Math & Physics Problems Wikia
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By: Tao Steven Zheng (郑涛)

Shang

(1600 – 1046 BC)

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.

Tortoise shell oracle bone

Western Zhou

西周

(1046 – 771 BC)

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

Gougu diagram

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

Spring-Autumn Period

春秋

(770 – 476 BC)

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

Lo shu


6th 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).

Warring States

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》.

Tsinghua bamboo strips

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

Qin

(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

(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).

Jiuzhang Suanshu

2nd 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.

Liu Hui

Jin

(265 – 420 AD)

c. 3rd – 5th 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. 5th 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.

Zu Chongzhi

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

(581 – 618 AD)

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

Tang

(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. 8th 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).

Yi Xing

Five Dynasties

五代十國

(907 – 979 AD)

Song

(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).

Qin Jiushao

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

(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.

Guo Shoujing

1299 AD: Zhu Shijie (朱世杰, 1249 – 1314 AD) publishes the Suanxue Qimeng《算学启蒙》.

1303 AD: Zhu Shijie (朱世杰, 1249 – 1314 AD) publishes the Siyuan Yujian《四元玉监》, now regarded as the highest achievement of ancient Chinese algebra.

Ming

(1368 – 1644 AD)

1581 AD: Zhu Zaiyu (朱载堉, 1536 – 1611 AD) computed the 12 equal temperaments.

Zhu Zaiyu

1592 AD: Cheng Dawei (程大位, 1533 – 1606 AD) publishes the Suanfa Tongzong《算法统宗》.

c. 1600 AD: Introduction of Western mathematics via Jesuits.

Qing

(1644 – 1911 AD)

1652 AD: Jesuits introduce logarithms to the Qing court.

1692 – 1763 AD: Ming Antu (明安图, 1692 – 1763 AD), the first person in China to study infinite series, and the first discoverer of Catalan numbers.

Ming Antu

1811 – 1882 AD: Li Shanlan develops transcendental functions, infinite series, and combinatorics from ancient Chinese mathematics

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