  For Gentzen, the aims were, along with those of Hilbert, to  understand the structure of mathematical proofs. This program was a  complete success as far as pure logic and arithmetic are concerned.  The methods of sequent calculus, especially, permit the analysis of  proofs with profound results. The grand aim of proof theory, a proof  of the consistency of analysis as in Hilbert's second Paris problem,  has not been carried through but is not excluded, either.