CHAPTER 17
Indian Mathematics
Takao Hayashi
I Vedic Mathematics
I.1 Vedas
Since the Vedas are religious texts produced by poets, we cannot expect in them
enough information for systematically describing the mathematical knowledge
of those times. We can only gather scattered terms for whole numbers, for basic
fractions, and for simple geometric figures.
TheR.gveda contains a number of numerical expressions. The Vedic poets were
particularly fond of three and seven as holy numbers, and often used their mul-
tiples such as 3 ¥7, 33 (= 3 ¥11), 3 ¥50, 3 ¥60, 3 ¥70, 3 ¥ 7 ¥70, and 333
(= 3 ¥111). It has been argued that the number of gods, 3339, mentioned in
R.gveda 3.3.9, is the sum of three numbers, namely, 33, 303, and 3003.
Although it has not been proved that the Vedic Indians had a place-value nota-
tion of numbers, this summation itself must have not been difficult for them
since their numeration system was basically decimal. They used the words eka,
das ́a,s ́ata,sahasra, and ayuta, for 1, 10, 10^2 , 10^3 , and 10^4. For multiples of 10^3
and of 10^4 they often used expressions based respectively on 10^2 and on 10^3 as
well; for example, 2 ¥ 103 =20 (vím.s ́ati)¥ 102 (s ́ata), 3 ¥ 104 =30 (trim.s ́at)¥
103 (sahasra), etc. The words for “hundred” and “thousand” are sometimes
employed in the sense of “a number of.” Thus, Indra is said to have destroyed a
hundred old fortresses of S ́ambara and slain a hundred thousand (s ́atam.sahas-
ram.) brave men of Varcin (ibid. 2.14.6). The number sixty seems to have had a
certain weight with the Vedic poets since we come across expressions like “a
thousand and sixty (1060) cows” (ibid. 1.126.3), “sixty thousand and ninety-
nine (60099) kings” (ibid. 1.53.9), and “sixty thousand ayuta (60¥ 103 ¥ 104 =
6 ¥ 108 ) of horses” (ibid.8.46.22), but its significance is not known.