 He then asserts, “The execution of this program is at present still an unsolved task”. During the following winter term 1917–18, Hilbert—with the assistance of Paul Bernays—gave a lecture course entitled Prinzipien der Mathematik. Here modern mathematical logic is invented in one fell swoop and completes the shift from structural to formal axiomatics. This dramatic shift allows the constructive, elementary definition of the syntax of theories and, in particular, of the concept of proof in a formal theory. This fundamental insight underpins the articulation of the consistency problem and seems to open a way of proving, meta-mathematically, that no proof in a formal theory establishes a contradiction.