Development of Mathematics in Ancient China

Chinese Math Texts

The history of Chinese math and mathematicians was mostly lost or destroyed over the centuries. For example, the despotic emperor Shih Huang-ti of the Ch'in dynasty (221-207 B.C.) ordered the burning of books in 213 B.C. Scholars in the following Han period (206 B.C. to 220 A.D.) had to transcribe China's literary and scientifice traditions from memory or remaining fragments of scroll.

Knowledge of astronomy and other areas was often handed down from father to son, and only later recorded in texts. Unfortunately, very few texts dedicated to mathematical astronomy have survived. 

Since the 16 century, Chinese math history has also been denied and ignored in the Western dominance of science and technology, both inside and outside China. 

However, there are several existing Chinese applied mathematics texts, which are collections of problems and solutions organized in chapters according to their practical applications. These texts proves that the Chinese were the first society to use some of the most basic and advanced mathematical principles and concepts utilized in modern times. Two of these texts are the Chou Pei and Chiu Chang.

Chou Pei

The oldest existing Chinese texts containing formal mathematical theories were produced during the Han period. The Arithmetic Classic of the Gnomon and the Circular Paths of Heaven (Chou Pei Suan Ching) is dated before the 3rd century B.C and contains various modern mathematical principles such as working with fractions using a common denominator, and proofs of many geometrical theories. The text contains an accurate process of division for finding out the square root of numbers.

In fact, the Chou Pei presents the oldest known proof of the right-angle triangle theory in the hsuan-thu diagram. This theory, commony known as the "Pythagorean theorem," shows that the sum of the squares of the legs of a right triangle is equal to the squares of the hypotenuse or a2+ b2 = c2.

The Chou Pei was not an isolated academic text shared only by a few ancient Chinese mathematicians. The principles in the text were reflected in the popular approach known as chi-chu, or "the piling up of squares" which was a process of using geometry to solve algebric problems.

Chiu Chang

Another 3rd century B.C. Han text, the Nine Chapters on the Mathematical Art (Chiu Chang Suan Shu), was very influencial in asian mathematics. This text was probably first written by Chang Tshang who made use of older works then in existence.

The Chiu Chang focus on applied mathematics in engineering and administration and include nine distinct chapters on impartial taxation (chun shu), engineering works (shang kung), the surveying of land (fang thien), etc. In total, 246 problem situations are presented, from those involving the payment for livestock, weights and measures, currency and tax collection to the construction of canals and simultaneous linear equations (fang chheng).

Other Texts

Other important Chinese math texts include the Mathematical Classic of Sun Tzu (Sun Tzu Suan Ching) written in the 3rd century A.D., and The Ten Mathematical Manuals (Suanjing Shi Shu). The 13 century text, Detailed Analysis of the Mathematical Rules in the Nine Chapters (Hsiang Chieh Chiu Chang Suan Fa), proved the theory known as "Pascal's Triangle" 300 years before Pascal was born.