## ABSTRACT

A popular view among historians of mathematics is: mathematics outside the sphere of Greek influence, such as Indian or Chinese mathematical traditions, was algebraic in inclination and empirical in practice, a marked contrast to Greek mathematics which was geometric and anti-empirical. The beginnings of Greek mathematics are often traced to the founding of the Pythagorean School with its peculiar mixture of mysticism and scientific curiosity. In experiments with strings of different lengths, the Pythagoreans arrived at a definition of musical notes in terms of the ratios of these strings. The chapter summarizes the distinctive feature of Greek mathematics which explains both its strengths and limitations. Throughout the history of China, the practical art of calculation played a central role in the process of conceptualization in mathematics. Interest in calculation was matched by the invention of a positional number system which lent itself easily to calculation.