Zur Schl├╝sselrolle Friedrich Schurs bei der Entstehung von David Hilberts ”Grundlagen der Geometrie”. (Friedrich Schur playing the leading part in the development of David Hilbert’s Foundations of Geometry). (German) Zbl 0584.01006

Mathemata, Festschr. H. Gericke, Boethius 12, 637-649 (1985).
[For the entire collection see Zbl 0557.00001.]
It is now known, by more recent research, that already before Hilbert substantial results in geometric axiomatics had been achieved. Hilbert’s Foundations of Geometry, however, contain only some bibliographical references, most added in later editions. In this article the real influence of F. Schur on Hilbert is described on the basis of new material. Indeed, the author proves convincingly that one of the most salient features of the Foundations: the proof of the theorem of Pappus with help of the axioms of congruence but without the Archimedean axiom and its position in axiomatics goes back directly to Schur. Hilbert never acknowledged this indebtedness.
Reviewer: W.S.Contro


01A55 History of mathematics in the 19th century
51-03 History of geometry
03-03 History of mathematical logic and foundations

Biographic References:

Schur, F.; Hilbert, David


Zbl 0557.00001