Chinese mathematics

Mathematics in China started as early as the 11th century BCE. The Chinese developed math on their own, including:

• Big and negative numbers
• Two numeral systems (binary and decimal)
• Algebra, geometry, number theory, and trigonometry

Math methods and books

During the Han dynasty, Chinese mathematicians worked on polynomial problems, using smart methods like diophantine approximation and regula falsi (a method to solve equations).

They also used continued fractions and found ways to calculate roots (like square roots). Important books from this time include:

• The Nine Chapters on the Mathematical Art
• The Book on Numbers and Computation

These books explained how to solve real-life problems using math. They described step-by-step methods and used a counting board for calculations. These texts had ideas similar to today’s Gaussian elimination and Horner's method in algebra.

• By the 13th century, during the Yuan dynasty, Chinese algebra reached a high point with a method called Tian Yuan Shu (method of the celestial unknown).
• These books explained how to solve real-life problems using math. They described step-by-step methods and used a counting board for calculations. These texts had ideas similar to today’s Gaussian elimination and Horner's method in algebra.
• By the 13th century, during the Yuan dynasty, Chinese algebra reached a high point with a method called Tian Yuan Shu (method of the celestial unknown).

Independent development

• Because of language and geography, Chinese math mostly developed separately from Greek and Mediterranean math. However, some ideas might have spread between Asia and the West during the Roman Empire.
• Many early Chinese math ideas match later discoveries in modern math. For example:
  • The Pythagorean theorem was known in China during the Duke of Zhou's time.
  • Pascal's Triangle was known in China long before Pascal, by the Song dynasty scholar Shen Kuo.

Pre-Imperial times

• One of the oldest math books is the I Ching (Yi Jing) from the Shang dynasty (1600–1050 BC). It used hexagrams and had ideas similar to binary numbers, as noted by Leibniz.

The Chinese had a decimal system early on and understood:

• Arithmetic
• Algebra
• Equations
• Negative numbers

They used counting rods to calculate. Math was also one of the Six Arts that students had to learn during the Zhou dynasty to be considered a well-rounded person (like a "Renaissance man").

Geometry and the Mo Jing

The first known Chinese book on geometry was the Mo Jing (c. 330 BCE), written by followers of Mozi.

It included:

• Definitions of points and lines, similar to those by Euclid and Plato
• Descriptions of space, parallels, and volume
• The idea that a point is the smallest part of a line and cannot be divided
• Terms for diameter, circumference, and radius

Other developments

Some books have unclear dates. For example, the Zhoubi Suanjing talks about the Pythagorean theorem and astronomy, but it may have been written much later than originally thought.

A recent discovery called the Tsinghua Bamboo Slips (from about 305 BCE) included the oldest known decimal multiplication table.

The abacus was first written about in the 2nd century BCE, along with bamboo stick math using a checkerboard-like system.

Other websites

• Early mathematics texts (Chinese) - Chinese Text Project
• Overview of Chinese mathematics
• Chinese Mathematics Through the Han Dynasty
• Primer of Mathematics by Zhu Shijie