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History of Hindu Mathematics: A Source Book v1.c7.s5.t1: Earliest Numerals

History of Hindu Mathematics: A Source Book v1.c7.s5.t1

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Earliest Numerals

v1.c7.s5.t1.1

The numerical figures contained in the seals and inscriptions of Mohenjo-daro, have not been completely deciphered as yet. The vertical stroke and combinations of vertical strokes arranged side by side, or one group below another, have been found. The numbers one to thirteen seem to have been written by means of vertical strokes, probably, as in the figures given below:³

v1.c7.s5.t1.2

³ Marshall, *l.c.*, pp. 450-52. See also "Mohenjo-daro—Indus Epigraphy" by G. R. Hunter (*JRAS*, April, 1932, pp. 470, 478ff.) who is more pronounced about the numerical values of some of the signs.

v1.c7.s5.t1.4

It is not yet quite certain whether there were special signs for greater numbers such as 20, 30, the hundreds and higher numbers. There are numerous other signs which are believed to represent such numbers, but there seems to be no means of finding out the true values of these signs at present.

v1.c7.s5.t1.5

Between the finds of Mohenjo-daro and the inscriptions of Aśoka, which contain numerals, there is a gap of 2,700 years or more. No written documents containing numerals and belonging to this intervening period have been so far discovered. The literary evidence, however, points to the use of numerical symbols at a very early date. The reference to the writing of the number eight in the *Ṛgveda* and the use of numerical denominations as big as 10¹² in the *Yajurveda Saṁhitā* and in several other Vedic works, quoted before, offer sufficient grounds for concluding that, even at that remote period, the Hindus must have possessed a well developed system of numerical symbols. The conclusion is supported by the fact that the Greek and the Roman numerical terminologies did not go beyond 10⁴, even after writing and a satisfactory numerical symbolism had been in use for several centuries.

v1.c7.s5.t1.6

The writings on the inscriptions of Aśoka show that in his time the use of numerical symbols in India was quite common.¹ The variations in the forms of the numerical signs suggest that the symbols had been in use for a long time.

v1.c7.s5.t1.7

¹ Megasthenes speaks of mile-stones indicating the distances and the halting places on the roads. The distances must have been written in numerical figures (Bühler, *l.c.*, p. 6; also *Indika of Megasthenes*, pp. 125-26). The complicated system of keeping accounts mentioned in the *Arthaśāstra* of Kauṭilya confirms the conclusion.

v1.c7.s5.t1.8

Most of the inscriptions of Aśoka and the following period are written in a script which has been called *Brāhmī*, whilst some are in a different script known as *Kharoṣṭhī*. The forms of the numerical symbols in the two scripts are different. We consider them separately.

Cites (4)