History of Mathematics in China

Rise & Fall

The Development of Mathematics

400 BC - 730 CE

Three Century Interlude

730 CE - 1030 CE

Zenith of Mathematics

1030 CE - 1300 CE

Decline of Mathematics/Closed Door Policy

1300 CE - 1846 CE

Intro of Western Mathematics

1592 CE - 1700 CE

Pre-Modern

Numerical notation, arithmetical computations, counting rods

400 BC

Calculations performed using small bamboo counting rods.Traditional decimal notation -- one symbol for each of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000, and 10000. Ex. 2034 would be written with symbols for 2,1000,3,10,4, meaning 2 times 1000 plus 3 times 10 plus 4

A Book on Arithmetic (Suan Shu Shu)

180 BC

A book of bamboo strips found in 1984 near Jiangling in Hubei province

The Nine Chapters on the Mathematical Art (Jiu Zhang Suan Shu)

100 BC

Collects mathematics to beginning of Han dynasty. 246 problems in 9 chapters. Longest surviving and most influential Chinese math book. Many subsequent commentaries.

The Arithmetical Classic of the Gnomon & the Circular Paths of Heaven

100 BC

Proof of the Pythagorean theorem

Sun Zi's Mathematical Manual

250 CE

Sun Zi wrote his mathematical manual which included the "Chinese Remainder Problem"

Sea Island Mathematical Manual

263 CE

Liu Hui commentary on Ch 9 of the Nine Chapters. Includes nine surveying problems involving indirect observations. Approximates pi by approximating circles polygons; approximates pi as 3.141014
States principle of exhaustion for circles
Suggests Calvalieri's principle to find accurate volume of cylinder

Xiahou Yang's Mathematical Manual

350 CE

Commentaries by Zu Chongzhi

450 CE

Da ming li (Da Ming Calendar) (462)
Zhui shu (Method of Interpolation)
Jiuzhang shu yi zhu (Commentary on the Methods and Essence of the `Nine Chapters')
Chong cha zhu (Commentary on Double Differences)

Zhang Qiuijan's Mathematical Manual

450 CE

Zu Geng's Method of Interpolation

500 CE

Zhen Luan's Arithmetic in 5 Classics

566 CE

Luan also wrote Mathematical Manual of the Five Government Departments and Memoir on Some Traditions of Mathematical Art.

Wang Xiatong's Continuation of Ancient Mathematics

625 CE

Li Chunfeng edited the Ten Books of Mathematical Classics

664 CE

This collection included the Jiuzhang suanshu (Nine Chapters of the Mathematical Art), Haidao suanjing (Sea Island Mathematical Manual), Sunzi suanjing (Master Sun's Mathematical Manual), Wucao suanjing (Mathematical Manual of the Five Government Departments), Wujing suanshu (Arithmetic in Five Classics), Zhang Qiujian suanjing (Zhang Qiujian's Mathematical Manual), Xiahou Yang suanjing (Xiahou Yang's Mathematical Manual), Zhui shu (Method of Interpolation), and Xugu suanjing (Continuation of Ancient Mathematics)

Liu Yi Discussion of Old Sources

1225 CE

Qin Jiushao's Mathematical Treatise in Nine Sections

1247 CE

Li Zhi's Sea Mirror of Circle Measurements

1248 CE

LI Zhi's New Steps in Computation

1259 CE

Yang Hui's Detailed Analysis of Mathematical Methods in "Nine Chapters"

1261 CE

Yang Hui's Computing Methods for Daily Use

1262 CE

Yang Hui's Alpha and Omega Selection on the Applications of Arithmetical Methods

1274 CE

Yang Hui's Methods of Computation

1274 CE

Yang Hui's Practical Rules of Arithmetic for Surveying

1275 CE

Zhu Shijie's Introduction to Mathematical Studies

1299 CE

Zhu Zhijie"s Precious Mirror of the Four Elements

1303 CE

Translation of Euclid's Elements first six books into Chinese

1607 CE

Matteo Ricci and Xu Guangqi translated Euclid's Elements

Collected Basic Principles of Mathematics

1723 CE

Supervised by Emperor Kang Xi (Aixinjueluo) (1654-1722), edited by Mei Juecheng, Chen Houyao, He Guozong, Ming Antu, Mei Wending, and others

Mei Wending's Commentaries

1761 CE

In 1761, Mei Juecheng complied Mei Wending's written commentaries into the Mei shi congshu jiyao (Collected Works of the Mei Family). It included several works on mathematics: Bisuan (Pen Calculations), Chou suan (Napier's bones), Du suan shi li (Proportional Dividers), Shao guang shi yi (Supplement to `What Width'), Fang cheng lun (Theory of Rectangular Arrays), Gougu ju yu (Right-angled Triangles), Jihe tong jie (Explanations in Geometry), Ping san jiao ju yao (Elements of Plane Trigonometry), Fang yuan mi ji (Squares and Circles, Cubes and Spheres), Jihe bu bian (Supplement to Geometry), Hu san jiao ju yao (Elements of Spherical Trigonometry), Huan zhong shu chi (Geodesy), and Qiandu celiang (Surveying Solids).