Algorithm
The word 'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to "algorismus". Al-Khwārizmī (, , c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now in Uzbekistan.
History of mathematics
In the 9th century, the Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī wrote several important books on the Hindu–Arabic numerals and on methods for solving equations. His book "On the Calculation with Hindu Numerals", written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West. The word "algorithm" is derived from the Latinization of his name, Algoritmi, and the word "algebra" from the title of one of his works, "Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala" ("The Compendious Book on Calculation by Completion and Balancing"). He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots, and he was the first to teach algebra in an elementary form and for its own sake. He also discussed the fundamental method of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which al-Khwārizmī originally described as "al-jabr". His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."