Informally speaking, an algorithm is a collection of simple instructions for carrying out a task. The notion of algorithm itself was not defined precisely until the twentieth century. Before 20-th century mathematicians had an intuitive notion of what algorithms were and relied on that notion when using algorithms. Intuitive notion of algorithm was insufficient for gaining deeper understanding of algorithms.Hilbert’s program forced the development of a formal notion of an algorithm.
An algorithm (derived from the name of mathematician al-Khwārizmī and transformed to match the Greek "arithmos"-number) is an effective method for solving a problem expressed as a finite sequence of steps. Algorithms are used for calculation, data processing, and many other fields.Each algorithm is a list of well-defined instructions for completing a task. Starting from an initial state, the instructions describe a computation that proceeds through a well-defined series of successive states, eventually terminating in a final ending state.