An Indian history of numbers
by Kim Plofker
Nature 459, 646-647 (4 June 2009) | doi:10.1038/459646a; Published online 3 June 2009
Buddha is said to have wooed his future wife by reeling off a huge number series.
In a world divided by culture, politics, religion and race, it is a relief to know one thing that stands above them — mathematics. The diversity among today's mathematicians shows that it scarcely matters who invents concepts or proves theorems; cold logic is immune to prejudice, whim and historical accident. And yet, throughout history, different families of humans have distilled the essence of the cosmos to capture the magic of numbers in many ways.
Mathematics in India shows just how different one of these ways was, and how culture and mathematical development are intimately connected. This carefully researched chronicle of the principal contributions made by a great civilization covers the earliest days of Indian history through to the beginning of the modern period. Regrettably, it stops short of the legendary mathematician Srinivasa Ramanujan (born 1887), whose name is still seen in today's research papers.
Kim Plofker's book fulfils an important need in a world where mathematical historiography has been shaped by the dominance of the Greco-Christian view and the Enlightenment period. Too little has been written on the mathematical contributions of other cultures. One reason for the neglect of Indian mathematics was Eurocentrism — British colonial historians paid it little attention, assuming that Indians had been too preoccupied with spiritual matters to make significant contributions to the exact sciences. Another reason is that many ancient Indian mathematical texts have long been extinct; often, the only indication that they existed comes from scholars who refer to the work of their predecessors. As Plofker wryly notes, two historians of Indian maths recently published articles in the same edited volume, wherein the estimates of their subject's origins differed by about 2,000 years.
Still, surviving Sanskrit texts reveal a rich tradition
of Indian mathematical discoveries lasting more than 2,500 years. In the Early
Vedic period (1200–600 BC), a
decimal system of numbers was already established in
Large numbers held immense fascination. Acclamations of praise to the air, sky, times of day or heavenly bodies were expressed in powers of ten that went to a trillion or more. Reputedly, the young Prince Buddha successfully competed for the hand of Princess Gopa by reciting a number table that included names for the powers of ten beyond the twentieth decimal place.
As in other early agricultural civilizations, Indian mathematics probably emerged in response to the need to measure land areas and keep track of financial transactions, incomes and taxation. A rigid caste and class hierarchy reserved the mystery of numbers for elite Brahmins. To maintain personal power, mathematical knowledge was jealously guarded. Its communication was deliberately made difficult, such as in the perplexing rhythmic chant of mathematician Aryabhatta in the fifth century AD: "makhi-bhakhi-phakhi- dhaki-nakhi-nakhi-nakhi-hasjha-skaki-kisga-sghaki-kighva-ghaki..." This recital of values of sine differences in arc minutes would be memorized by aspiring mathematicians in much the same way as verses of the sacred text Bhagavadgita.
The book details the impressive achievements of Indian
mathematicians, from Aryabhatta through Brahmagupta, Mahavira, Bhaskara and
Madhava, until the Sanskrit tradition became irrelevant with the invasion of
modern mathematics from
But how peculiarly Indian was early Indian mathematics?
Did it evolve in isolation or did it absorb ideas and knowledge from elsewhere?
Cultural pride in their recently reinvigorated country causes some Indians to
claim that all worthwhile mathematics originated in ancient
The chapter entitled 'Exchanges with the Islamic World'
is of particular significance. The Muslim conquest of
The book carefully separates fact from hyperbole, copiously quoting formulae. This makes for heavy reading in places, and one wishes that it had been interspersed with vignettes and light anecdotes. It is more of a research monograph than a popular book. But that is the price that scholarship exacts.
Mathematics in India explains how the early development of Indian Maths was influenced by religion, by the need to build temples of specific proportions and to meet astrological imperatives. Similarly, it could be argued that Islamic mathematics was religiously motivated — for example, by the need to know the precise times of daily prayers, and to determine the direction of the holy Kaaba (the Qibla). But a quadratic equation solved by whoever, by whatever means and for whatever purpose must give exactly the same solutions. Ultimately, mathematics is mathematics.
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