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SCIENCE 



[N. S. Vol. XXV. No. 649 



agreed upon which will admit at the outset 

 of stamping a mathematical thought and 

 theorem as borrowed or independent. The 

 most striking feature in the history of this 

 science is the fact that the same results, 

 even in the highest branches of it, have 

 frequently been obtained by different 

 peoples and at various epochs, with little 

 or no possibility of pointing out an his- 

 torical connection between such coinci- 

 dences. The quadrature of the circle, for 

 example, was made the object of correct 

 speculation in China, even in pre-Christian 

 times; or the rule of Horner 'for solving 

 equations of all orders, ' established in 1819, 

 was known to the Chinese 520 years earlier, 

 when, in an arithmetical treatise published 

 in 1299, roots were extracted as high as the 

 thirteenth power.* Paul Harzer," astron- 

 omer at the University of Kiel, last year 

 submitted the mathematical knowledge of 

 ancient Japan to a careful and ingenious 

 examination, and has arrived at the con- 

 clusion that the Japanese found spontane- 

 ously adequate evaluations of the ratio ir, 

 and made the independent discovery of the 

 binomial theorem, which they utilized for 

 obtaining important results. Modem criti- 

 cism, with its aggressiveness towards the 

 groundwork of human knowledge, towards 

 even that which seems most secure, has 

 recently attacked also the foundations of 

 mathematics, generally looked upon as the 

 most unobjectionable science, and has desig- 

 nated its results, like those of other sciences, 

 as more or less conventional, not necessi- 

 tated by the nature of the human mind." 

 To us, mathematics is essentially an out- 

 come of human culture; and the question 

 arising from an anthropological view-point 



* A. Wylie, ' Jottings on the Science of the 

 Chinese Arithmetic,' in his ' Chinese Researches ' 

 (Shanghai, 1897), pp. 163, 184, 185. 



" Paul Harzer, ' Die exakten Wissenschaften im 

 alten Japan,' Kiel, 1905. 



" Harzer, ibid., p. 26. 



is, Are the phenomena of mathematical 

 thoughts to be considered as on an equal 

 footing with those of language, religion or 

 medicine, and, accordingly, capable of 

 methodical anthropological treatment, or 

 are they the particular productions of in- 

 dividual thinkers, and, accordingly, con- 

 ducive only to an exclusively historical 

 analysis? It is impossible for the present 

 to pronounce a verdict on this intricate 

 problem, though I should like to say tenta- 

 tively, and with all reserve, that the present 

 state of our knowledge of the mathematics 

 of India, China and Japan would almost 

 seem rather to favor the acceptance of the 

 former theory. At all events, the ventila- 

 tion of this question is well illustrative of 

 the paramount importance of the study of 

 the history of mathematics and its principal 

 bearings on our views of the intellectual 

 history of man. 



The practical proposition which I finally 

 wish to lay before you is, that working 

 committees, cooperative in character, be 

 organized, each consisting of a limited 

 number of members selected equally from 

 students of natural sciences and students 

 of anthropology, especially those in Ori- 

 ental fields, and pursuing given problems 

 viriius unitis. Bach of these unions, 

 which need not be of an official character, 

 but may be freely private voluntary alli- 

 ances of interested students, should be in 

 charge of a particular branch of science. 

 Altogether, seven may be necessary— one 

 for the study of the history of mathematics 

 and astronomy; others for that of cultural 

 plants, domestic animals, physics, chem- 

 istry, technology and medicine. Each com- 

 mittee should be so constituted that the 

 united forces of its laborers will represent 

 a consummate systematic knowledge of the 

 subject in question, and take up, suggest, 

 encourage and elaborate pending problems 

 by the concerted action of all its partici- 



