Algorithm
The word "algorithm" itself derives from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized "Algoritmi". A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928. Later formalizations were framed as attempts to define "effective calculability" or "effective method". Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939.
Arche
Arche (; ) is a Greek word with primary senses "beginning", "origin" or "source of action" (: from the beginning, οr : the original argument), and later "first principle" or "element", first so used by Anaximander (Simplicius in Ph. 150.23). By extension, it may mean "first place, power", "method of government", "empire, realm", "authorities" (in plural: ), "command". The first principle or element corresponds to the "ultimate underlying substance" and "ultimate undemonstrable principle". In the philosophical language of the archaic period (8th to 6th century BC), "arche" (or "archai") designates the source, origin or root of things that exist. In ancient Greek philosophy, Aristotle foregrounded the meaning of "arche" as the element or principle of a thing, which although undemonstrable and intangible in itself, provides the conditions of the possibility of that thing.