Page:Popular Science Monthly Volume 80.djvu/601

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CHINESE MATHEMATICS

CHINESE MATHEMATICS
By Professor DAVID EUGENE SMITH

TEACHERS COLLEGE, COLUMBIA UNIVERSITY

NO one who is interested in China and in things Chinese, and no one to whom the evolution of thought appeals, can fail to appreciate the recent articles by Dr. Edmunds, the learned president of the Canton Christian College, upon science among the Chinese.[1] His extensive travels in all portions of the country, his own scientific attainments, his wide acquaintance with Chinese scholars, his connection with numerous scientific expeditions, and his official position at the head of one of the most progressive colleges in the country, all qualify him to speak as one having authority.

It is, however, quite natural that one whose tastes are not primarily in the line of mathematics should fail to do justice to the work of Chinese scholars in this field. It is true that this work was not of a high order, and yet it must be said that it ranked with that which was being done in other branches of science, and had not the relatively low standing that would be inferred from Dr. Edmund's statements. These statements are summarized in the following:

The study of arithmetic has attracted attention among the Chinese from early times, and notices found in historical works indicate some treatises[2] extant even in the Han Dynasty (206 B.C.-A.D. 214), followed by a great number of general and particular works down to the Sung Dynasty (1020-1120 A.D.). The Hindu processes in algebra were known to Chinese mathematicians, but though studied even after intercourse between the countries had ceased, these branches made slow progress down to the end of the Ming Dynasty (A.D. 1368-1644).[3]

Now as a matter of fact there is a good deal known of the mathematics of China in the pre-Christian era, and in certain respects their algebra in the Middle Ages was much in advance of that of their European contemporaries. Furthermore, this algebra appears to have been indigenous to China. While Sanskrit was known there very early, and by about 800 A.D. was even taught in Japan (through the writings of the great scholar, Kōbō Daishi), there is nothing in the mathematics of either country that shows dependence upon any known works of Hindu scholars. On the contrary, it would seem that Brahmagupta, who

  1. The Popular Science Monthly, Vol. LXXTX., p. 521; Vol. LXXX., p. 22.
  2. Misprinted "treaties" in the original.
  3. Vol. LXXIX., p. 527. Substantially repeated in Vol. LXXX., p. 30.