Li Zhi

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Li Zhi


Scholar and mathematician


Early Life. Li Zhi was born in Shandong, where his father practiced medicine. His father later became so unsure of his diagnoses that he ended his participation in the profession. Li Zhi then studied law but soon gave it up for the Confusican classics and became an expert on belles lettres. In 1191 the father obtained thtjinshi degree in the category of prose literature and was employed as a magistrate. Li Zhi had been tremendously intelligent and an enthusiastic student since boyhood, but his early years were influenced by his father’s career. Li Zhi dedicated himself seriously to study and began to show a genius in literature.

Scholar-Official. Li Zhi became close friends with future eminent men of letters and emerged as a literary celebrity and well-educated scholar whose reputation became well known in Henan. In 1230, at the late age of thirty-eight, he gained his Jinshi degree in prose literature and was employed as a county registrar in Shanxi. By that time Henan was threatened by the Mongol invasion. Li assumed personal charge of the accounting office, where he achieved excellent results, unquestionably owing to his mathematical skills. In 1232, however, Jin forces were defeated by the Mongols. In the following year many famous Jin scholar-officials became prisoners of war and refugees. Li Zhi, like many of his former colleagues and friends, wandered homelessly in Hebei, Shanxi, and Henan.

Teaching. During these years, Li Zhi had the time to improve not only his literary skills but also his mathematical knowledge by studying ancient treatises and devoting himself industriously to scholastic inquiry. In 1251 he returned home and established, with the assistance of the local populace, a private academy. Soon students from far and near came to his academy. Li Zhi began six years of concentrated teaching and research, until he was summoned by the Mongol government.

Qubilai. In 1257 the future Mongol khan Qubilai, acting on the recommendation of his Chinese advisers, summoned Li Zhi, as well as other Chinese scholars, to the capital. Qubilai was greatly impressed by Li Zhi’s suggestion on how to rule China, but he was unable to implement the proposal, or those suggested by other intellectuals, since he did not hold any position as yet. Even so, from such contacts Qubilai understood more clearly the problems of governing China, and he implemented some of these recommendations after his accession to the throne.

Mathematician. Since Qubilai did not appoint Li Zhi to any official position, Li returned to his former residence and resumed his mathematical research. He continued working on circular measurements. Dissatisfied with traditional computation methods, he corrected and elaborated them in a treatise called Yigu Yanduan (New Steps in Computation) in three chapters. This work was completed in August 1259 but was published posthumously in 1282. Li Zhi’s other existing works are two treatises on mathematics. His major contribution to mathematics consisted of verifying and elaborating solutions to complex problems of circular measurement that were proposed by earlier and contemporary scholars.

Scholar. In 1260, shortly after his enthronement, Qubilai called several Jin scholars and notables to serve his new government. Li Zhi was among those men invited, and he went to the Mongol’s capital with several former colleagues and friends. In September he was appointed as Hanlin academician in charge of imperial documents. Li Zhi, however, declined the offer on the grounds of ill health, and his request was granted. A year later Li Zhi was called to court for the second time and reappointed Hanlin academician. He quit because of sickness after a month in office. Li Zhi did not have any achievements in government affairs but was a versatile scholar and prolific writer on the subject of the classics, devoting most of his life to study and authorship. He deserves to be regarded as one of the greatest mathematicians in Chinese history.


Yoshio Mikami, The Development of Mathematics in China and Japan, second edition (New York: Chelsea, 1974).

Li Yan and Du Shiran, Chinese Mathematics: A Concise History, translated by John N. Crossley and Anthony W. C. Lun (Oxford: Clarendon Press; New York: Oxford University Press, 1987).