|Algorithms are a central notion in computer science/informatics nowadays. As a specific procedure for solving problems, they appeared and continue to appear outside the context of computers and programming languages as a part of the search for accurate ways of expressing algorithms as well as of adequate ways for talking about their qualities. Both the formulation and the verbal evaluation of the algorithm were inherent to the mathematical environment and related to the justification of the solution as a new mathematical result. Language of mathematics is an expression commonly used in connection with computers. However, as translating of the language of mathematics into machine language was found to be extremely laborious, this task was left to the compilers for various programming languages. Of the new programming languages, one was chosen as the publication language. The algorithmic language, abbreviated as ALGOL, thus became a major language for exchanging algorithms in an easily comparable way by formalizing expressions for loops and branches in the notation of algorithms. The paper will attempt to show what kind of mathematical culture stimulated the formulation of exact algorithms while their authors could not even think of trying the algorithms out on a computer.