c. 1300 BC: Oracle bones inscriptions (甲骨文) indicate the earliest use of a decimal place value system, with records of one year being 365.25 days.

WesternZhou

西周

(1046 – 771 BC)

c. 1000 BC: Astronomical conversations between the Duke of Zhou (周公, fl. 11^{th} century BC) and Shang Gao (商高, fl. 11^{th} century BC), with possibly the first statement of the gougu theorem (勾股定理) in China.

c. 9^{th} century BC: Zhou Yi 《周易》64 hexagrams represent the permutations of a binary set.

Spring-AutumnPeriod

春秋

(770 – 476 BC)

c. 650 BC: Lo Shu 《洛书》: 3x3 magic square.

6^{th} century BC: Laozi (老子) mentions the use of counting rods in the Daodejing 《道德经》.

c. 500 BC: Confucian school of thought promote the study of mathematics under the “Six Arts” (六艺).

WarringStates

戰國

(475 – 221 BC)

c. 450 – 250 BC: Mohist contributions to the study of logic, physics, and geometry were compiled in the Mojing《墨经》.

c. 305 BC:Tsinghua bamboo strips-Calculation Table《清华简-算表》 : oldest decimal multiplication table excavated to date.

Qin

秦

(221 – 206 BC)

221 - 206 BC:Shu《数》: earliest surviving mathematics text (written on bamboo strips) excavated to date.

213 BC: Burning of books (mathematics texts most likely were not destroyed).

Han

漢

(206 BC – 220 AD)

c. 200 BC: Negative numbers used in ancient China.

c. 200 – 186 BC: Completion of the Suan Shu Shu《算数书》, which includes the earliest usage of the double false position method.

c. 170 BC: Zhang Cang (张苍, 253 - 152 BC) is credited for reconstructing the Jiuzhang Suanshu《九章算术》after the burning of books (according to Liu Hui).

2^{nd} century BC: Astronomers study modular congruences for calendrics.

c. 100 BC: Completion of the Zhoubi Suanjing《周髀算经》.

c. 50 BC: Music theorist Jing Fang (京房, 78 - 37 BC) computes the 53 equal temperaments.

c. 1 AD: Liu Xin (刘歆, c. 50 BC - 23 AD) used decimal fractions, and gave the approximation π = 3.1457.

c. 50 AD: Completion of the Jiuzhang Suanshu《九章算术》, which includes the earliest use of Horner’s method and Gaussian elimination.

c. 100 AD: Zhang Heng （张衡, 78 – 139 AD）writes the Suan Wang Lun《算罔论》, gave the approximations π = √10 and π = 730/232.

c. 200 AD: Xu Yue （徐岳, ? - 220 AD）writes the Shushu Jiyi《数术记遗》, which mentions large numbers in powers of 10 and the earliest description of the abacus.

Three Kingdoms

三國

(220 – 280 AD)

c. 220 AD: Zhao Shuang (赵爽, c. 180 - 250 AD) writes his commentary of the Zhoubi Suanjing《周髀算经注》.

263 AD: Liu Hui (刘徽, c. 225 – 295 AD) completes his commentary of the Jiuzhang Suanshu《九章算术注》, which includes the Haidao Suanjing《海岛算经》, the approximation π = 3927/1250, the use of Cavalieri Principle for determining volumes, and geometric proofs by dissection.

Jin

晉

(265 – 420 AD)

c. 3^{rd} – 5^{th} centuries AD: Sun Zi (孙子, ? - ?), author the Sunzi Suanjing《孙子算经》, which included the earliest surviving source of galley division algorithm, and the Chinese remainder theorem.

North and South Dynasties

南北朝

(420 – 581 AD)

c. 430 AD: Xiahou Yang (夏侯阳, fl. 5^{th} century AD) authored the Xiahou Yang Suanjing《夏侯阳算经》.

c. 460 AD: Zu Chongzhi (祖冲之, 429 – 500 AD) computed the bound 3.1415926 < π < 3.1415927 and gave the approximation π = 355/133.

c. 470 AD: Zhang Qiujian (张邱建, c. 430 - 490 AD) writes the Zhang Qiujian Suanjing《张邱建算经》, which includes the earliest hundred fowls problem (百鸡问题).

c. 480 AD: Zu Geng (祖暅, 450 – 520 AD) discovers the precise formula for the volume of the sphere and authored the Zhui Shu《缀术》.

Sui

隋

(581 – 618 AD)

c. 600 AD: Liu Zhuo (刘焯, 544 – 610 AD) introduced quadratic interpolation to Chinese astronomy.

Tang

唐

(618 – 907 AD)

c. 625 AD: Wang Xiaotong (王孝通, c. 580 – 640 AD), author of Jigu Suanjing《缉古算经》, provided solutions to certain cubic and quartic equations.

656 AD: Li Chunfeng (李淳风, 602 – 670 AD) annotated ten mathematical texts for the imperial curriculum.

c. 712 - 720 AD: Gautama Siddha (瞿昙悉达, fl. 8^{th} century AD) translates Indian astronomical treatises, introduces Hindu numerals and trigonometric tables into Chinese mathematics.

c. 721 -724 AD: Yi Xing^{[1]} (一行, 683 – 727 AD) calculates the number of configurations on a Go board, and tabulates the first tangent table.
[1] Birth name Zhang Sui (张遂).

Five Dynasties

五代十國

(907 – 979 AD)

Song

宋

(960 – 1279 AD)

c. 1050 AD: Jia Xian (贾宪, c. 1010 – 1070 AD) discovers the binomial theorem and Pascal’s triangle to extend Horner’s method for solving polynomials of degree n > 3.

c. 1086 - 1093 AD: Shen Kuo (沈括, 1031 – 1095 AD) records his studies on finite series, combinatorics, and spherical trigonometry in the Mengxi Bitan《梦溪笔谈》.

1247 AD: Qin Jiushao (秦九韶, 1202 – 1261 AD), publishes the Shushu Jiuzhang《数书九章》, generalizes the Chinese remainder theorem (大衍求一术) and Horner’s method (正负开方法).

1248 AD: Li Ye (李冶, 1192 – 1279 AD), publishes of the Ceyuan Haijing《测圆海镜》, and develops the tianyuan algebra (天元术) to solve geometry problems that reduce to polynomial equations.

c. 1260 AD: Yang Hui (杨辉, 1238 – 1298 AD) writes several mathematics texts on magic squares, magic circles, and advocated for mathematical proofs of theorems and algorithms.

Yuan

元

(1279 – 1368 AD)

1276 – 1281 AD: Xu Heng（许衡, 1209－1281 AD）, Guo Shoujing (郭守敬, 1231 – 1316 AD) and Wang Xun (王恂, 1235 – 1281 AD) introduces cubic interpolation and spherical trigonometry into Chinese astronomy.

c. 1280 AD: Introduction of Islamic mathematics and astronomy into China.