The Decimal System of Numeration

The history of the remotest civilization is always shrouded in mystery and surrounded by controversy. The conclusions of a scientist can be challenged only on the grounds of accuracy of his experimental work and on the validity of his theory. But the conclusions of a historian can always be challenged more seriously on the grounds of insufficient data and knowledge, not. to speak of his personal or national affections and prejudices. Civilization is spread over distant lands and languages. No one can vouchsafe that he has had access to all the extant literature in the different languages, that he has really mastered the meaning and the spirit of the different texts, and that he has not been misled by the translations or interpretations given by his predecessors.

The last word on the history of ancient civilization will never be said. A mathematician who writes the history of his science is by the very nature of human tendencies first a historian, and then a mathematician. Examples are not wanting when he has become unfortunately a politician. The conclusions as regards dates and origin of the  achievements of ancient Indian mathematicians, and even of the extent of their knowledge, as made by some of the Western historians have been severely criticized by Indian scholars as unfair and prejudiced. The writings by Indian S€scholars of their own history have been comparatively few, and have not received the attention that they deserve at the hands of the historians of the West. A similar state of affairs exists in all probability as regards the achievements of other ancient civilizations like those of China, Chaldea and Egypt.

Under such circumstances, the best thing for a historian is to set the facts as he finds them or as he understands them, and allow the people of the world to interpret and assess these facts according to their own understanding of the subject.


The most fundamental contribution of ancient India to the progress of civilization is the invention of what is called the decimal system of numeration including the invention of the number “Zero”.

The characteristic feature of this system is the usage of nine digits and a symbol for zero to denote all integral numbers, by assigning a place-value to the digits. This system is so simple and is now learnt by children of tender age all over the world, thflt the profundity of its invention is easily lost sight of. The profundity of its invention is understood only when one realities the difficulty of making progress in arithmetic with other systems, such as the Greek system of numerals I, II, III, X, C, L etc. The Greek method of representing numbers by geometrical segments, and the slow progress of mathematics in the West before the advent of the Indian system to the West are sufficient illustrations of the handicap of the people who were not acquainted with the decimal system.

During the earlier decades of this century as well as in the last century, attempts were made to credit this invention wholly or in part to the Arabs. But mathematicians are now generally convinced that the invention is entirely the work of the ancient Hindus, and that the Arabs were the people who carried this invention to the states of Africa and of Europe.

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