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.
Mathetics
Seymour Papert, MIT mathematician, educator, and author, explains the rationale behind the term "mathetics" in Chapter 5 (A Word for Learning) of his book, "The Children's Machine". The origin of the word, according to Papert, is not from "mathematics," but from the Greek, "mathēmatikos", which means "disposed to learn." He feels this word (or one like it) should become as much part of the vocabulary about education as is the word pedagogy or instructional design.