page_title: Chinese mathematics
section_title: Early Chinese mathematics
hierarchical_section_title: Chinese mathematics / Early Chinese mathematics
caption_attribution_description: English: Oracle bone script numeral system
context_page_description: Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system, algebra, geometry, number theory and trigonometry.
  In the Han Dynasty, the Chinese made substantial progress on finding the nth root of positive numbers and solving linear congruence equations. The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes to solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they included inverse elements as well as Euclidean divisions. The texts provide procedures similar to that of Gaussian elimination and Horner's method for linear algebra and modular method for Diophantine equation, respectively. The achievement of Chinese algebra reached its zenith in the 13th century, when Li Jingzhai invented tiān yuán shù.
context_section_description: Simple mathematics on oracle bone script date back to the Shang Dynasty (1600–1050 BC). One of the oldest surviving mathematical works is the I Ching, which greatly influenced written literature during the Zhou Dynasty (1050–256 BC). For mathematics, the book included a sophisticated use of hexagrams. Leibniz pointed out, the I Ching (Yi Jing) contained elements of binary numbers.
  Since the Shang period, the Chinese had already fully developed a decimal system. Since early times, Chinese understood basic arithmetic (which dominated far eastern history), algebra, equations, and negative numbers with counting rods. Although the Chinese were more focused on arithmetic and advanced algebra for astronomical uses, they were also the first to develop negative numbers, algebraic geometry (only Chinese geometry) and the usage of decimals.
  Math was one of the Liù Yì (六艺) or Six Arts, students were required to master during the Zhou Dynasty (1122–256 BC). Learning them all perfectly was required to be a perfect gentleman, or in the Chinese sense, a "Renaissance Man". Six Arts have their roots in the Confucian philosophy.
  The oldest existent work on geometry in China comes from the philosophical Mohist canon of c. 330 BC, compiled by the followers of Mozi (470–390 BC). The Mo Jing described various aspects of many fields associated with physical science, and provided a small wealth of information on mathematics as well. It provided an 'atomic' definition of the geometric point, stating that a line is separated into parts, and the part which has no remaining parts (i.e. cannot be divided into smaller parts) and thus forms the extreme end of a line is a point. Much like Euclid's first and third definitions and Plato's 'beginning of a line', the Mo Jing stated that "a point may stand at the end (of a line) or at its beginning like a head-presentation in childbirth. (As to its invisibility) there is nothing similar to it." Similar to the atomists of Democritus, the Mo Jing stated that a point is the smallest unit, and cannot be cut in half, since 'nothing' cannot be halved. It stated that two lines of equal length will always finish at the same place, while providing definitions for the comparison of lengths and for parallels, along with principles of space and bounded space. It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch. The book provided word recognition for circumference, diameter, and radius, along with the definition of volume.
  The history of mathematical development lacks some evidence. There are still debates about certain mathematical classics. For example, the Zhoubi Suanjing dates around 1200–1000 BC, yet many scholars believed it was written between 300–250 BC. The Zhoubi Suanjing contains an in-depth proof of the Gougu Theorem (a special case of the Pythagorean Theorem) but focuses more on astronomical calculations. However, the recent archaeological discovery of the Tsinghua Bamboo Slips, dated c. 305 BC, has revealed some aspects of pre-Qin mathematics, such as the first known decimal multiplication table.
  The abacus was first mentioned in the second century BC, alongside 'calculation with rods' (suan zi) in which small bamboo sticks are placed in successive squares of a checkerboard.
caption: Oracle bone script numeral system
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