Mathematics in China
"Chinese mathematics" was defined by Chinese in ancient times as the "art of calculation". This art was both a practical and a spiritual one.
[...] Let us examine the mathematical contributions that Liu Hui made in writing his commentary. First we should note that he introduced a different approach to mathematics from that of the text on which he was commentating. The original text gave methods to solve various problems, but the methods were merely prescriptions without justification. What Liu Hui added was a more mathematical approach in providing at least principles on which the calculations are based. His methods are not exactly "proofs" in our understanding of a mathematical proof today. [...]
[...] Let us give some dates for the events Liu Hui describes. The Qin dynasty preceded the Han dynasty and it was the Qin ruler Shih Huang Ti who tried to reform education by destroying all earlier learning. He ordered all books to be burnt in 213 BC and Zhang Cang, who Liu Hui refers to, did his reconstruction around 170 BC Most historians, however, would not believe that the original text of the Nine Chapters was nearly as old as Liu Hui believed. [...]
[...] The Chinese Counting System 1. Origins The first true evidence of mathematical activity in China can be found in numeration symbols on tortoise shells and flat cattle bones (commonly called oracle bones, dated from the Shang dynasty, 14th century B.C.) : These numerical inscriptions contain code symbols which are based on a decimal system, and they employed a positional value system. Early Chinese mathematics had a great influence on other later civilizations, in India, Japan, Korea and other countries. The numeration system used in the modern world had its origins 34 centuries ago in Shang China. [...]
[...] to 4th Century A.D.), the Shang numerals were developed into a system and used on a counting board and a set of counting-rods (“chousuan”). Chinese computational methods were based on many mechanical aids including a large variety of counting boards. Indeed, the evolution and development of counting rod numerals continued for about 3000 years in China, from 14 century BC. to 13th century AD. (they were used in Japan until 19th century). The abacus The abacus is perhaps the best known counting board, but it was only developed around the 16th century. [...]
[...] Of course, the dating using units of length is not conclusive. Consider the fact that Britain changed to a decimal currency in 1970. If you pick up a book with mathematics problems given in decimal currency then we could argue as above and say that the book was written after 1970. However new editions of popular textbooks were brought out when the currency changed, so many older books appeared in decimal editions. The Nine Chapters on the Mathematical Art was certainly an important text, so may have had its units of length brought up to date as it evolved. [...]