Wu Jing (, 15th century),

courtesy name A courtesy name (), also known as a style name, is a name bestowed upon one at adulthood in addition to one's given name. This practice is a tradition in the East Asian cultural sphere, including China, Japan, Korea, and Vietnam.Ulrich Theobald ...

Xinmin (),

art name An art name (pseudonym or pen name), also known by its native names ''hào'' (in Mandarin), ''gō'' (in Japanese), ''ho'' (in Korean), and ''tên hiệu'' (in Vietnamese), is a professional name used by East Asian artists, poets and writers. The ...

Zhu Yi Weng (), was a Chinese accountant, mathematician, and writer of the

Ming dynasty The Ming dynasty (), officially the Great Ming, was an Dynasties in Chinese history, imperial dynasty of China, ruling from 1368 to 1644 following the collapse of the Mongol Empire, Mongol-led Yuan dynasty. The Ming dynasty was the last ort ...

who in 1450 published the

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

treatise ''Jiuzhang Suanfa Bilei Daquan'' (, "Complete Description of the Nine Chapters on Arithmetical Techniques").

Life

According to the 1488 foreword to Wu Jing's book written by Xiang Qi (), a

Ministry of Justice A Ministry of Justice is a common type of government department that serves as a justice ministry. Lists of current ministries of justice Named "Ministry" * Ministry of Justice (Abkhazia) * Ministry of Justice (Afghanistan) * Ministry of Just ...

administrator who also hailed from Renhe (, modern

Hangzhou Hangzhou ( or , ; , , Standard Mandarin pronunciation: ), also romanized as Hangchow, is the capital and most populous city of Zhejiang, China. It is located in the northwestern part of the province, sitting at the head of Hangzhou Bay, whi ...

), Wu apparently worked as an accountant for several local officials and had a hand on the census, land surveys, and taxations of

Zhejiang Zhejiang ( or , ; , also romanized as Chekiang) is an eastern, coastal province of the People's Republic of China. Its capital and largest city is Hangzhou, and other notable cities include Ningbo and Wenzhou. Zhejiang is bordered by Jiang ...

province.

Work

''Jiuzhang Suanfa Bilei Daquan'' originally contained nine chapters excluding the "table of contents" chapter. After a fire destroyed many printing woodblocks, Wu Jing's grandson Wu Ne () added some materials as he prepared the manuscript for re-printing. Currently, there are at least four extant copies from the

, housed separately in four libraries in

Beijing } Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...

and

Shanghai Shanghai (; , , Standard Mandarin pronunciation: ) is one of the four direct-administered municipalities of the People's Republic of China (PRC). The city is located on the southern estuary of the Yangtze River, with the Huangpu River flow ...

. Every chapter begins with a topic from an "ancient" mathematical book, followed by Wu Jing's explanation of how real-life problems are solved with arithmetics. For example, in the first chapter, "Land" (), Wu described how to approximate land areas of different shapes and included 214 problems.

Reception

Because he was concerned with real-life problems, Wu Jing often preferred approximations over exact solutions. The Ming-period mathematician

Cheng Dawei Cheng may refer to: Chinese states * Chengjia or Cheng (25–36 AD) * Cheng Han or Cheng (304–338) * Zheng (state), or Cheng in Wade–Giles Places * Chengdu, abbreviated as Cheng * Cheng County, in Gansu, China * Cheng Township, in Malacca, Ma ...

criticized Wu's work as "disorganized and containing numerous mistakes" in his ''

Suanfa tongzong ''Suanfa tongzong'' ( zh, 算法統宗) is a mathematical text written by sixteenth century Chinese mathematician Cheng Dawei (1533–1606) and published in the year 1592. The book contains 595 problems divided into 17 chapters. The book is essent ...

'' (1592). The

Qing The Qing dynasty ( ), officially the Great Qing,, was a Manchu-led imperial dynasty of China and the last orthodox dynasty in Chinese history. It emerged from the Later Jin dynasty founded by the Jianzhou Jurchens, a Tungusic-speaki ...

-period scholar Mei Wending, however, considered Wu's work superior to ''Suanfa tongzong''. Wu did not come up with new ways of solving older problems; he did, however, invent new methods of using the

abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hin ...

. He also proposed using colors and visualization to solve math (especially geometric) problems, which may have influenced Chinese

cartography Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an im ...

. The modern mathematician Qian Baocong noticed several identical arithmetic methods in Wu's work and the slightly later ''

Treviso Arithmetic The ''Treviso Arithmetic'', or ''Arte dell'Abbaco'', is an anonymous textbook in commercial arithmetic written in vernacular Venetian language, Venetian and published in Treviso, Italy, in 1478. The author explains the motivation for writing thi ...

'' (1478).Lao 1999, p. 344–345.

References

* {{DEFAULTSORT:Wu, Jing 15th-century Chinese mathematicians Chinese accountants Mathematicians from Zhejiang Medieval Chinese mathematicians Ming dynasty scholars Writers from Hangzhou