Chinese mathematics

Chinese mathematics began developing around the 11th century BCE. Chinese mathematicians created their own number system. They could work with very large numbers and even negative numbers. They used different ways to write numbers, like binary and decimal systems. They studied algebra, geometry, number theory, and trigonometry.

During the Han dynasty, Chinese mathematicians made big progress in solving equations. They used special methods and tools, like regula falsi and continued fractions, to solve hard math problems. Important books from this time, such as The Nine Chapters on the Mathematical Art and The Book on Numbers and Computation, showed how to solve everyday math problems using counting boards. These books included methods similar to modern techniques like Gaussian elimination and Horner's method.

Chinese mathematics grew a lot during the Yuan dynasty in the 13th century with the creation of tian yuan shu. Even though Chinese and Mediterranean mathematics developed mostly on their own, there might have been some sharing of ideas across Asia. Chinese mathematicians knew about important ideas like the Pythagorean theorem and Pascal's triangle long before they were well known in Europe.

Pre-imperial era

The Shang dynasty (c. 1600 BC – c. 1050 BC) had early ideas about math. One old book called the I Ching used special shapes called hexagrams. It also had early ideas about binary numbers.

Since this time, Chinese people used a decimal system. They learned arithmetic, algebra, equations, and negative numbers with tools called counting rods. They used math for astronomical work, but also made advances in algebraic geometry and decimals.

Math was one of the Six Arts for students to learn in the Zhou dynasty (1122–256 BCE). An old book from the Mohist group around 330 BCE talked about shapes, lines, and circles. The Zhoubi Suanjing is another old book with ideas about shapes and stars.

Qin dynasty

Not much is known about Qin dynasty mathematics or earlier times because of the burning of books and burying of scholars around 213–210 BC. But we can learn from civil projects and historical evidence.

The Qin dynasty developed a standard system of weights. Major construction projects, like the Great Wall of China, needed many math skills. Builders used formulas to calculate sizes and shapes for structures.

A special find in Hong Kong, bought by the Yuelu Academy, included old bamboo cash with the earliest known example of a math treatise written on it. This shows that people in the Qin time were already using math in everyday life.

Han dynasty

Further information: Science and technology of the Han dynasty § Mathematics and astronomy

During the Han dynasty, Chinese mathematicians learned more about numbers. They made a way to write big and small numbers, including how to show zero, using special rods on a board. They could add, take away, multiply, and divide. They also found ways to solve puzzles with many answers.

Two important books from this time are Book on Numbers and Computation and Jiuzhang suanshu. These books helped people solve everyday problems, like sharing land or money, using smart steps. They also tried to find a better way to measure around circles.

Three Kingdoms, Jin, and Sixteen Kingdoms

In the third century, Liu Hui wrote important books about math. One of these books was called Haidao Suanjing. He used special methods to measure land and figured out the value of π to be 3.1416, which was a very good guess for that time.

In the fourth century, Zu Chongzhi did even better work with π, calculating it to seven decimal places. This was the most accurate for nearly a thousand years. He also found smart ways to measure the space inside shapes like spheres. His work included many clever math ideas that were very advanced for his time.

Tang dynasty

By the Tang dynasty, learning math became common in big schools. A book called The Ten Computational Canons was made, and it included ten important Chinese math works. This book was used for math tests in the government.

One famous mathematician, Wang Xiaotong, wrote a book called Jigu Suanjing. In it, he solved special kinds of math problems called cubic equations. The Chinese also learned math from India. They translated tables of sines into their own books. They were very good at geometry and algebra, but they did not use trigonometry as much as other countries at that time.

Song and Yuan dynasties

Mathematician Jia Xian found new ways to calculate square and cubic roots during the Northern Song dynasty.

Four great mathematicians stood out during the Song and Yuan dynasty: Yang Hui, Qin Jiushao, Li Zhi, and Zhu Shijie. They used smart methods to solve equations. Yang Hui was the first to discover and prove "Pascal's Triangle". Li Zhi used algebra to solve geometry problems, and Zhu Shijie wrote important books on math.

Qin Jiushao added the symbol for zero to Chinese math. He also solved very hard equations.

Ming dynasty

After the Yuan dynasty ended, China focused less on math and science. Instead, people studied botany and pharmacology more. Math was not part of the tests for scholars, so they paid less attention to it.

During this time, tools like the abacus became very popular. In the 15th century, the abacus changed into a new form called suan pan. It was easy to use and carry. A famous book, Suanfa Tongzong, was written by Cheng Dawei in 1592. It taught many ways to do calculations and was used for over 300 years. Later, visitors like Matteo Ricci brought books about Western science to China, but many Chinese scholars still liked their own old books.

Qing dynasty

Under the Kangxi Emperor, Chinese mathematics grew. He learned about Western math from visiting scholars and encouraged learning from other cultures. Mei Goucheng and other mathematicians created a large book called Shuli Jingyun, which shared Western math ideas with Chinese scholars.

Later, the Qianlong Emperor helped collect and organize old Chinese math books. Important works from earlier times were found and shared again, sparking new interest and study in math.

Western influences

In 1840, the First Opium War made China open up to the world. This led to more study of Western mathematics. In 1852, the Chinese mathematician Li Shanlan and the British missionary Alexander Wylie worked together to translate important math books. At first, Chinese scholars were unsure about Western knowledge, but they learned it was important for China.

In modern China

After China became a modern republic in 1912, Chinese mathematics grew strongly again. Many Chinese mathematicians have made big achievements. For example, Shiing-Shen Chern became a leader in geometry and won the Wolf Prize. Terence Tao, a child prodigy and Fields Medal winner, was the youngest ever to compete in the International Mathematical Olympiad. Other mathematicians like Yitang Zhang and Chen Jingrun also made important discoveries.

People's Republic of China

After China was founded in 1949, the government worked hard to improve science even with few resources. The Chinese Academy of Sciences started that same year, and the Institute of Mathematics began in 1952. In the next 18 years, China published more math papers than ever before, reaching world-class levels.

During a tough time called the Cultural Revolution, science faced challenges. But after that time ended, math in China grew again. Important achievements include a mathematician named Xia Zhihong proving the Painlevé conjecture in 1988, and Shen Weixiao helping prove another major idea called the Real Fatou conjecture in 2007.

IMO performance

China has done very well at the International Mathematical Olympiad, often winning top scores and having entire teams earn perfect gold medals.

Main article: International Mathematical Olympiad

In education

The earliest known use of a book for learning mathematics in China was in the second century CE. Two young students, Ma Xu and Zheng Xuan, studied a famous math book called the Nine Chapters on Mathematical Procedures. Some experts think that math may have been taught by speaking, like how some medicines were passed down. Another old math text, the Suàn shù shū, looks like it was made from different pieces and then put together into one book.