The article investigates the genesis of the algorithm concept. It is mentioned that the concept of algorithm and algorithmic thinking appeared much earlier than the word algorithm. The linguistic and methodological bases of mathematics and, in particular, of algorithmization, the role of the algorithm concept in the educational process and other human activities are analyzed. Algorithmics are a fundamental requirement in solving many types of problems and, in particular, in computer science. Algorithmic thinking means the presence of skills and competencies to apply algorithms to solve problems and to be aware of sequences of algorithms in the logical demonstration of statements. The content of the article is developed in the aspects of th...