Li Ye

This article is about the mathematician. For other representatives of the name see: Li Ye (disambiguation)

Li Ye ( Chinese  李 冶 , Pinyin Li Yě ), also: Li Chi or Li Zhi (* 1192 in Daxing , Beijing City ; † 1279 in Hebei Province ) was a Chinese mathematician in the Song and Yuan dynasties .

Life

Nothing is known about Li Yes's childhood and youth. However, he must have had a good upbringing and training. His father Li Yu served as an assistant to an officer in Tahsing. In 1230, Li Ye passed the difficult civil administration exam. Li Ye was first as registrar and later as governor of Chün-cou ( Henan Province ). The capital of the area fell into the hands of the Mongols in 1232 . Li Ye fled and lived in hiding and in humble circumstances, probably mostly in Shanxi Province . Only then did Li Ye begin to deal more closely with scientific questions. After 1251, Li lived as a scholar near Mount Feng-lung in Hopeh Province . In 1257 Kublai Khan had him track down and entered into an exchange of views with him on principles of governance, the training of state officials and the causes of earthquakes . Li lived under Mongol rule for several years, spending his time studying and teaching students. When Kublai became great khan in 1260 , he wanted to persuade Li Ye to a high position. Li declined out of consideration for his age and illness. In 1265, however, Li was forced by Kublai to fill a chair at the Hanlin Academy to study the history of the Liao and Jurchen kingdoms . After a few months, Li returned to the vicinity of Feng-lung and spent the last years of his life teaching students.

Mathematical work

Representation of the equation 2x³ + 15x² + 166x-4460 = 0

Two mathematical writings have come down from Li, which are of the greatest importance for the assessment of Chinese mathematics of the time. In 1248 the are sea circle calculation ( Ce yuan hai jing ) and 1259 New steps of calculating ( Yi gu yan duan ) written Service. A complete translation of these works into a European language is not available, so that the assessment has to be limited to the comments. The sea ​​level of the circle calculation contains tasks about circles inscribed in triangles, for example. The New Steps in Computation seeks to reduce geometrical problems and other tasks to algebraic equations. Original methods were used to solve the equations that were only discovered much later in Europe.

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

${\displaystyle 2x^{3}+15x^{2}+166x-4460=0}$

in front. Crossing out the last digit means that the number is to be taken negative. This form of representation was used almost exclusively by Li Ye. Other authors used black ink for positive numbers and red ink for negative numbers. The coefficients are arranged in a table in this form of representation. The equation is brought to normal form at the beginning. This also involves introducing and recognizing negative numbers .

The degree of the equations shows that Li Ye did not limit himself to trivial tasks. Li Ye's method for solving equations is called the method of the heavenly element ( tian-yuan shu ), where tian-yuan means the variable of the element and shu means method. This procedure is largely identical to the Horner scheme . However, with his method, Li Ye had to determine the digits of the root through step-by-step experimentation and find various auxiliary equations for the given equation through linear substitution .

The method that Li Ye mainly explained in his treatises is an excellent achievement in Chinese mathematics. His method appeared outside of China with al-Kaschi in the 15th century, with François Viète in 1600 and with Paolo Ruffini in 1804 .

literature

• Hans Wußing , Wolfgang Arnold: Biographies of important mathematicians. Aulius Verlag & Deubner, ISBN 3-7614-1191-X .

Web links

• John J. O'Connor, Edmund F. Robertson :  Li Ye. In: MacTutor History of Mathematics archive .