# Li Ye (mathematician)

Li Ye (李 冶Chinese, Pinyin Li Ye), also: Chi Li or Li Zhi (* 1192 in Tahsing, today Beijing, † 1279 in Hopei Province ) was a Chinese mathematician in the Song Dynasty.

## Life

About the Childhood and Youth Li Yes, nothing is known. However, he must have enjoyed a good education and training. His father Li Yu served as an assistant to an officer in Tahsing. 1230 was the Ye Li difficult exam in the civil administration. Li Ye first worked as a registrar, and later as Governor of Chun - cou (Henan province). The capital of the territory fell into the hands of the Mongols in 1232. Li Ye fled and lived hidden and probably in simple ratios mostly in the province of Shanxi. Only because Li Ye began precisely to deal with scientific matters. After 1251, Li lived as a scholar in the vicinity of the mountain Feng -ment in the province of Hopei. 1257 Kublai Khan had him track down and joined with him in an exchange of views on the principles of governance, the training of public officials and the causes of earthquakes. Li lived for several years in Mongolian rule and spent his time in study and teaching of students. When Kublai Khan was big in 1260, this Li Ye wanted to move to a high official position. Li refused with regard to his age and his illness. Li 1265 but was forced by Kublai, a chair at the Hanlin Academy to occupy, to deal with the history of the kingdoms Liao and Jurchen. After a few months, Li returned again in the near Feng -ment and spent his last years trying to teach students.

## Mathematical work

By Li two mathematical writings have survived, which are of utmost importance for the assessment of Chinese mathematics that time. In 1248, the sea level of the circle calculation (Ce yuan hai jing ) and 1259 New steps of the calculation ( Yi gu yan duan ) have been written. A full translation of these works into a European language is not available, so you have to be limited in the evaluation of the comments. The sea level of the circle calculation includes tasks circles which are inscribed, for example triangles. The New steps of calculation strives mainly due geometrical problem and other tasks to algebraic equations. This original methods were used to solve the equations that have been discovered in Europe until much later.

The Chinese number system was from the beginning a decimal position system; Equations can therefore be relatively easily written. When Li Ye example, there is the equation

Before. The crossing out the last number means that the number is to be taken negatively. This form of representation used almost exclusively Li Ye. Other writers used for positive numbers black, red for negative ink. The coefficients are tabulated in this presentation. The equation is placed at the beginning of the normal form. Thus, the introduction and knowledge of negative numbers is connected.

Reveals himself, Ye Li was not only limited to trivial tasks based on the degree of the equations. The method for solving equations is, in Li Ye method of the celestial element ( tian shu -yuan ), where tian -yuan means the variable of the element and shu method. This process is largely identical to the Horner scheme. However, Li Ye had to determine in its method, the digits of the root by gradually try and find the given equation by linear substitution of different auxiliary equations.

The method that Ye Li in his treatises mainly explained, is an outstanding achievement of Chinese mathematics. His method stepped outside China at Al -Kashi in the 15th century, 1600 by François Viète and 1804 with Paolo Ruffini on.