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From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term. according to Savage [1987], an algorithm is a computational process defined by a Turing machine".

Algorithms are essential to the way computers process data. Typically, when an algorithm is associated with processing information, data can be read from an input source, written to an output device and stored for further processing.

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.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n.

Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable.

It derives from the intuition of "memory" as a scratchpad. For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming.

Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by flow of control.Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B.The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b).An algorithm is an effective method that can be expressed within a finite amount of space and time 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" those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 19, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–.

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