New Thoughts on Ancient & Modern Mathematics

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It has given me immense pleasure to write foreword of the book entitled "New Thoughts on Ancient and Modern Mathematics" in regard to Indian historical discourse on science and technology. India has been the birth place of scientific and mathematical innovation since time immemorial. The ancient texts justify that India excelled in the branch of mathematics and engineering during Indus Valley Civilization, which was one of the biggest civilization during its contemporaries like Egyptian and Mesopotamian. Indus Valley Civilization was a highly urbanized civilization with sophisticated knowledge of mathematics. The well developed urban layouts, watertight walls, elaborate drainage system, dock of Lothal are the evidences of engineering and mathematics. All the bricks used in the structure of Indus Valley have an absolute ratio of 4:2:1 for the length, width and height. Even today, in brick technology, this ratio is relevant for optimal bonding of bricks. Indus Valley Civilization was very particular using the ratios and used a series of binary and decimal ratios, that is ratios of 1,2,4,8,16,32,64 which were binary and ratios of 10, 20, 40, 160, 300, 640, 1600, 8000 and 12800. The inhabitants of Indus Civilization designed a ruler - the Mohenjodaro ruler-whose unit of length (approximately 1.32 inches or 3.4 centimetres) was divided into ten equal parts.

Vedic texts provide evidence for the use of large numbers. By the time of Yajurvedassamihita, numbers as high as 102 were being included in the text. The Satapatha Brahmana contains rules for geometric construction. The Sulba Sutras list rules for the construction of sacrificial fire altars. These altars have different shapes but occupy the same area. We find the use of Boolean logic, null operator in the work of Sanskrit grammarian, Panini.

During post Vedic period, Pingala contributed immensely to mathematics. He authored the Chhandas Shastra in which we find the enumerable of syllabic combinations, Pascal's triangle, binomial co-efficients and Fabonacci numbers. Jain texts classify numbers into three classes- enumerable, innumerable and infinite. The infinite numbers were further divided into five types- the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere and the infinite perpetually. Jain mathematicians were the first to use the word 'Shunya" to refer to zero. More than a millennium later, their appellation became the English word "zero".

**Contents and Sample Pages**