Method

Algorithm

Overview

In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning).

In contrast, a heuristic is an approach to solving problems without well-defined correct or optimal results. For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation.

As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and input, a computation occurs at each step, eventually producing output and terminating. The transition between states can be non-deterministic; randomized algorithms incorporate random input.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

In the original texts

Passages from public-domain books where Algorithm is discussed.

BESSER detailed several lessons learned from his work at Berkeley with Imagequery, especially the advantages and disadvantages of using X-Windows. In the latter category, for example, retrieval is tied directly to one's data, an intolerable situation in the long run on a networked system. Finally, BESSER described a project of Jim Wallace at the Smithsonian Institution, who is mounting images in a extremely…
Library of Congress, Workshop on Electronic Texts
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The exercise of logical reason is always concerned with these absolutely general conditions. In its broadest sense, the discovery of mathematics is the discovery that the totality of these general abstract conditions, which are concurrently applicable to the relationships among the entities of any one concrete occasion, are themselves inter-connected in the manner of a pattern with a key to it. This pattern of…
Alfred North Whitehead, Science and the modern world
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The notion of continuity depends upon that of _order_, since continuity is merely a particular type of order. Mathematics has, in modern times, brought order into greater and greater prominence. In former days, it was supposed (and philosophers are still apt to suppose) that quantity was the fundamental notion of mathematics.
Bertrand Russell, Mysticism and Logic and Other Essays
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When, from the observation of a number of individual instances, we ascend to a general proposition, or when, by combining a number of general propositions, we conclude from them another proposition still more general, the process, which is substantially the same in both instances, is called Induction. When from a general proposition, not alone (for from a single proposition nothing can be concluded which is not…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
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There are nevertheless, in mathematics, some examples of so-called Induction, in which the conclusion does bear the appearance of a generalization grounded on some of the particular cases included in it. A mathematician, when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the _law_ of the series, does not hesitate to fill up any number…
John Stuart Mill, A System of Logic
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Algorithm

Overview

In the original texts

Philosophers who discussed Algorithm

Related ideas

Place in the tradition