in mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ (about this sound listen) al-gə-ridh-əm) is an unambiguous specification of how to solve a class of problems. algorithms can perform calculation, data processing and automated reasoning tasks. an algorithm is an effective method that can be expressed within a finite amount of space and time[1] and in a well-defined formal language[2] for calculating a function.[3] starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, proceeds through a finite[5] number of well-defined successive states, eventually producing output [6] and terminating at a final ending state. the transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7] the concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the entscheidungsproblem (the decision problem ) posed by david hilbert in 1928. subsequent formalizations were framed as attempts to define effective calculability [8] or effective method ;[9] those formalizations included the gödel–herbrand–kleene recursive functions of 1930, 1934 and 1935, alonzo church s lambda calculus of 1936, emil post s formulation 1 of 1936, and alan turing s turing machines of 1936–7 and 1939. giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem. the word algorithm is a combination of the latin word algorismus, named after al-khwarizmi[11][12] and the greek word arithmos, i.e. αριθμός, meaning number . al-khwārizmī (persian: خوارزمی‎, 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.[13][14] about 825, he wrote a treatise in the arabic language, which was translated into latin in the 12th century under the title algoritmi de numero indorum. this title means algoritmi on the numbers of the indians , where algoritmi was the translator s latinization of al-khwarizmi s name.[15] al-khwarizmi was the most widely read mathematician in europe in the late middle ages, primarily through his other book, the algebra.[16] in late medieval latin, algorismus, english algorism , the corruption of his name, simply meant the decimal number system . in the 15th century, under the influence of the greek word ἀριθμός number (cf. arithmetic ), the latin word was altered to algorithmus, and the corresponding english term algorithm is first attested in the 17th century; the modern sense was introduced in the 19th century.[17] in english, it was first used in about 1230 and then by chaucer in 1391. english adopted the french term, but it wasn t until the late 19th century that algorithm took on the meaning that it has in modern english. another early use of the word is from 1240, in a manual titled carmen de algorismo composed by alexandre de villedieu. it begins thus: haec algorismus ars praesens dicitur, in qua / talibus indorum fruimur bis quinque figuris. which translates as: algorism is the art by which at present we use those indian figures, which number two times five. the poem is a few hundred lines long and summarizes the art of calculating with the new style of indian dice, or talibus indorum, or hindu numerals.