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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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II.4 Algorithms

Jean-Luc Chabert

1 What Is an Algorithm?

It is not easy to give a precise definition of the word “algorithm.” One can provide approximate synonyms: some other words that (sometimes) mean roughly the same thing are “rule,” “technique,” “procedure,” and “method.” One can also give good examples, such as long multiplication, the method one learns in high school for multiplying two positive integers together. However, although informal explanations and well-chosen examples do give a good idea of what an algorithm is, the concept has undergone a long evolution: it was not until the twentieth century that a satisfactory formal definition was achieved, and ideas about algorithms have evolved further even since then. In this article, ...

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