A ̄ryabhat.a I’s terminology for series, citi, etc., too, is probably related to the
S ́ulbasu ̄tras, whose main theme was the piling (citi) of bricks for Vedic altars.
II Gan.ita (Mathematics)
II.1 Up to the 5th century – prologue
It is but natural that one who calculates most in a society is called a calculator.
Before the introduction and spread of horoscopic astrology and mathematical
astronomy to the Indian subcontinent, the occupation that, in Indian society,
required calculations most seems to have been that of the accountant, since he
was called either gan.akaorsam.khya ̄yaka, both meaning “a calculator.” In the
Maha ̄bha ̄rata (2.5.62) the sage Na ̄rada recommends to the king Yudhis.t.hira that
he make his calculator (gan.aka) and scribe (lekhaka) report to him the revenue
and expenditure every morning. Kaut.ilya’s Arthas ́a ̄stra (1.19.9), too, refers to
the same daily task of a king. The salary of a king’s calculator and scribe is 500
pan.aseach, while the highest salary, 48,000 pan.as, is paid to a minister, a prince,
etc., and the lowest, 60 pan.as, to a servant who takes care of animals (ibid.
5.3.3–17). The superintendents of governmental departments are said to be
assisted by five persons, namely, calculators (sam.khya ̄yakas), scribes (lekhakas),
inspectors of coins (ru ̄pa-dars ́akas), receivers of balances (nı ̄vı ̄-gra ̄hakas), and
supervisors (uttara ̄dhyaks.as) (ibid. 2.9.28). According to a later law book, the
Br.haspatismr.ti(1.1.81–90), a court consists of ten elements including a gan.aka,
who calculates money and assets, and a lekhaka, who writes sentences.
The 107th story, Gan.akamoggalla ̄nasutta, of the Majjhimanika ̄yanarrates a dis-
course of the Buddha with a bra ̄hman.agan.akanamed Moggalla ̄na, from which
we know: (1) that a gan.akalived on calculation (gan.ana ̄), (2) that a gan.akatook
live-in pupils (anteva ̄sins) and taught them calculation (san.kha ̄na), and (3) that a
gan.akafirst taught his pupils to count from one to one hundred. The gan.ana ̄and
thesan.kha ̄nain this story seem to mean respectively calculation (or mathemat-
ics) in general and a relatively elementary skill of computation beginning with
the counting of numbers.
According to the Arthas ́a ̄stra (1.2–5), a prince learns lipi(writing) and
sam.khya ̄naafter his hairdressing rite, and then, after his initiation rite, learns the
four disciplines (vidya ̄s), namely, philosophy, the Vedas with related fields, pra-
ctical knowledge like agriculture and commerce, and politics. This sam.khya ̄nais
perhaps as elementary as the san.kha ̄naof Moggalla ̄na, although a calculator in
general is called not a gan.akabut a sam.khya ̄yakain the Arthas ́a ̄stra.
In the Maha ̄bha ̄rata (3.70), the king R.tuparn.a is proud of his ability in
sam.khya ̄nain addition to that in dice, when he correctly estimates, without count-
ing, the number of nuts, 2095, on two branches of a Vibhı ̄taka tree (Terminalia
bellerica).Thissam.khya ̄na, therefore, contains a sort of statistical estimate of the
quantities of nuts, crops, etc. The san.kha ̄naof the Jaina canonical text, T.ha ̄n.am.ga
indian mathematics 365