Mathematics in India
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Did you know that Vedic priests were using the socalled
Pythagorean theorem to construct their fire
altars in 800 BCE?; that the differential equation
for the sine function, in finite difference form, was
described by Indian mathematician-astronomers
in the fifth century CE?
power series for arctangent and, with ingenious
summation methods, used to accurately compute
π in southwest India in the fourteenth century?
If any of this surprises you, Plofker’s book is for
you.
Her book fills a huge gap: a detailed, eminently
readable, scholarly survey of the full scope of
Indian1 mathematics and astronomy (the two were
inseparable in India) from their Vedic beginnings
to roughly 1800. There is only one other survey,
Datta and Singh’s 1938 History of Hindu Mathematics,
recently reprinted but very hard to obtain
in the West (I found a copy in a small specialized
bookstore in Chennai). They describe in some
detail the Indian work in arithmetic and algebra
and, supplemented by the equally hard to find Geometry
in Ancient and Medieval India by Sarasvati
Amma (1979), one can get an overview of most
topics.2 But the drawback for Westerners is that
neither gives much historical context or explains
the importance of astronomy as a driving force
for mathematical research in India. While Western
scholars have been studying traditional Indian
mathematics since the late eighteenth century and
Indian scholars have been working hard to assemble
and republish surviving Sanskrit manuscripts,
a widespread appreciation of the greatest achievements
and the unique characteristics of the Indian
approach to mathematics has been lacking in the
West. Standard surveys of the history of mathematics
hardly scratch the surface in telling this
story.3 Today, there is a resurgence of activity in
this area both in India and theWest. The prosperity
and success of India has created support for a new
generation of Sanskrit scholars to dig deeper into
the huge literature still hidden in Indian libraries.
Meanwhile the shift in the West toward a multicultural
perspective has allowed us Westerners to
shake off old biases and look more clearly at other
traditions. This book will go a long way to opening
the eyes of all mathematicians and historians of
mathematics to the rich legacy of mathematics to
which India gave birth.