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This work explores a possible course of evolution of mathematics in ancient times in India when there was no script, no place-value system, and no zero. Reviewing examples of time-reckoning, large numbers, sacrificial altar-making, and astronomy, it investigates the role of concrete objects, natural events, rituals and names in context-dependent arithmetic, revealing its limited scope confined to counting, addition and subtraction. Higher operations, namely, multiplication, division and fractional calculations had to wait until the advent of symbolic numerals and procedures for computation. It is argued that the impression of these higher operations in a period usually known as the Vedic times is caused by inadvertent interpolation of present knowledge of mathematics in modern readings of the ancient texts.
Jaidev Dasgupta (Thu,) studied this question.