The Foundation of Algebra in Medieval Islam

Algebra, in its basic form, that is the classification and solution of linear and quadratic equations, was founded around 820 AD with the composition of the book al-Jabr wa al-Maqabalah by Mohammad ibn Musa Khwarizmi. He defined algebraic entities for the first time and introduced mathematical operations on these entities as algebraic operations. He classified linear and quadratic equations into “6 standard forms” and presented the conditions for the existence of the root of these equations, and also provided geometrical proofs for the correctness of these solutions. He showed that all linear and quadratic equations can be converted into these “6 standard forms” by algebraic operations, and he presented the general method of solving all linear and quadratic equations. Some European historians of mathematics have tried to doubt the foundation of algebra by Khwarizmi. Some others have considered Diophantus Arithmetica as the source of inspiration for Khwarazmi’s Algebra, or at least both books as a continuation of the tradition rooted in Babylonian mathematics. But these views are not widely accepted today. In Medieval Islam, all the scholars agreed about the foundation of Algebra by Khwarizmi, and only a mathematician named Abu Barza considered his grandfather Abd al-Hamid ibn Wase‘ as the predecessor of Khwarizmi, although Abu Kamel Shuja‘ ibn Aslam strongly rejected this claim and others scholars of Medieval Islam have also emphasized the superiority of Khwarizmi.