Mahaviracharya
Mahāvīra (mathematician)
9th-century Indian mathematician
Mahāvīra (or Mahaviracharya, "Mahavira the Teacher") was a 9th-century Indian Jain mathematician possibly born in Mysore, in India.[1][2][3] He authored Gaṇita-sāra-saṅgraha (Ganita Sara Sangraha) or the Compendium on the gist of Mathematics in 850 CE.[4] He was patronised by the Rashtrakuta emperor Amoghavarsha.[4] He separated astrology from mathematics. It is the earliest Indian text entirely devoted to mathematics.[5] He expounded on the same subjects on which Aryabhata and Brahmagupta contended, but he expressed them more clearly. His work is a highly syncopated approach to algebra and the emphasis in much of his text is on developing the techniques necessary to solve algebraic problems.[6] He is highly respected among Indian mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle; rhombus; circle and semicircle.[7] Mahāvīra's eminence spread throughout southern India and his books proved inspirational to other mathematicians in Southern India.[8] It was translated into the Telugu language by Pavuluri Mallana as Saara Sangraha Ganitamu.[9]
He discovered algebraic identities like a3 = a (a + b) (a − b) + b2 (a − b) + b3.[3] He also found out the formula for nCr as
[n (n − 1) (n − 2) ... (n − r + 1)] / [r (r − 1) (r − 2) ... 2 * 1].[10] He devised a formula which approximated the area and perimeters of ellipses and found methods to calculate the square of a number and cube roots of a number.[11] He asserted that the square root of a negative number does not exist.[12]