Chinese mathematics

Mathematics in China began developing on its own by the 11th century BCE. Chinese mathematicians created their own system of numbers, including very large and negative numbers, and used many different ways to write numbers, like binary and decimal systems. They also studied algebra, geometry, number theory, and trigonometry.

During the Han dynasty, Chinese mathematicians made big steps forward in solving equations. They used special methods and tools, like regula falsi and continued fractions, to find answers to complex math problems. Important books from this time, such as The Nine Chapters on the Mathematical Art and The Book on Numbers and Computation, showed detailed ways 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 most during the Yuan dynasty in the 13th century with the creation of tian yuan shu. Even though Chinese and Mediterranean mathematics developed mostly separate from each other, 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 widely known in Europe.

Pre-imperial era

The Shang dynasty (c. 1600 BC – c. 1050 BC) saw early developments in Chinese mathematics. One of the oldest surviving mathematical works is the I Ching, which influenced later writing and included a sophisticated use of hexagrams. It even contained elements of binary numbers, as noted by Leibniz.

Since the Shang period, the Chinese had a fully developed decimal system. They understood basic arithmetic, algebra, equations, and negative numbers using counting rods. Although their focus was often on arithmetic and algebra for astronomical purposes, they were also pioneers in developing negative numbers, algebraic geometry, and the use of decimals.

Math was one of the Six Arts that students needed to master during the Zhou dynasty (1122–256 BCE). The oldest existing work on geometry in China comes from the philosophical Mohist canon around 330 BCE. It described basic geometric ideas, such as points, lines, and shapes, and even included terms for circumference, diameter, and radius. The Zhoubi Suanjing is an important ancient text that includes proofs of geometric theorems and focuses on astronomical calculations.

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. However, 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 advanced 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 made big steps in understanding numbers. They created a system to show big and small numbers, including how to show zero, using special rods on a board. They could solve problems like adding, taking away, multiplying, and dividing. They also figured out ways to find square and cube roots, and solve puzzles with many answers.

Two important books from this time show these ideas: Book on Numbers and Computation and Jiuzhang suanshu. These books helped people solve everyday problems, like sharing land or money, using smart steps instead of just guessing. They even tried to find a better way to measure around circles, though they used a simple number for it.

Three Kingdoms, Jin, and Sixteen Kingdoms

In the third century, Liu Hui wrote important books about math, including one called Haidao Suanjing. He used methods to measure land and calculated the value of π to be 3.1416, a very good guess for his time.

In the fourth century, Zu Chongzhi made even better calculations for π, getting it right to seven decimal places, which was the best for almost 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 ahead of their time.

Tang dynasty

By the Tang dynasty, studying mathematics became common in big schools. A book called The Ten Computational Canons was created, which 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 where he solved cubic equations, which are equations with three-degree powers. The Chinese also learned about math from India, translating tables of sines into their own books. Although they were very good at geometry and algebra, they did not use trigonometry as much as other countries did at the time.

Song and Yuan dynasties

Mathematician Jia Xian developed a special method for finding 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 clever methods to solve equations, including a technique known as the "Horner" rule centuries before it was known in Europe. Yang Hui was the first to discover and prove "Pascal's Triangle". Li Zhi used algebra to solve geometry problems, while Zhu Shijie wrote important books on math.

Qin Jiushao introduced the symbol for zero into Chinese math. He also solved very complex equations, including one with the tenth power.

Ming dynasty

After the Yuan dynasty ended, China focused less on math and science and more on botany and pharmacology. Math was not important in the imperial examinations, and scholars paid less attention to it.

During this time, tools like the abacus became very popular. In the 15th century, the abacus evolved into a form called suan pan, which was easy to use and carry. A famous book called Suanfa Tongzong, written by Cheng Dawei in 1592, taught many computational methods and was used for over 300 years. Later, missionaries like Matteo Ricci brought Western scientific works to China, but many Chinese scholars preferred their own classical texts.

Qing dynasty

Under the Kangxi Emperor, Chinese mathematics saw a time of growth. 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, which brought a big increase in studying 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 studying Western knowledge, but they soon saw that it was important for China to do so.

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, winning medals at just 10 years old. Other mathematicians like Yitang Zhang and Chen Jingrun also made important discoveries in numbers and primes.

People's Republic of China

After China was founded in 1949, the government focused on science despite limited resources. The Chinese Academy of Sciences was created in 1949, and the Institute of Mathematics began in 1952. Over the next 18 years, China published more math papers than ever before, reaching world-class levels.

During a difficult time called the Cultural Revolution, science suffered. But after that period 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 been very successful 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 dates back to 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 believe that math was taught through spoken words, similar to how medicine might have been passed down. The style of another old math text, the Suàn shù shū, shows it was put together from different sources and then organized into a single book.