c. 1300 BC: Oracle bones 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 and Shang Gao, with possibly the first statement of the gougu (Pythagorean) theorem in China

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

Spring-AutumnPeriod 春秋(770 – 476 BC)

c. 650 BC: First reference to the Lo Shu 3x3 magic square.

6^{th} century BC: Laozi mentions the use of counting rods in the Daodejingc. 500 BC: Confucian school of thought promote the study of mathematics under the “Six Arts”

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

305 BC:Tsinghua bamboo strips: oldest decimal multiplication table excavated to date

Qin 秦(221 – 206 BC)

213 BC: Burning of books

Han 漢(206 BC – 220 AD)

c. 200 BC: Negative numbers used in ancient China
c. 200 BC – 186 BCE: Completion of the Suan Shu Shu, which includes the earliest usage of the double false position method

c. 170 BC: Zhang Cang is credited for reconstructing the Jiuzhang Suanshu after the burning of books

2^{nd} century BC: Earliest description of the Chinese abacus, and perhaps the study of modular congruences for calendrics
c. 100 BC – 100 AD: Completion of the Zhoubi Suanjingc. 50 BC: Music theorist Jing Fang computes the 53 equal temperaments
c. 1 AD: Liu Xin used decimal fractions, and approximated pi as 3.1457
78 – 139 AD: Zhang Heng writes the Suan Wang Lun, approximated pi as 730/232
179 CE: Finalization of the Jiuzhang Suanshu, which includes the earliest use of Horner’s method and Gaussian elimination

Three Kingdoms 三國 (220 – 280 AD)

c. 225 – 295 AD: Liu Hui wrote the Jiuzhang Suanshu Commentary and Haidao Suanjing, approximated pi as 3927/1250, applied the Cavalieri Principle for calculating volumes, provided geometric proofs by dissection

Jin 晉(265 – 420 AD)

c. 3^{rd} – 5^{th} centuries AD: Sun Zi, author the Sunzi Suanjing, which included the earliest surviving source of galley division algorithm, and the Chinese remainder problem

North and South Dynasties 南北朝 (420 – 581 AD)

429 – 500 AD: Zu Chongzhi computed the bound 3.1415926 < pi < 3.1415927 and gave the approximation 355/133 for pi

c. 450 AD: Obscure mathematicians Zhang Qiujian and Xiahou Yang authored the Zhang Qiujian Suanjing and Xiahou Yang Suanjing450 – 520 AD: Zu Geng, with his father Zu Chongzhi, found the precise formula for the volume of the sphere and co-authored the Zhui Shu

Sui 隋 (581 – 618 AD)

544 – 610 AD: Liu Zhuo introduced quadratic interpolation in Chinese astronomy

Tang 唐 (618 – 907 AD)

580 – 640 AD: Wang Xiaotong, author of Jigu Suanjing, provided solutions to certain cubic and quartic equations
602 – 670 AD: Li Chunfeng annotated ten mathematical texts for the imperial curriculum

683 – 727 AD: Yi Xing calculated the number of configurations on a Go board

c. 720 AD: Gautama Siddha translates of Indian astronomical treatises, and the introduction of trigonometric ratios into Chinese

Five Dynasties 五代十國(907 – 979 AD)

Song 宋(960 – 1279 AD)

c. 1010 – 1070 AD: Jia Xian discovered the binomial theorem and Pascal’s triangle to extend Horner’s method for solving polynomials of degree n > 3
1031 – 1095 AD: Shen Kuo recorded his studies on finite series, combinatorics, and spherical trigonometry in the Mengxi Bitan1192 – 1279 AD: Li Ye, author of the Ceyuan Haijing, develops the Tianyuan algebra to solve geometry problems that reduce to polynomial equations

1202 – 1261 AD: Qin Jiushao, author of the Shushu Jiuzhang, generalized the Chinese remainder theorem and Horner’s method

1238 – 1298 AD: Yang Hui wrote several math texts on magic squares, magic circles, and advocated for mathematical proofs of theorems and algorithms

Yuan 元 (1279 – 1368 AD)

1231 – 1316 AD: GuoShoujing introduced cubic interpolation and spherical trigonometry into Chinese astronomy

1249 – 1314 AD: Zhu Shijie authored the Suanxue Qimeng and Siyuan Yujian, regarded as the highest achievement of ancient Chinese algebra
c. 1300 AD: Introduction of Islamic mathematics and astronomy into China

Ming 明(1368 – 1644 AD)

1533 – 1606 AD: Cheng Dawei, author of the Suanfa Tongzong, greatly influenced Japanese mathematics in the 17^{th} century