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.
Algorithm characterizations
"Goodness" of an algorithm, "best" algorithms: Knuth states that "In practice, we not only want algorithms, we want "good" algorithms..." He suggests that some criteria of an algorithm's goodness are the number of steps to perform the algorithm, its "adaptability to computers, its simplicity and elegance, etc." Given a number of algorithms to perform the same computation, which one is "best"? He calls this sort of inquiry "algorithmic analysis: given an algorithm, to determine its performance characteristcis" (all quotes this paragraph: Knuth Vol. 1 p. 7)