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included Berlinski definition
An '''algorithm''' is a procedure for carrying out a task which, given an initial state, will terminate in a clearly defined end-state. It can be thought of as a recipe, or a step-by-step method, so that in following the steps of the algorithm one is guaranteed to find the solution or the answer. The name is derived from a corruption of [[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwārizmī]], the Persian astronomer and mathematician who wrote a treatise in Arabic in 825 AD entitled: ''On Calculation with Hindu Numerals''. This was translated into Latin in the 12th century as ''Algoritmi de numero Indorum''. The title translates as "Al-Khwārizmī on the numbers of the Indians", with ''Algoritmi'' being the translator's rendition of the original author's name in Arabic. Later writers misunderstood the title, and treated ''Algoritmi'' as a Latin plural of the neologism ''Algoritmus'' or ''Algorithmus'', and took its meaning to be 'calculation method'. In the Middle Ages there were many variations of this, such as alkorisms, algorisms, algorhythms etc.
An '''algorithm''' is a procedure for carrying out a task which, given an initial state, will terminate in a clearly defined end-state. It can be thought of as a recipe, or a step-by-step method, so that in following the steps of the algorithm one is guaranteed to find the solution or the answer. One commentator describes it as:<ref>David Berlinski, ''The Advent of the Algorithm: The Idea that Rules the World'' (Harcourt Inc.: 2000).</ref>
{{cquote|a finite procedure, written in a fixed symbolic vocabulary, governed by precise instructions, moving in discrete Steps 1, 2, 3, ..., whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end.}}
The name is derived from a corruption of [[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwārizmī]], the Persian astronomer and mathematician who wrote a treatise in Arabic in 825 AD entitled: ''On Calculation with Hindu Numerals''. This was translated into Latin in the 12th century as ''Algoritmi de numero Indorum''. The title translates as "Al-Khwārizmī on the numbers of the Indians", with ''Algoritmi'' being the translator's rendition of the original author's name in Arabic. Later writers misunderstood the title, and treated ''Algoritmi'' as a Latin plural of the neologism ''Algoritmus'' or ''Algorithmus'', and took its meaning to be 'calculation method'. In the Middle Ages there were many variations of this, such as alkorisms, algorisms, algorhythms etc.
There are two main current usages:
There are two main current usages: