Editing Chinese mathematics (section)

== Pre-imperial era ==
[[File:Chinese_pythagoras.jpg|thumb|280x280px|Visual proof for the (3, 4, 5) triangle as in the [[Zhoubi Suanjing]] 500–200&nbsp;BCE]]
[[File:OracleBoneScriptNumeralSystem.png|thumb|Oracle bone script numeral system]]
[[File:Chounumerals.svg|right|thumb|280x280px|counting rod place value decimal]] [[Shang dynasty]] (1600–1050&nbsp;BC). One of the oldest surviving mathematical works is the ''[[I Ching]]'', which greatly influenced written literature during the [[Zhou dynasty]] (1050–256&nbsp;BC). For mathematics, the book included a sophisticated use of [[hexagram]]s. [[Leibniz]] pointed out, the I Ching (Yi Jing) contained elements of [[binary number]]s.

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]].{{Citation needed|date=October 2008}} Although the Chinese were more focused on arithmetic and advanced algebra for [[Astronomy|astronomical]] uses, they were also the first to develop negative numbers, [[algebraic geometry]], and the usage of decimals.

Math was one of the [[Six Arts]] students were required to master during the [[Zhou dynasty]] (1122–256 BCE). Learning them all perfectly was required to be a perfect gentleman, comparable to the concept of a "[[Polymath|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 {{circa|330 BCE}}, compiled by the followers of [[Mozi]] (470–390&nbsp;BCE). 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.{{sfn|Needham|1959|p=91}} 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."{{sfn|Needham|1959|p=92}} Similar to the [[atomist]]s of [[Democritus]], the ''Mo Jing'' stated that a point is the smallest unit, and cannot be cut in half, since 'nothing' cannot be halved."{{sfn|Needham|1959|p=92}} It stated that two lines of equal length will always finish at the same place,"{{sfn|Needham|1959|p=92}} while providing definitions for the ''comparison of lengths'' and for ''parallels'',"{{sfn|Needham|1959|pp=92–93}} along with principles of space and bounded space.{{sfn|Needham|1959|p=93}} It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch.{{sfn|Needham|1959|pp=93–94}} The book provided word recognition for circumference, diameter, and radius, along with the definition of volume.{{sfn|Needham|1959|p=94}}

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&nbsp;BC, yet many scholars believed it was written between 300 and 250&nbsp;BCE. 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 {{circa|305 BCE}}, has revealed some aspects of pre-Qin mathematics, such as the first known [[decimal]] [[multiplication table]].<ref name="Nature2">{{Cite journal |last=Qiu |first=Jane |author-link=Jane Qiu |date=2014-01-07 |title=Ancient times table hidden in Chinese bamboo strips |url=https://www.nature.com/articles/nature.2014.14482 |journal=Nature |language=en |doi=10.1038/nature.2014.14482 |issn=0028-0836 |s2cid=130132289 |access-date=2023-11-17 |doi-access=free}}</ref>

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.<ref name="Ifrah 20012">{{Cite book |last=Ifrah |first=Georges |url=https://archive.org/details/unset0000unse_w3q2 |title=The universal history of computing: from the abacus to the quantum computer |date=2001 |publisher=Wiley |isbn=978-0-471-39671-0 |location=New York}}</ref>