Thābit ibn Qurra
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Thābit ibn Qurra, was a polymath known for his work in mathematics, medicine, astronomy, and translation. He lived in Baghdad in the second half of the ninth century during the time of the Abbasid Caliphate.
Pages from Thābit's Arabic translation of Apollonius' Conics
Algebra
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Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
The Rhind Papyrus from ancient Egypt, dated around 1650 BCE, is one of the earliest documents discussing algebraic problems.
Al-Khwarizmi's The Compendious Book on Calculation by Completion and Balancing provided a general account of how linear and quadratic equations can be solved through the methods of "reducing" and "balancing".
Garrett Birkhoff developed many of the foundational concepts of universal algebra.
Image: Francois Viete