- INDIA 21
As Plato said, one class of people will find this argument a sufficient justification
for being a mathematician; another class will not. By reading the motivations given
by other mathematicians for their work, the reader may either find arguments
to convince that second group of people, or else come to agree with them and
Hamming.
2. India
From archaeological excavations at Mohenjo Daro and Harappa on the Indus River
in Pakistan it is known that an early civilization existed in this region for about
a millennium starting in 2500 BCE. This civilization may have been an amalgam
of several different cultures, since anthropologists recognize five different physical
types among the human remains. Many of the artifacts that were produced by
this culture have been found in Mesopotamia, evidence of trade between the two
civilizations.
The Aryan civilization. The early civilization of these five groups of people disap-
peared around 1500 BCE, and its existence was not known in the modern world
until 1925. The cause of its extinction is believed to be an invasion from the north-
west by a sixth group of people, who spoke a language closely akin to early Greek.
Because of their language these people are referred to as Aryans. The Aryans grad-
ually expanded and formed a civilization of small kingdoms, which lasted about a
millennium.
Sanskrit literature. The language of the Aryans became a literary language known
as Sanskrit, in which great classics of literature and science have been written.
Sanskrit thus played a role in southern Asia analogous to that of Greek in the
Mediterranean world and Chinese in much of eastern Asia. That is, it provided a
means of communication among scholars whose native languages were not mutually
comprehensible and a basis for a common literature in which cultural values could
be preserved and transmitted. During the millennium of Aryan dominance the
spoken language of the people gradually diverged from written Sanskrit. Modern
descendants of Sanskrit are Hindi, Gujarati, Bengali, and others. Sanskrit is the
language of the Mahabharata and the Ramayana, two epic poems whose themes
bear some resemblance to the Homeric epics, and of the Upanishads, which contain
much of the moral teaching of Hinduism.
Among the most ancient works of literature in the world are the Hindu Vedas.
The word means knowledge and is related to the English word wit. The composition
of the Vedas began around 900 BCE, and additions continued to be made to them
for several centuries. Some of these Vedas contain information about mathematics,
conveyed incidentally in the course of telling important myths.
Hindu religious reformers. Near the end of the Aryan civilization, in the second
half of the sixth century BCE, two figures of historical importance arise. The
first of these was Gautama Buddha, the heir to a kingdom near the Himalayas,
whose spiritual journey through life led to the principles of Buddhism. The second
leader, Mahavira, is less well known but has some importance for the history of
mathematics. Like his contemporary Buddha, he began a reform movement within
Hinduism. This movement, known as Jainism, still has several million adherents
in India. It is based on a metaphysic that takes very seriously what is known in
some Western ethical systems as the chain of being. Living creatures are ranked