Sridhara

Śrīdhara or Śrīdharācārya was an Indian mathematician, known for two extant treatises about arithmetic and practical mathematics, Pāṭīgaṇita and Pāṭīgaṇita-sāra, and a now-lost treatise about algebra, Bījagaṇita.

Life

Very little is known about Śrīdhara's life beyond mentions of his mathematical work by later mathematicians and the content of his extant treatises, which do not contain biographical details such as his parents, teachers, or birthplace. Various scholars have suggested he came from the Bengal region or from South India. Based on example problems in his works mentioning Shiva, and a dedication in Pāṭīgaṇita-sāra, he was probably a Shaivite Hindu.
He was mentioned by Bhāskara II, and made apparent reference to Brahmagupta. Govindasvāmin quoted a passage also found in Pāṭīgaṇita-sāra, and overlapping material is found in the work of Mahāvīra, from which historians estimate Śrīdhara to have lived in the 8th or early 9th century.
He has sometimes been conflated with other medieval Indian scholars also named Śrīdhara.

Works

Śrīdhara wrote two extant mathematical treatises. The first, Pāṭīgaṇita, also called Bṛhat-Pāṭi and Navaśatī, extensively covered the practical mathematics of the time including arithmetic and mensuration. It is believed to have originally included 900 stanzas, but only 251 are extant, and many topics mentioned in the table of contents have been lost. The second, Pāṭīgaṇita-sāra, also called Triśatikā because it was written in three hundred verses, is an abridged summary of Pāṭīgaṇita. It discusses counting of numbers, natural number, zero, measures, multiplication, fraction, division, squares, cubes, rule of three, interest-calculation, joint business or partnership, and mensuration.
He also wrote a work on algebra, Bījagaṇita, which has been lost, but some quotations remain in the works of later mathematicians. Some historians believe that Śrīdhara may have authored another mathematical treatise called Gaṇita-pan̄caviṁśī.
His notable works include–

He gave an exposition on the zero. He wrote, "If zero is added to any number, the sum is the same number; if zero is subtracted from any number, the number remains unchanged; if zero is multiplied by any number, the product is zero".
In the case of dividing a fraction he has found out the method of multiplying the fraction by the reciprocal of the divisor.
He presented a method of completing the square to solve quadratic equations, sometimes called Śrīdhara's method or the Hindu method. Because the quadratic formula can be derived by completing the square for a generic quadratic equation with symbolic coefficients, it is called Śrīdharācārya's formula in some places.