Forgotten Mathematicians: Chinese Maths

It can be said that Chinese mathematics had the longest booming period, which lasted from the Christian era to the 14th century AD. Ancient Chinese mathematics witnessed three ‘golden ages’ during the Western and Eastern Han Dynasties, the Wei, Jin and the Northern and Southern Dynasties and finally the Song and Yuan Dynasties (where the development of mathematics reached its height).

The simple, yet efficient ancient Chinese numbering system, which dates back to the 2nd millennium BCE, used bamboo rods arranged in different ways to represent the numbers 1 to 9. They were then placed in columns to represent the units, tens, hundreds etc. Consequently, it can be noted that they used the decimal place value system similar to the one we use today, and in fact was the first of this kind of number system. The Chinese adopted it over a thousand years before the West and it made complex calculations very quick and easy.

However, the Chinese had no concept of ‘zero’ (this was developed by Indian mathematicians), thus limiting their calculations.

Note that although the abacus is largely considered a Chinese invention, some variations of the abacus were being used in Mesopotamia, Egypt and Greece much earlier than in China.

The Chinese were fascinated by patterns in mathematics, and paid particular attention to magic squares – squares of numbers where each row, column and diagonal added up to the same total – as they were considered to have great spiritual and religious significance. The oldest known magic square is the Lo Shu Square, which dates back to 650 BCE. It is a 3×3 square where each row, column and diagonal adds up to 15.

Lo Shu Square

The main difference between the Chinese and ancient Greek mathematics is that whilst the Greek focused on proving theorems, the Chinese devoted their time to creating efficient calculating methods, especially those for solving equations. They created advanced methods for solving systems of linear equations, equations of higher degree and indeterminate equations.

Liu Hui (around 220 AD)

Liu Hui is considered one of the most famous Chinese mathematicians. He published the book ‘The Nine Chapters on the Mathematical Art’, which contained the solutions to mathematical problems that were written in the form of decimal fractions. He was one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations. In the Nine Chapters, he proposed an algorithm to calculate the value of π, by an approximation using a regular polygon with 192 sides.

Furthermore, he commented on a diagram of a seemingly identical proof to the famous Pythagorean Theorem:

“the relations between the hypotenuse and the sum and difference of the other two sides whereby one can find the unknown from the known”

He was also a pioneer in the field of empirical solid geometry. For example, he discovered that a wedge with a rectangular base and both sloping sides could be broken into a pyramid and also a tetrahedral wedge.

Lastly, he contributed thought analysis on building canal and river dykes as well as helping in the development of cartography through his commentary on ‘Nine Chapter’.

Sun Tzu (3rd Century CE)

Sun Tzu’s biggest contribution was creating the Chinese Remainder Theorem. It is considered one of the jewels of mathematics and is used in a variety of fields, from Chinese astronomers in the 6th century AD to today in Internet cryptography. The diagram below illustrates the theorem:

The Chinese Remainder Theorem

Qin Jiushao

The 13th Century is considered to be one of the three Golden Ages of Chinese mathematics, and there were over 30 prestigious mathematics schools in China. However, although contemporary authors mention his ambitious and cruel personality, perhaps the most brilliant Chinese mathematician of this era was Qin Jiushao.

Jiushao wrote the book ‘Mathematical Writings in Nine Sections’, which is divided into nine categories each containing nine problems.

The two most important methods he created are for the solution of simultaneous linear congruences and an algorithm for obtaining a numerical solution of higher degree polynomial equations based on a process of successively better approximations, which was rediscovered in Europe in the 19th century and is known as the Ruffini-Horner method.

All in all, the Chinese contributed hugely to mathematics and continue to produce excellent mathematicians, such as Yitang Zhang.

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