 Gödel’s results were certainly surprising, but some sort of incompleteness phenomenon was not totally unexpected. The possibility of incompleteness in the context of set theory was discussed by Bernays and Tarski already in 1928, and von Neumann, in contrast to the dominant spirit in Hilbert’s program, had considered it possible that logic and mathematics were not decidable. Gödel himself had mentioned the possibility of an undecidable problem concerning real numbers in his thesis in 1929 (see Dawson 1985). Hilbert (1928), on the other hand, had assumed that Peano Arithmetic and other standard theories were complete. Apparently Gödel was also impressed by Brouwer, who in his lecture in Vienna in 1928 had suggested that mathematics is inexhaustible and cannot be completely formalized (see Wang 1987, 84; and the section on Brouwer’s view of the formalist program in the entry on  the development of intuitionistic logic).