While the Americans have encountered first the "DO loops" of FORTRAN (1954), the "for loops" of ALGOL are derived from the earlier use in Europe of "for loops" in programming (actually "für loops", Heinz Rutishauser, 1951), which in turn had been preceded by the use in mathematics of the "for-all" quantifier (Gerhard Gentzen, 1935), which includes an implicit loop (and in many more recent programming languages, starting with Alphard in 1974, it is preferred for the most frequent loops to use a syntax essentially identical to the mathematical notation from 1935, i.e. like "forall X in A do ...").