53* Notes on Indian Mathematics, — Arithmetical Notation 



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By G. R. Kate, Bureau of Education^ Simla. 



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We are told that our modem arithmetical Dotation is of 

 Indian origin. Peacock, Chasles, Woepcke, Cantor, Bayley, 

 Biihler, Macdonnell and others state this more or less emphatically, 

 and the encyclopaedias and dictionaries follow suit. A careful 

 examination, however, of the material now available seems to 

 point out that the hypothesis as to Indian origin was arrived at 

 without sufficient warrant. Such an examination shows, at any 

 rate, that many of the premises that were utilised are unsound. 



In the first place the opinions of the commentators were 

 taken as gospel by the early orientalists, and, secondly, the opinions 

 of the orientalists were taken as gospel by the mathematicians. 

 Numerous examples of the false premises used and the resulting 

 errors could be quoted, but as many will be noticed in the 

 course of this essay, they may be passed by for the present. 

 The following statement, which has been employed to show that 

 our modern notation was in use in very early times in India,' 

 is an extreme illustration : *' The invention of nine figures {anca) 

 with the device of places to make them suffice for all numbers 

 being ascribed to the beneficent creator of the universe*** 

 (Krishna, 16th Cent.)» No one would now dream of taking 

 such a statement as evidence, but " the Brahmin view in 

 possession of the field, when Europeans entered India, has been 

 regarded so long with reverence among us that it seems almost an 

 impertinence now to put forward any other.**^ ^g^ however, it 

 18 now known for certain that the old Indian commentators are 

 often unreliable we must, to arrive at any safe conclusion, treat 

 most of their glosses as of no value as interpretations. The commen- 

 tators were often given to ** expressions of vague boasting, of am- 

 biguous import and of doubtful authority "^ and those who have 

 trusted in them (e.gr. Colebrook) have naturally fallen into error* As 

 Rhys Davids says, we must now abandon " the unhappy system 

 of taking these ancient records in the sense attributed to them by 

 modern commentators."'*' 



The kind of evidence regarding notation that can be accepted 

 without fear is such as is recorded on coins and in genuine 

 inscriptions. Evidence in manuscripts can only be accepted 



^ Colehrodk, Algebra from the SansJcrit, p. 4; Encyclopaedia Britannica, 

 ii, 526. 



* Rhys Davids, Buddhist India, p. iii. 3 ib. p. 319, ♦ ib. p. 162. 



