Li Ye (; 1192–1279), born Li Zhi (),

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 ...

Li Jingzhai (),Breard, Andrea. (Jan 01, 2021).
Li Ye: Chinese mathematician
. ''

Encyclopaedia Britannica An encyclopedia (American English) or encyclopædia (British English) is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into articles ...

''. Accessed 7 February 2021.Li, Ye (1192-1279) 李, 冶 (1192-1279)
IdRef: ''Identifiants et Référentials pour l'enseignement supérieur et la recherche'' (French). Accessed 19 February 2018. was a Chinese scientist and writer who published and improved the

tian yuan shu ''Tian yuan shu'' () is a Chinese system of algebra for polynomial equations. Some of the earliest existing writings were created in the 13th century during the Yuan dynasty. However, the tianyuanshu method was known much earlier, in the Song dy ...

method for solving

polynomial equation In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term ''algebraic equation' ...

s of one variable. Via encyclopedia.com. Along with the 4th-century Chinese astronomer

Yu Xi Yu Xi (虞喜; 307–345 AD), courtesy name Zhongning (仲寧), was a Chinese astronomer and writer of the Jin dynasty (266–420 AD). He is best known for his discovery of the precession of the equinoxes, independently of the earlier ancient Gr ...

, Li Ye proposed the idea of a

spherical Earth Spherical Earth or Earth's curvature refers to the approximation of figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. I ...

instead of a flat one before the advances of European science in the 17th century.

Name

Li Ye was born Li Zhi, but later changed his name to Li Ye to avoid confusion with the third Tang emperor who was also named Li Zhi, removing one stroke from his original name to change the character. His name is also sometimes written as Li Chih or Li Yeh. His literary name was Renqing () and his

appellation An appellation is a legally defined and protected geographical indication primarily used to identify where the grapes for a wine were grown, although other types of food often have appellations as well. Restrictions other than geographical boun ...

was Jingzhai ().

Life

Li Ye was born in Daxing (now Beijing). His father was a secretary to an officer in the Jurchen army. Li passed the

civil service examination Civil service examinations are examinations implemented in various countries for recruitment and admission to the civil service. They are intended as a method to achieve an effective, rational public administration on a merit system for recruiti ...

in 1230 at the age of 38, and was administrative prefect of

Jun prefecture Junzhou or either Jun Prefecture (均州) was a '' zhou'' (prefecture) in imperial China, seated in modern Danjiangkou, Hubei, China. It existed (intermittently) between the years 585 and 1912. Geography The administrative region of Junzhou in th ...

Henan Henan (; or ; ; alternatively Honan) is a landlocked province of China, in the central part of the country. Henan is often referred to as Zhongyuan or Zhongzhou (), which literally means "central plain" or "midland", although the name is al ...

province until the Mongol invasion in 1233. He then lived in poverty in the mountainous

Shanxi province Shanxi (; ; Chinese postal romanization, formerly romanised as Shansi) is a landlocked Provinces of China, province of the China, People's Republic of China and is part of the North China region. The capital and largest city of the province is ...

. In 1248 he finished his most known work ''Ceyuan haijing'' (, ''Sea mirror of circle measurements''). Li then returned to

Hebei Hebei or , (; alternately Hopeh) is a northern province of China. Hebei is China's sixth most populous province, with over 75 million people. Shijiazhuang is the capital city. The province is 96% Han Chinese, 3% Manchu, 0.8% Hui, an ...

. In 1257

Kublai Khan Kublai ; Mongolian script: ; (23 September 1215 – 18 February 1294), also known by his temple name as the Emperor Shizu of Yuan and his regnal name Setsen Khan, was the founder of the Yuan dynasty of China and the fifth khagan-emperor of th ...

, grandson of

Genghis Khan ''Chinggis Khaan'' ͡ʃʰiŋɡɪs xaːŋbr />Mongol script: ''Chinggis Qa(gh)an/ Chinggis Khagan'' , birth_name = Temüjin , successor = Tolui (as regent)Ögedei Khan , spouse = , issue = , house = Borjigin , ...

, ordered Li to give advice on science. In 1259 Li completed ''Yigu yanduan'' (, ''New steps in computation''), also a mathematics text. After becoming

Khan Khan may refer to: *Khan (inn), from Persian, a caravanserai or resting-place for a travelling caravan *Khan (surname), including a list of people with the name *Khan (title), a royal title for a ruler in Mongol and Turkic languages and used by ...

, Kublai twice offered Li government positions, but Li was too old and had ill health. In 1264 Li finally accepted a position at the

Hanlin Academy The Hanlin Academy was an academic and administrative institution of higher learning founded in the 8th century Tang China by Emperor Xuanzong in Chang'an. Membership in the academy was confined to an elite group of scholars, who performed sec ...

, writing official histories. However, he had a political fallout and resigned after a few months, again citing ill health. He spent his final years teaching at his home near

Feng Lung Feng may refer to: *Feng (surname), one of several Chinese surnames in Mandarin: **Féng (surname) ( wikt:冯 féng 2nd tone "gallop"), very common Chinese surname **Fèng (surname) ( wikt:鳳 fèng 4th tone "phoenix"), relatively common Chinese fa ...

mountain in Yuan,

. Li told his son to burn all of his books except for ''Sea mirror of circle measurements''. However, other mathematical and literary texts.

Mathematics

Ceyuan haijing

Ceyuan haijing ''Ceyuan haijing'' () is a treatise on solving geometry problems with the algebra of Tian yuan shu written by the mathematician Li Zhi in 1248 in the time of the Mongol Empire. It is a collection of 692 formula and 170 problems, all derived from ...

