Li Ye (; 1192–1279), born Li Zhi (),

courtesy name A courtesy name ( zh, s=字, p=zì, l=character), also known as a style name, is an additional name bestowed upon individuals at adulthood, complementing their given name. This tradition is prevalent in the East Asian cultural sphere, particula ...

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

Encyclopaedia Britannica An encyclopedia is a reference work or compendium providing summaries of knowledge, either general or special, in a particular field or discipline. Encyclopedias are divided into article (publishing), articles or entries that are arranged Alp ...

''. 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 mathematician, politician, 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 (mathematics), field, often the field of the rational numbers. For example, x^5-3x+1=0 is a ...

s of one variable. Via encyclopedia.com. Along with the 4th-century Chinese astronomer Yu Xi, Li Ye proposed the idea of a

spherical Earth Spherical Earth or Earth's curvature refers to the approximation of the 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 Ancient Greek philos ...

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 used to identify where the ingredients of a food or beverage originated, most often used for the origin of wine grapes. Restrictions other than geographical boundaries, s ...

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

Henan Henan; alternatively Honan is a province in Central China. Henan is home to many heritage sites, including Yinxu, the ruins of the final capital of the Shang dynasty () and the Shaolin Temple. Four of the historical capitals of China, Lu ...

province until the Mongol invasion in 1233. He then lived in poverty in the mountainous Shanxi province. In 1248 he finished his most known work ''Ceyuan haijing'' (, ''Sea mirror of circle measurements''). Li then returned to

Hebei Hebei is a Provinces of China, province in North China. It is China's List of Chinese administrative divisions by population, sixth-most populous province, with a population of over 75 million people. Shijiazhuang is the capital city. It bor ...

. In 1257,

Kublai Khan Kublai Khan (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 and first emperor of the Mongol-led Yuan dynasty of China. He proclaimed the ...

, grandson of

Genghis Khan Genghis Khan (born Temüjin; August 1227), also known as Chinggis Khan, was the founder and first khan (title), khan of the Mongol Empire. After spending most of his life uniting the Mongols, Mongol tribes, he launched Mongol invasions and ...

, ordered Li to give advice on science. In 1259, Li completed ''Yigu yanduan'' (, ''New steps in computation''), also a mathematics text. After becoming Khan, Kublai twice offered Li government positions, but Li was too old and in 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. It has also been translated as "College of Literature" and "Academy of the Forest of Pen ...

, 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 mountain in Yuan,

. Li told his son to burn all of his books except for ''Sea mirror of circle measurements''.

Mathematics

Ceyuan haijing

Ceyuan haijing (''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 or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle ( turn or 90 degrees). The side opposite to the right angle i ...

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 ''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 (筭) are small bars, typically 3–14 cm (1" to 6") 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. ...

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 of the form ''x – r''. It was described by Paolo Ruffini in 1809. The rule is a special case of synthetic division in which the ...

and Horner scheme.

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 J ...

(''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 romanization of Chinese, romanized Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty#Eastern Han (25–220 AD), Eastern Han dynasty. Educated in the capital citi ...

like a

crossbow A crossbow is a ranged weapon using an Elasticity (physics), elastic launching device consisting of a Bow and arrow, bow-like assembly called a ''prod'', mounted horizontally on a main frame called a ''tiller'', which is hand-held in a similar f ...

bullet and ball, respectively). However, the idea of a flat earth was criticized by the Jin dynasty astronomer Yu Xi (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 , '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 imagined reality) can ...

until the 17th century during the late Ming and early

Qing The Qing dynasty ( ), officially the Great Qing, was a Manchu-led Dynasties of China, imperial dynasty of China and an early modern empire in East Asia. The last imperial dynasty in Chinese history, the Qing dynasty was preceded by the ...

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 circumnaviga ...

of the globe. The flat Earth theory in Chinese science was finally overturned in the 17th-century. Jesuits in China also introduced the spherical Earth model advanced by

ancient Greeks Ancient Greece () was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity (), that comprised a loose collection of culturally and linguistically re ...

such as

Philolaus Philolaus (; , ''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 Pythagorean tradition and ...

and

Eratosthenes Eratosthenes of Cyrene (; ; – ) was an Ancient Greek polymath: a Greek mathematics, mathematician, geographer, poet, astronomer, and music theory, music theorist. He was a man of learning, becoming the chief librarian at the Library of A ...

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 projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of t ...

s such as

Matteo Ricci Matteo Ricci (; ; 6 October 1552 – 11 May 1610) was an Italian Jesuit priest and one of the founding figures of the Jesuit China missions. He created the , a 1602 map of the world written in Chinese characters. In 2022, the Apostolic See decl ...

's '' Kunyu Wanguo Quantu'' 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