Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China

The Hindu-Arabic numeral system (1, 2, 3, ...) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to support this claim.This book provides considerable evidence to show that the Hindu-Arabic numeral system, in spite of its commonly accepted name, has its origins in the Chinese rod numeral system. This system was in use in China from antiquity till the 16th and 17th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetric operations, and also used by mathematicians to develop arithmetic and algebra.Sun Zi Suanjing (The Mathematical Classic of Sun Zi) written around 400 AD is the earliest existing work to have a description of the rod numerals and their operations. With this treatise as a central reference, the first part of the book discusses the development of arithmetric and the beginnings of algebra in ancient China and, on the basis of this knowledge, advances the thesis that the Hindu-Arabic numeral system has its origins in the rod numeral system. Part Two gives a complete translation of Sun Zi Suanjing.

Lam Lay Yong is a retired professor of Mathematics at the National University of Singapore. Based on her extensive publications on the history of Chinese mathematics which include this book and A Critical Study of the Yang Hui Suan Fa, as well as numerous articles in international journals such as Historia Mathematica, Archive for History of Exact Sciences, Isis and Archives Internationales D¹Histore des Sciences, she was awarded the Kenneth O. May Medal by the International Commission on the History of Mathematics.

Ang Tian Se was Professor of Chinese Studies, University of Malaya, Malaysia, and Head of Chinese Studies at Edith Cowan University, Australia. He is now Professor of Chinese Studies at Universiti Tunku Abdul Rahman, Malaysia.