Notes on Indian Mathematics. 



503 



Vol. Ill, No. 7.] 



[N.S.} 



mathematics ; these points also indicate pretty certainly that the 

 work in question was not of unalloyed Indian origin. 



VIII. 



I have indicated roughly the main points of my arguments by 

 which, 1 believe, my original proposition is proved. The task I set 

 myself was to show that the current conceptions as to the origin 

 of our modern arithmetical notation have not very secure founda- 

 tions and that the question is worth reopening; and further, 

 that popular misconceptions of the range and influence of 

 Hindu mathematics need some correction. The second part of my 

 task is only indicated in the above notes, which I may supplement 

 later on, but as regards the question of notation I think enough 

 has been said to cause those interested and better qualified to 

 judge than I to reopen or, perhaps rather, to restate the question. 

 The character of the Indian scripts ; the evidence of inscriptions ; 

 the nature of the early notations in use among the Hindus ; the 

 nature of their mathematical works ; the very custom at the 

 present time among those Hindus who work on purely indige- 

 nous lines point to a foreign origin of the modern notation 

 as probable ; while the foundations of the arguments of those 

 who believe in an Indian origin are now shown to be either 

 absolutely unsound, or, when not absolutely unsound, at least 

 unreliable ; and consequently the Indian theory, if it is to stand, 

 must be restated. 



