Śrīdhara

Śrīdhara, Śrīdharācārya or Śrīdhara Acharya ( c. 870 CE – c. 930 CE) was an Indian mathematician, Sanskrit pundit and philosopher. Sridhara was an Indian mathematician who wrote on practical applications of algebra and was one of the first to give a formula for solving quadratic equations.

Sridhara is the author of two mathematical treatises, namely the Trisatika (Pāṭīgaṇitasara ) and the Pāṭīgaṇita. Bijaganita, Navasati, and Brhatpati are the other works from Sridhara.

Pāṭīgaṇita aims at providing a complete course of arithmetic and mensuration. Logistics and determinations are the two main sections in Pāṭīgaṇita.

Logistics: (1) saṅkalita (addition), (2) vyvakalita (subtraction, (3) pratyutpanna (multiplication), (4) bhāgahāra (division), (5) varga (square), (6) varga-mūla (square root), (7) ghana (cube), (8) ghana-mūla (cube root), (9-16) the same operations for fractions, (17-22) kalāsavarṇa (reduction of fractions of six varieties), (23) trairāśika (rule of three), (24) vyasta-trairāśika(inverse rule of three), (25) pañcarāśika (rule of five), (26) sapta-rāśika (rule of seven), (27) nava-rāśika (rule of nine), (28) bhāṇḍa-pratibhāṇḍa (barter of commodities), and (29) jīva-vikraya (sale of living beings).

Determinations: (1) miśraka (mixtures), (2) śreḍhī (series), (3) kṣetra (plane figures), (4) khāta (excavations), (5) citi (piles of bricks), (6) krākaca (sawn pieces of timber), (7) rāśi (heaps or mounds of grain), (8) chāyā (shadow), and (9) śūnya-tatva (the mathematics of zero).

The works of Śrīdharācārya were so popular which brought a great name to Śrīdharācārya. The following verse which is in appreciation of him both by the Hindus and Jainas gives an idea of the unique position attained by him as a mathematician.

उत्तरतो सुरनिलयं दक्षिणतो मलयपर्वतं यावत् ।

प्रागपरोदधिमध्ये नो गणकः श्रीधरादन्यः ॥

"Up to the abode of the gods (Himalayas) towards the north and up to the Malaya mountain towards the south and between the eastern and western oceans, there is no mathematician except Śrīdhara."