Paul Hertz’ contribution to proof theory: normal-form results for deductions

Amongst the most central results in proof theory are normal-form results for deductions. Such results were first presented, not by David Hilbert, who first formulated the idea of a mathematical theory of mathematical proofs (in 1904), but by Paul Hertz (in 1922). Hertz’ work (and relationship to Hilbert) has not received the attention it deserves. I discuss both in detail, as well as the theoretical role normal-form results play within proof theory. An unpublished manuscript by Heinrich Behmann commenting on Hertz’ work is published (with translation) as an appendix.