The History of Arithmetical Notation

Abstract

THE invention of the decimal notation, which involves the use of zero and the assignment of local value to digits, made such an immense alteration in the character of arithmetical calculations that it would be extremely interesting to know its origin. It became familiar in Europe mainly through Mohammedan sources; hence the term Arabic, as opposed to Roman notation. But the discovery of Sanskrit literature and of Indian works on mathematics led to the theory that the real inventors of the system were the Hindus. The object of Mr. Kaye, in the paper referred to below,1 is to show that this conclusion has been based on insufficient evidence, and that the whole question requires further and more careful consideration, including a critical study of Indian texts, to avoid being misled by spurious documents. Mr. Kaye gives in the first place a series of arguments which go far to prove that there is no trustworthy evidence for the use of the new notation in India before the-ninth century A.D., and that, if a single inscription prove untrustworthy, we shall have to fix the tenth century as the earliest date attested. Another point on which there can be no doubt that he is right is that the Arabic epithet hindashi, applied to the decimal notation, certainly does not mean Indian, the word for which, is hindi, and cannot be connected with hindashi by any regular Arabic method of word-formation; not to mention that hindashi usually means “geometrical,” and was derived from a Persian word by the Arabic lexicographers themselves. There is no probability in favour of Colebrooke's conjecture that the Indian work translated by Alfarazi was entitled “Siddhanta”; and it is clear enough that after Brah-magupta there was a decline in the study of mathematics in India.