 It is extraordinary that the community of mathematical logicians took so long to discover the calculi of natural deduction (and the sequent calculi), once Frege, in 1879, had cracked the previously hidden grammatical code of multiply quantified sentences. It is remarkable that Gödel, in 1929, could have demonstrated the completeness of first-order logic before Gentzen’s natural formulation of it, when that logic was available only in the forms of the highly unnatural deductive calculi devised by Frege, by Hilbert, and by Russell and Whitehead. 