  At the request of Bernays, Ackermann reproduced Gentzen's proof in  terms of Hilbert's   epsilon-calculus  in 1940. Ackermann's paper was the starting point of Kreisel's 1951  “no-counterexample” interpretation of arithmetic. It was  a surprise when the publication of Gödel's collected papers  brought to light his “Zilsel-lecture” in Vienna in 1938:  he outlines there this interpretation as a reformulation of Gentzen's 1935 proof. (The matter is discussed in great detail in Tait (2005)  who himself had worked on the no-counterexample interpretation and  its extension to analysis in the 1960s.)