Early examples of resource-consciousness (Q1876091)

``The question regarding the number of uses of a certain sentence in a proof of another sentence first surfaced in logic in the mid 1930s with the work of Fitch and Tarski, which may be considered to belong to what came to be known after Meredith and Prior (1963) as implicational BCK logic.'' H. Brandes, in his doctoral dissertation of 1907 (published in 1908), asks for the minimal number of times that a certain axiom has to be used (other axioms being allowed any number of times) for a proof of a certain form of the Pythagorean theorem. Perhaps this is the earliest example of ``resource-consciousness''. ``In 1905, G. Hessenberg proved that the threefold application of the Pappus axiom, together with the trivial axioms for plane projective geometry, implies the Desargues axiom. It follows that this holds for the affine case as well.'' However, the minimality of this ``three'' was never discussed by him or many others who worked later on this topic, until in 1931 M. Dehn formulated it. The author concludes that the number of uses of hypotheses (considered as resources) originates in the foundations of geometry (neither in computer science nor in logic).