Al-Khwarizmi

Al-Khwarizmi was a ninth-century Persian mathematician and astronomer whose works helped establish algebra and spread Hindu-Arabic numerals through the medieval Islamic world and Europe.

House of Wisdom: A scholarly institution in Abbasid Baghdad associated with collecting, translating, and producing works of learning. Baghdad’s scholarly culture provides the setting commonly associated with his career.
Completing the square: A method for solving quadratic equations by rewriting a quadratic expression as a perfect square. His treatment of quadratic equations relies on geometric forms of this procedure.
The Compendious Book on Calculation by Completion and Balancing: Al-Khwarizmi’s Arabic treatise presenting methods for solving linear and quadratic equations. This work established a durable systematic treatment of algebra.
Algorithm: A finite, specified procedure for carrying out a calculation or solving a problem. The word derives through Latin forms of Al-Khwarizmi’s name.
Hindu-Arabic numeral system: A positional decimal number system using ten digits, including zero. His arithmetic treatise helped transmit this numeral system westward.
Quadratic equation: An equation whose highest power of the unknown is two. He classified and solved quadratic equations using rhetorical procedures.
Kitāb al-Jamʿ wa al-Tafrīq bi-Ḥisāb al-Hind: An arithmetic work by Al-Khwarizmi that introduced Hindu calculation methods; its Arabic original is lost. Its Latin transmission helped carry Hindu-Arabic arithmetic into Europe.
Algebra: A branch of mathematics that represents quantities and relationships with symbols and equations. The term derives from al-jabr, a word in the title of his algebra treatise.
Indian mathematics: Mathematical traditions developed in the Indian subcontinent, including decimal place value and zero. Indian mathematical work supplied key ideas in the arithmetic he presented.
Decimal place-value system: A base-ten notation in which a digit’s position determines its value. His arithmetic work explained calculation using positional numerals.

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