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Li Ye (mathematician)
Li Ye (Chinese: 李冶; Wade–Giles: Li Yeh; 1192–1279), born Li Zhi (Chinese: 李治), courtesy name Li Jingzhai (Chinese: 李敬斋), was a Chinese mathematician, politician, and writer who published and improved the tian yuan shu method for solving polynomial equations of one variable. Along with the 4th-century Chinese astronomer Yu Xi, Li Ye proposed the idea of a spherical Earth instead of a flat one before the advances of European science in the 17th century.
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 (Chinese: 仁卿; Wade–Giles: Jen-ch’ing) and his appellation was Jingzhai (Chinese: 敬斋; Wade–Giles: Ching-chai).
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 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 (測圓海鏡, Sea mirror of circle measurements). Li then returned to Hebei.
In 1257, Kublai Khan, grandson of Genghis Khan, ordered Li to give advice on science. In 1259, Li completed Yigu yanduan (益古演段, 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, 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, Hebei. Li told his son to burn all of his books except for Sea mirror of circle measurements.
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 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 tian yuan shu, "coefficient array method" or literally "method of the celestial unknown". The method was known before him in some form. It is a positional system of rod numerals to represent polynomial equations.
For example, 2x2 + 18x − 316 = 0 is represented as
which is equal to 
in Arabic Numbers.
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Li Ye (mathematician)
Li Ye (Chinese: 李冶; Wade–Giles: Li Yeh; 1192–1279), born Li Zhi (Chinese: 李治), courtesy name Li Jingzhai (Chinese: 李敬斋), was a Chinese mathematician, politician, and writer who published and improved the tian yuan shu method for solving polynomial equations of one variable. Along with the 4th-century Chinese astronomer Yu Xi, Li Ye proposed the idea of a spherical Earth instead of a flat one before the advances of European science in the 17th century.
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 (Chinese: 仁卿; Wade–Giles: Jen-ch’ing) and his appellation was Jingzhai (Chinese: 敬斋; Wade–Giles: Ching-chai).
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 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 (測圓海鏡, Sea mirror of circle measurements). Li then returned to Hebei.
In 1257, Kublai Khan, grandson of Genghis Khan, ordered Li to give advice on science. In 1259, Li completed Yigu yanduan (益古演段, 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, 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, Hebei. Li told his son to burn all of his books except for Sea mirror of circle measurements.
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 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 tian yuan shu, "coefficient array method" or literally "method of the celestial unknown". The method was known before him in some form. It is a positional system of rod numerals to represent polynomial equations.
For example, 2x2 + 18x − 316 = 0 is represented as
which is equal to in Arabic Numbers.