``Algorithm'' is named after the 9th C Persian mathematician **Abu
Ja'far Mohammed ibn Mûsâ al-khowârizm** who wrote, around
825 A.D., the book

Loosely, an algorithm is a finite, systematic procedure. One the simplest and also historically most important description of an algorithm is in terms of the Turing Machine (TM).

**Alan Turing's 1936** paper proved the existence of a simple,
general form (universal language) thought to underly all possible
algorithmic computations. A Turing machine can (as far as is known)
carry out any well-defined series of formal operations.