earliest period of Indian science, it is exceptional when we know the authorship of a text
or an idea. For example, although Yajnavalkya and Lagadha describe considerable astronomy,
we do not know if this was developed by them or they merely summarized what was then well
known. Likewise we are not sure of the individual contributions in the Shulba Sutras--- of
Baudhayana, Apastamba, and other authors--- which describe geometry, or in Pingala's
Chhandahsutra which shows how to count in a binary manner. The major exception to the
anonymous nature of early Indian science is the grammatical tradition starting with
Panini. This tradition is an application of the scientific method where the infinite
variety of linguistic data is generated by means of a limited number of rules.
With Aryabhata, we enter a new phase in which it becomes easier to trace the
authorship of specific ideas. But even here there remain other aspects which are not so
well understood. For example, the evolution of Indian medicine is not as well documented
as that of Indian mathematics. Neither do we understand well the manner in which the
philosophical basis underlying Indian science evolved.
Thus many texts speak of the relativity of time and space---abstract
concepts that developed in the scientific context just a hundred years ago. The Puranas
speak of countless universes, time flowing at different rates for different observers and
The Mahabharata speaks of an embryo being divided into one hundred
parts each becoming, after maturation in a separate pot, a healthy baby; this is how the
Kaurava brothers are born. There is also mention of an embryo, conceived in one womb,
being transferred to the womb of another woman from where it is born; the transferred
embryo is Balarama and this is how he is a brother to Krishna although he was born to
Rohini and not to Devaki. There is an ancient mention of space travellers wearing airtight
suits in the epic Mahabharata which may be classified as an early form of science fiction.
Universes defined recursively are described in the famous episode of
Indra and the ants in Brahmavaivarta Purana. Here Vishnu, in the guise of a boy, explains
to Indra that the ants he sees walking on the ground have all been Indras in their own
solar systems in different times! These flights of imagination are to be traced to more
than a straightforward generalization of the motions of the planets into a cyclic
universe. They must be viewed in the background of an amazingly sophisticated tradition of
cognitive and analytical thought.
The context of modern science fiction books is clear: it is the
liberation of the earlier modes of thought by the revolutionary developments of the 20th
century science and technology. But how was science fiction integrated into the mainstream
of Indian literary tradition two thousand years ago? What was the intellectual ferment in
which such sophisticated ideas arose?
Of the eighteen early siddhantas the summaries of only five are
available now. In addition to these siddhantas, practical manuals, astronomical tables,
description of instruments, and other miscellaneous writings have also come down to us.
The Puranas also have some material on astronomy. Here we just list some of the main names
in astronomy after 450 CE.
Aryabhata (born 476) is the author of the first of the later
siddhantas called Aryabhatiyam which sketches his mathematical, planetary, and cosmic
theories. This book is divided into four chapters: (i) the astronomical constants and the
sine table, (ii) mathematics required for computations, (iii) division of time and rules
for computing the longitudes of planets using eccentrics and epicycles, (iv) the armillary
sphere, rules relating to problems of trigonometry and the computation of eclipses.
The parameters of Aryabhatiyam have, as their origin, the
commencement of Kaliyuga on Friday, 18th February, 3102 BCE. He wrote another book where
the epoch is a bit different.
Aryabhata took the earth to spin on its axis; this idea appears to
have been his innovation. He also considered the heavenly motions to go through a cycle of
4.32 billion years; here he went with an older tradition, but he introduced a new scheme
of subdivisions within this great cycle.
That Aryabhata was aware of the relativity of motion is clear from
this passage in his book,``Just as a man in a boat sees the trees on the bank move in the
opposite direction, so an observer on the equator sees the stationary stars as moving
precisely toward the west.''
Varahamihira (died 587) lived in Ujjain and he wrote three important
books: Panchasiddhantika, Brihat Samhita, and Brihat Jataka. The first is a summary of
five early astronomical systems including the Surya Siddhanta. (Incidently, the modern
Surya Siddhanta is different in many details from this ancient one.) Another system
described by him, the Paitamaha Siddhanta, appears to have many similarities with the
ancient Vedanga Jyotisha of Lagadha.
Brihat Samhita is a compilataion of an assortment of topics that
provides interesting details of the beliefs of those times. Brihat Jataka is a book on
astrology which appears to be considerably influenced by Greek astrology.
Brahmagupta of Bhilamala in Rajasthan, who was born in 598, wrote
his masterpiece, Brahmasphuta Siddhanta, in 628. His school, which was a rival to that of
Aryabhata, has been very influential in western and northern India. Brahmagupta's work was
translated into Arabic in 771 or 773 at Baghdad and it became famous in the Arabic world
One of Brahmagupta's chief contributions is the solution of a
certain second order indeterminate equation which is of great significance in number
Another of his books, the Khandakhadyaka, remained a popular
handbook for astronomical computations for centuries.
Bhaskara (born 1114), who was from the Karnataka region, was an
outstanding mathematician and astronomer. Amongst his mathematical contributions is the
concept of differentials. He was the author of Siddhanta Shiromani, a book in four parts:
(i) Lilavati on arithmetic, (ii) Bijaganita on algebra, (iii) Ganitadhyaya, (iv)
Goladhyaya on astronomy. He epicyclic-eccentric theories of planetary motions are more
developed than in the earlier siddhantas.
Subsequent to Bhaskara we see a flourishing tradition of mathematics
and astronomy in Kerala which saw itself as a successor to the school of Aryabhata. We
know of the contributions of very many scholars in this tradition, of whom we will speak
only of two below.
Madhava (c. 1340-1425) developed a procedure to determine the
positions of the moon every 36 minutes. He also provided methods to estimate the motions
of the planets. He gave power series expansions for trigonometric functions, and for pi
correct to eleven decimal places.
Nilakantha (c. 1444-1545) was a very prolific scholar who wrote
several works on astronomy. It appears that Nilakantha found the correct formulation for
the equation of the center of the planets and his model must be considered a true
heliocentric model of the solar system. He also improved upon the power series techniques
The methods developed by the Kerala mathematicians were far ahead of
the European mathematics of the day.
Source: T.R.N. Rao and S. Kak, Computing Science in Ancient India. USL Press, Lafayette, 1998.
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