 Note that the solvability Hilbert is referring to here concerns solvability of mathematical problems in general and not just mechanically solvable. It is shown however in Mancosu et al. 2009 (p. 94), that this general aim of solving every mathematical problem, underpins two particular convictions of Hilbert namely that (1) the axioms of number theory are complete and (2) that there are no undecidable problems in mathematics.