Scope and development of Hindu Mathematics

The Hindu name for mathematics is Gaṇita, literary meaning of Gaṇita is "the science of calculation". This name is very ancient one and occurs abundantly in Vedic literature. The Vedāṅga Jyotiśa (c 1200 B.C) gives Gaṇita the highest place of honour as mentioned in the below shloka, among the sciences which form the Vedāṅga.

यथा शिखा मयूराणां नागानां मणयो यथा ।

तद्वद् वेदाङ्गशास्त्राणां गणितं मूर्धनि स्थितम् ॥

Meaning : "As the crests on the heads of peacocks, as the gems on the hoods of snakes, so is Gaṇita at the top of the sciences known as Vedāṅga." In ancient Buddhist literature we find mention of three classes of Gaṇita : (1) mudrā ("finger arithmetic"), (2) gaṇanā ("mental arithmetic") and (3) saṃkhyāna ("higher arithmetic in general"). The word saṃkhyāna has been used for Gaṇita in several old works. At this remote period Gaṇita included astronomy, but geometry (kṣetra-gaṇita) belonged to a different group of sciences known as Kalpasūtra.

It is considered that some time before the beginning of  the Christian era, there was a revival of Hindu Gaṇita. The effect of this revival on the scope of Gaṇita was great. Astronomy (Jyotiśa) became a separate subject and geometry (kṣetra-gaṇita) came to be included within its scope. The subjects considered in the Hindu Gaṇita of the early revival period consisted of the following.


 * 1) Parikarma (fundamental operations)  2. Vyahāra (determinations) 3. Rajju (rope, meaning geometry)

4. Rāśi (Rule of three) 5. Kalāsavarṇa (operations with fractions) 6. Yāvāt tāvat (as many as, meaning simple equations)

7. Varga (Square, meaning quadratic equations) 8. Ghana (Cube, meaning cubic equations) 9. Varga-varga (biquadratic equations)

10. Vikalpa (permutations and combinations).

Hence Gaṇita came to mean mathematics in general, while 'finger arithmetic' as well as 'mental arithmetic' were excluded from the scope of its meaning. To do calculations in Gaṇita ,the use of some writing material was essential. The calculations were performed on a board (pāṭī) with a piece of chalk or on sand (dhūli) spread on the ground or on the pāṭī.

Hence the terms pāṭī-gaṇita ("science of calculation on the board") or dhūli-karma ("dust-work") came to be used for higher mathematics. Later on the section of gaṇita dealing with algebra was given the name Bīja-gaṇita. The first to effect this separation was Brahmagupta(628), but he did not use the term Bīja-gaṇita. The chapter dealing with algebra in his Brāhma-sphuṭa-siddhānta is called Kuṭṭaka. Śrīdharācārya(750) regarded Pāṭī-gaṇita and Bīja-gaṇita as separate and wrote separate commentaries on each. This distinction between Pāṭī-gaṇita and Bīja-gaṇita has been preserved by later writers.

Also See
हिंदू गणित का विस्तार और विकास