Saturday, June 20, 2009

Religion and Mathematics

Seeking the direction of Mecca, times of prayers, lunar dates for religious festivals - all of these helped fuel astronomy, spherical trigonometry, and mathematics among Muslims in medieval times (also see the first part of the lecture by George Saliba: Islam and the Transformation of Greek Science). Here is a review of a book, Mathematics in India by Kim Plofker, and it highlights a similar role of religion in the development of mathematics in India:
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 India, together with rules for arithmetical operations (ganita) and geometry (rekha-ganita). These were encoded in a complex system of chants, prayers, hymns, curses, charms and other religious rituals. Cryptic phrases called sutras contained arithmetical rules for activities such as laying out a temple or arranging a sequence of sacrificial fires.
Very cool. And what better way to express love than a number table:
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.
But there are underlying practical reasons that drive the use of inventive mathematics:

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 Europe in the nineteenth century.
And on the exchange between Islamic and Indian intellectual cultures involving mathematics:
The chapter entitled 'Exchanges with the Islamic World' is of particular significance. The Muslim conquest of India brought with it the Islamic mathematical tradition, which was founded on Greek mathematics. Muslims made important advances in maths between the ninth and thirteenth centuries. Greco-Islamic and Indian mathematics were structured quite differently, with the former emphasizing proof and the latter, result. Probably because of Islamic influence, Indian ideas on the nature of mathematical proof moved in the direction of greater rigour.
The book, however, looks dense and not easy to read:

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.

And the same can be said for science, in general. Read the full review here.

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