astronomer, but his as-
tronomical treatise, the Brahmasphutasiddhanta (literally The Corrected Brahma
Siddhanta), contains several chapters on computation (Ganita). The Hindu interest
in astronomy and mathematics continued unbroken for several centuries, producing
important work on trigonometry in the tenth century.
2.7. Bhaskara II. Approximately 500 years after Brahmagupta, in the twelfth
century, the mathematician Bhaskara, the second of that name, was born on the
site of the modern city of Bijapur. He is the author of the Siddhanta Siromani, in
four parts, a treatise on algebra and geometric astronomy. Only the first of these
parts, known as the Lilavati, and the second, known as the Vija Ganita,^4 concern
us here. Bhaskara says that his work is a compendium of knowledge, a sort of
textbook of astronomy and mathematics. The name Lilavati, which was common
among Hindu women, seems to have been a fancy of Bhaskara himself. Many of
the problems are written in the form of puzzles addressed to this Lilavati.
Bhaskara II apparently wrote the Lilavati as a textbook to form part of what
we would call a liberal education. His introduction reads as follows:Having bowed to the deity, whose head is like an elephant's, whose
feet are adored by gods; who, when called to mind, relieves his
votaries from embarrassment; and bestows happiness on his wor-
shippers; I propound this easy process of computation, delightful
by its elegance, perspicuous with words concise, soft and correct,
and pleasing to the learned. [Colebrooke, 1817, p. 1]As a final advertisement at the end of his book, Bhaskara extols the pleasure
to be derived from learning its contents:Joy and happiness is indeed ever increasing in this world for those
who have Lilavati clasped to their throats, decorated as the mem-
bers are with neat reduction of fractions, multiplication, and invo-
lution, pure and perfect as are the solutions, and tasteful as is the
speech which is exemplified. [Colebrooke, 1817, p. 127]* This Sanskrit word means literally source computation. It is compounded from the Sanskrit
root vij- or bij-, which means seed. As discussed in Chapter 13, the basic idea of algebra is to
find one or more numbers (the "source") knowing the result of operating on them in various ways.
The word is usually translated as algebra.