Be that as it may, it seems that Gödel actually arrived at the first exact observations about incompleteness via a different route, during his attempts to contribute to Hilbert’s program, and not to undermine it (see Dawson 1997: Ch. IV). Namely, in 1930, Gödel made an effort to advance Hilbert’s program by attempting to prove the consistency of analysis (or, second-order arithmetic) with the resources of arithmetic, and thus reduce the consistency of the former to the consistency of the latter.