Emergence of Mathematics in Ancient India: A Reassessment

2011

Historical development of algebra occurred in three stages; rhetorical or prose algebra, syncopated or abbreviated algebra and symbolic algebra-known as "school algebra". The analysis of this paper suggests that the first civilization to develop symbolic algebra was the Vedic Indians. The philosophical and religious ideas influenced the development of the decimal system and arithmetic and that led to algebra. Symbolic algebra appears to be deep rooted in Vedic philosophy. The Vedic mathematic were of a high level at an early period. The Hindus applied algebra freely creating formulas that simplified calculations. In geometry and trigonometry they developed formulas useful to understand the physical world satisfying the needs of religion (apara and para vidya). Geometrical focus, logic and proof type are features of Greek mathematics "boldness of conception, abstraction, symbolism" are evident in Indian mathematics. From history, a number of implications can be drawn. Real life, imaginative and creative problems that encourage risk should be the focus in student learning; allowing students freely move between symbols, numbers and magnitudes rather than taking a static unchanging view. Concrete, pictorial and symbolic modes are present in ancient learning. Real life practical, philosophical and religious needs in concert motivated progress to symbolic algebra. The historical analysis supports the use of rich context based problems that stimulate and motivate students to raise levels higher to transfer knowledge. The road from arithmetic to algebra was clearly in line with current emphasis in mathematics education but at an early stage in human history..

The Tamil inscriptions of the medieval period provide a very detailed account on the land measures in minute fractions. In the Medieval period, the villages were completely measured and documented, especially in the fertile Kāviri delta and other cultivable areas, for accurately assessing tax. The land measurements are discussed in terms of various units of measures, especially miniscule fractions, and the calculations of taxable and tax-free areas are also specified in some of the inscriptions. This paper presents a preliminary account of the fractions, numbers and arithmetic calculations found in the Medieval Tamil inscriptions. In the study of history of science, the development and use of concepts related numbers, fractions and arithmetic calculations form an important component. There is a lot scope to research on the history of science and traditional knowledge systems in India, and when we look at this subject objectively, without any emotional attachment and pride, there is much to learn from these traditional concepts of science, which can be very useful for academic understanding as well as for imparting cognitive skills among the youngsters as part of the contemporary education. In the area of history of numbers, arithmetic calculations and mathematics in India, much research has been done (Bag 1979; Joseph 2011), and in this paper, I present a preliminary survey of the numbers, fractions and arithmetic calculations that were used in Tamil region in the historical period. Simple arithmetic calculations were used for day-today accounting and for the assessment of land revenue during the medieval period. The Tamil inscriptions, literature and palm-leaf manuscripts serve as important sources for understanding the fractions, numbers and arithmetic calculations. Specific symbols or markers were used to identify these fractions, apart from specific words. The land measurement, weight and volume measurements of various materials donated to the temple are also listed out in minute detail, in the inscriptions. In the medieval period, there were accountants who calculated the land area and assessed them for tax, and maintained detailed accounts of the lands and taxes to be collected. The use of numbers or counting, perhaps began in the prehistoric period, when people calculated the number of people, fruits and other countable elements that were essential for their day-today activities. Nowadays people tend to visualize the figures such as 10, 100, 200 and 1000 as complete; but, the perception of these decimal based numbers as complete entities is nothing, but our own imagination. The number of body parts such as head, eyes, fingers that humans have perhaps helped in counting numbers in the very early stages of history. In the

Boletin De La Asociacion Matematica Venezolana, 2002

2019

This paper is an endeavor how chronologically since inception and into growth of mathematics occurred in Ancient India with an effort of counting to establish the numeral system through different ages, i.e., Rigveda, Yajurvada, Buddhist, Indo-Bactrian, Bramhi, Gupta and Devanagari Periods. Ancient India's such contribution was of immense value helped to accelerate the progress of Mathematical development up to modern age as we see today.

Definition and classification of ancient Indian mathematics and its use in measures of space, survey on earth etc.

Boston Studies in the Philosophy of Science, 2010

A renewed interest for contextualization in indological studies 1 , is but slowly affecting publications on Indian mathematics. The isolation of history of mathematics within the general field of indology derives partly from a lively historiographical trend of technical and patriotic history of mathematics which remains oblivious to social science. Preservation plays a role as well: precious little information exists on the context in which mathematics and astronomy were practiced in India in the past 2 . To overcome this problem some historians of science have turned to periods (XVIth-XIXth century) and places where institutions, libraries and many texts help us contextualize their mathematical and astronomical ideas 3 .

INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT

The history of any ancient civilization is often surrounded by mystery and controversy. Still, Western scholars have not given sufficient credit to the work of some ancient Indian mathematicians, notably Brahmagupta, Bodhayana and Bhaskara II, despite the fact that their entire works were translated into English by the nineteenth-century British Sanskrit scholar Henry Thomas Colebrooke. In the initial part was done by The purpose of this article is to lay out the facts and leave the reader free to interpret and evaluate them according to his own understanding of the subject. Sincere efforts have been made to bring the contribution of some ancient Indian mathematicians to the public. Keywords:- Right angled triangle, Decimal system, Alphanumeric system, Shulva Sutra.

This book is part of a major project undertaken by the Centre for Studies in Civilizations (New Delhi), being one of a total of ninety-six planned volumes. The author is a statistician and computer scientist by training, who has concentrated on historical matters for the last ten years or so. However, the book has very ambitious aims, proposing an alternative philosophy of mathematics and a deviant history of the calculus. Throughout, there is an emphasis on the need to combine history and philosophy of mathematics, especially in order to evaluate properly the history of mathematics in India, in particular the history of the calculus.

Ancient Indian Leaps into Mathematics, 2010

While there was an awareness of ancient Indian mathematics in the West since the sixteenth century, historians discuss the Indian mathematical tradition only after the publication of the first translations by Colebrooke in 1817. Its reception cannot be comprehended without accounting for the way new European mathematics was shaped by Renaissance humanist writings. We show by means of a case study on the algebraic solutions to a linear problem how the understanding and appreciation of Indian mathematics was deeply influenced by humanist prejudice that all higher intellectual culture, in particular all science, had risen from Greek soil.