A Concise History of Science in India c7.s3.1

c7.s3.1

Despite great interest attached to mathematics by the Jainas of ancient India, very little of their mathematical effort has unfortunately survived to this day. We have of course the mid-ninth century mathematical classic *Gaṇita-sāra-saṃgraha* by Mahāvīra (*c.* A.D. 850), but no such comparable work belonging to the pre-Christian centuries is extant. We only have a few fragments or insertions in canonical or other types of non-mathematical literature from which to judge of their early achievements. That a good body of mathematical literature must have existed at one time seems indicated in Mahāvīra's own statement in which he described himself as a mere compiler from the great ocean of the knowledge of mathematics from which long lines of holy sages had skilfully gathered many precious mathematical gems. About the first century B.C. the *Sthānāṅga-sūtra*, a Jaina canonical work, listed several mathematical topics which used to be cultivated at that time. These topics are: *saṃkhyāyana* (science of numbers), *parikarma* (fundamental operations), *vyavahāra* (subjects of treatment), *rajju* (geometry, like *śulba*), *rāśi* (heap, solid mensuration), *kalāsavarṇa* (fractions), *yāvat-tāvat* (equations, algebra), *varga* (square, quadratic equations), *ghana* (cube, cubic equations), *varga-varga* (biquadratic equations) and *vikalpa* (permutations and combinations). The Sanskrit version of the above enumeration in Pali runs as follows: