If you want to know what “algorithm” means in everyday usage, feel free to go to the end of this entry and read only the last two paragraphs. If, instead, you want to see how deep the rabbit hole goes, keep reading from here.

The term “algorithm” comes from the Latin “algorithmus,” a word that emerged in the Middle Ages and derives from the expression “al-Khuwārizmī,” the nickname of the Persian mathematician Muḥammad ibn Mūsa, who lived in the ninth century. Strictly speaking, when we talk about an algorithm, we mean a procedure or systematic method for solving all problems of a certain kind. In other words, it is a finite sequence of instructions that, if followed to the letter, lead to the solution of every specific problem belonging to a certain family of problems.

Suppose, for example, that you want to know whether one bag contains more or fewer objects than a second bag. An algorithm for doing this consists of pairing each object in the first bag with an object in the second bag (making sure that no object belongs to more than one pair) until one of the two bags has no more objects left to pair. If we have paired all the objects in the first bag but not all those in the second, then the first contains fewer objects than the second. If we have paired all the objects in the second bag but not all those in the first, then the first contains more objects than the second. If we have paired all the objects in both the first and the second bag, then the first bag contains as many objects as the second. It does not matter what kind of objects the two bags contain, nor how many objects are in one bag or the other. In any case, this procedure will allow us to determine which bag contains more objects.

In this sense, an algorithm represents an abstract scheme for manipulating objects that can be implemented in a machine. A computer program, for example, is precisely a way of implementing an algorithm in a physical computing system.

The word “algorithm,” however, is often used in reference to artificial intelligence (AI) to indicate, on the one hand, methods for generating specific AI programs and, on the other, specific AI programs themselves. We speak, for example, of unsupervised learning algorithms, reinforcement learning algorithms, and deep learning algorithms. An algorithm, in this sense, is a particular technique that allows us to define a program and adapt it to a given task through a training process—or a program obtained through one of these techniques.

The word algorithm (or even “the algorithm”) is also used to refer to a recommendation system (RecSys), such as those used by social networks. These are information-filtering systems that provide suggestions about the relevance of information to a particular user.

Francesco A. Genco

(translated by MIRAI)