(''Sea mirror of circle measurements'') is a collection of 170 problems, all related to the same example of a circular city wall inscribed in a

right triangle A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right an ...

and a square. They often involve two people who walk on straight lines until they can see each other, meet or reach a tree in a certain spot. The purpose of book was to study intricate geometrical relations with algebra and provide solutions to equations. Many of the problems are solved by polynomial equations, which are represented using a method called

, "coefficient array method" or literally "method of the celestial unknown".Needham, Joseph; Wang, Ling. (1995)

959 Year 959 ( CMLIX) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * April - May – The Byzantines refuse to pay the yearly tribute. A Hungari ...

''Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth'', vol. 3, reprint edition. Cambridge: Cambridge University Press. , p. 45. The method was known before him in some form. It is a positional system of

rod numeral Counting rods () are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written fo ...

s to represent

s. For example, 2x² + 18x − 316 = 0 is represented as which is equal to in Arabic Numbers. The (''yuan'') denotes the unknown x, so the numerals on that line mean 18x. The line below is the constant term (-316) and the line above is the coefficient of the quadratic (x²) term. The system accommodates arbitrarily high exponents of the unknown by adding more lines on top and negative exponents by adding lines below the constant term. Decimals can also be represented. Later, the line order was reversed so that the first line is the lowest exponent. Li does not explain how to solve equations in general, but shows it with the example problems. Most of the equations can be reduced to the second or sometimes third order. It is often assumed that he used methods similar to

Ruffini's rule In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a Binomial (polynomial), binomial of the form ''x – r''. It was described by Paolo Ruffini (mathematician), Paolo Ruffini in 1804. The rule i ...

and

Horner scheme In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horn ...

Yigu yanduan

Yigu yanduan ''Yigu yanduan'' (益古演段 Old Mathematics in Expanded Sections) is a 13th-century mathematical work by Yuan dynasty mathematician Li Zhi. Overview ''Yigu yanduan'' was based on Northern Song mathematician Jiang Zhou's (蒋周) ''Yigu Ji ...

(''New steps in computation'') is a work of more basic mathematics written soon after Li Ye completed Ceyuan haijing, and was probably written to help students who could not understand ''Sea mirror of circle measurements''. Yigu yanduan consists of three volumes dedicated to solving geometrical problems on two tracks, through

Tian yuan shu ''Tian yuan shu'' () is a Chinese system of algebra for polynomial equations. Some of the earliest existing writings were created in the 13th century during the Yuan dynasty. However, the tianyuanshu method was known much earlier, in the Song dy ...

and geometry. It also contained algebraic problems, but with slightly different notations.

Astronomy and shape of the earth

The ''huntian'' () theory of the

celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...

stipulated that the earth was flat and square, while the heavens were spherical in shape, along with celestial bodies such as the sun and moon (described by 1st-century AD polymathic scientist and statesman

Zhang Heng Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, ma ...

like a

crossbow A crossbow is a ranged weapon using an elastic launching device consisting of a bow-like assembly called a ''prod'', mounted horizontally on a main frame called a ''tiller'', which is hand-held in a similar fashion to the stock of a long fi ...

bullet and ball, respectively). However, the idea of a flat earth was criticized by the Jin dynasty astronomer

(fl. 307-345 AD), who suggested a rounded shape as an alternative. In his ''Jingzhai gu zhin zhu'' (), Li Ye echoed Yu's idea that the Earth was spherical, similar in shape to the heavens but smaller in size, arguing that it could not be square since that would hinder the movement of the heavens and celestial bodies. However, the idea of a spherical earth was not accepted in mainstream Chinese science and

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 ...

until the 17th century during the late

Ming 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 ...

and early

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 ...

periods, with the advent of evidence of European

circumnavigation Circumnavigation is the complete navigation around an entire island, continent, or astronomical object, astronomical body (e.g. a planet or natural satellite, moon). This article focuses on the circumnavigation of Earth. The first recorded circ ...

of the globe. The flat Earth theory in Chinese science was finally overturned in the 17th-century.

Jesuits in China The history of the missions of the Jesuits in China is part of the history of relations between China and the Western world. The missionary efforts and other work of the Society of Jesus, or Jesuits, between the 16th and 17th century played a si ...

also introduced the spherical Earth model advanced by

ancient Greeks Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cultu ...

such as

Philolaus Philolaus (; grc, Φιλόλαος, ''Philólaos''; ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pytha ...

and

Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria ...

Cullen, Christopher. (1993). "Appendix A: A Chinese Eratosthenes of the Flat Earth: a Study of a Fragment of Cosmology in Huainanzi", in Major, John. S. (ed), ''Heaven and Earth in Early Han Thought: Chapters Three, Four, and Five of the Huananzi''. Albany: State University of New York Press. , p. 269-270. and presented in

world map A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of map projection, projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensiona ...

s such as

Matteo Ricci Matteo Ricci, SJ (; la, Mattheus Riccius; 6 October 1552 – 11 May 1610), was an Italians, Italian Society of Jesus, Jesuit Priesthood in the Catholic Church, priest and one of the founding figures of the Jesuit China missions. He create ...

's ''

Kunyu Wanguo Quantu Kunyu Wanguo Quantu, printed in Ming China at the request of the Wanli Emperor in 1602 by the Italian Catholic missionary Matteo Ricci and Chinese collaborators, the mandarin Zhong Wentao, and the technical translator Li Zhizao, is the earliest ...

'' published in Ming-dynasty China in 1602.

Name

Life

Mathematics

Ceyuan haijing

Yigu yanduan

Astronomy and shape of the earth

See also

References

Further reading