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## ca. Chinese Mathematics

The ancient Chinese mathematics ranged from 1400 BC (Shang dynasty) to 6th-century AD. In this period, a positional number system with the basis $10$ was invented, which was equally revolutionary with respect to calculations as the sexagesimal system used by the Sumers and the Babylonians. The decimal system is still used today worldwide. The Chinese have also invented the abacus, which was used to simplify every-day calculations. With respect to the basic arithmetic operations, the abacus was as helpful and powerful as today’s pocket calculators and is still being used in some parts of China.

The most important, purely mathematical book of the ancient Chinese mathematics is Cheng Ch’iu Chien Suan-ching (the Nine Chapters on the Mathematical Art), which can be dated back to the dynasty Han, 220 AD. It contains “problems” from practical arithmetics which are solved using algebraic equations. Square roots, for instance $$751\frac 12=\sqrt{564752\frac 14}$$
are calculated as well as systems of linear equations are sometimes written as coefficient matrix, e.g.

$$\begin{array}{rcrcrcl} 3x&+&2y&+&z&=&39\\ 2x&+&3y&+&z&=&34\\ x&+&2y&+&3z&=&26\\ \end{array}$$

is written as $$\pmatrix{3& 2&1\\ 2& 3&1\\ 1&2&3}$$ and are solved using calculations applied to these matrices. The matrices contain sometimes negative numbers, which appear for the first time worldwide in China.

Despite these revolutionary inventions, Chinese mathematics did not develop much further over centuries. The reason for this was the special education system, in which students had to memorize classic results. They passed the exams only if they were able to recite the old texts from memory.