Mathematical Culture and Thought

Mathematical Culture and Thought

The Foundation of Algebra in Medieval Islam

Document Type : Original

Author
Y. Karamati
Institute for the History of Science, University of Tehran, Iran
10.30504/mct.2022.1328.1925
Abstract
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.
Keywords
algebra
Mohammad ibn Musa Khwarizmi
al-Jabr wa al-Maqabalah
Abd al-Hamid ibn Wase‘
Abu Barza
Abu Kamel Shuja‘ ibn Aslam
Diophantus
Arithmetica

Subjects

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  • Receive Date 30 September 2022
  • Accept Date 15 October 2022
  • Publish Date 21 January 2023