The History of Mathematics: A Brief Course

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  1. INDIA 23


These verses are known collectively as the Sulva Sutras or Sulba Sutras. The name
means Cord Rules and probably reflects the use of a stretched rope or cord as a way
of measuring length. The root sulv originally meant to measure or to rule, although
it also has the meaning of a cord or rope; sutra means thread or cord, a common
measuring instrument. In the case of the Vedas the objects being measured with
the cords were altars. The maintenance of altar fires was a duty for pious Hindus,
and because Hinduism is polytheistic, it was necessary to consider how elaborate
and large the fire dedicated to each deity was to be. This religious problem led to
some interesting problems in arithmetic and geometry.
Two scholars who studied primarily the Sanskrit language and literature made
important contributions to mathematics. Pingala, who lived around 200 BCE,
wrote a treatise known as the Chandahsutra, containing one very important math-
ematical result, which, however, was stated so cryptically that one must rely on a
commentary written 1200 years later to know what it meant. Later, a fifth-century
scholar named Panini standardi2«d the Sanskrit language, burdening it with some
4000 grammatical rules that make it many times more difficult to learn than any
other Indo-European language. In the course of doing so, he made extensive use of
combinatorics and the kind of abstract reasoning that we associate with algebra.
These subjects set the most ancient Hindu mathematics apart from that of other
nations.


2.2. Buddhist and Jaina mathematics. As with any religion that encourages
quiet contemplation and the renunciation of sensual pleasure, Jainism often leads
its followers to study mathematics, which provides a different kind of pleasure,
one appealing to the mind. There have always been some mathematicians among
the followers of Jainism, right down to modern times, including one in the ninth
century bearing the same name as the founder of Jainism. The early work of
Jaina mathematicians is notable for algebra (the Sthananga Sutra, from the second
century BCE), for its concentration on topics that are essentially unique to early
Hindu mathematics, such as combinatorics (the Bhagabati Sutra, from around 300
BCE), and for speculation on infinite numbers (the Anuyoga Dwara Sutra, probably
from the first century BCE). Buddhist monks were also very fond of large numbers,
and their influence was felt when Buddhism spread to China in the sixth century
CE.

2.3. The Bakshali Manuscript. A birchbark manuscript unearthed in 1881 in
the village of Bakshali, near Peshawar, is believed by some scholars to date from the
seventh century CE, although Sarkor (1982) believes it cannot be later than the end
of the third century, since it refers to coins named dinara and dramma, which are
undoubtedly references to the Greek coins known as the denarius and the drachma,
introduced into India by Alexander the Great. These coins had disappeared from
use in India by the end of the third century. The Bakshali Manuscript contains
some interesting algebra, which is discussed in Chapter 14.

2.4. The siddhantas. During the second, third, and fourth centuries CE, Hindu
scientists compiled treatises on astronomy known as siddhantas. The word sid-
dhanta means a system.^3 One of these treatises, the Surya Siddhanta (System of

(^3) A colleague of the author suggested that this word may be cognate with the Greek idon, the
aorist participle of the verb meaning see.

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