Chapter 55 - David Hilbert, Grundlagen der geometrie, first edition (1899)

Abstract

In mathematics David Hilbert's Grundlagen der Geometrie was an influential work that led by its axiomatic method to a new thinking in all mathematical fields in the 20th century. In addition, following in the traces of Euclid, it became the classical textbook for geometry in educating mathematicians and mathematics teachers for nearly the whole century. Towards the end of the 19th, century a remarkable change came about in the field of the foundations of geometry. For the first time David Hilbert constructed the axioms in what was subsequently to be their usual sequence. In this manuscript the arrangement of the later Festschrift is already apparent: axioms, proofs of independences, segment arithmetic, Desargues's theorem, Pascal's theorem, and problems concerning constructability. The manuscript Grundlagen der Euklidischen Geometrie (EG) contains an exhaustive discussion of those areas that were mostly treated in brief in the vacation course. The logical meaning of the axioms was studied by construction of arithmetical models. Amongst these were proofs of independence for axioms of the first two groups. The book had some consequences for physics, which gained Hilbert's attention from the 1900s onwards. For during the 1910s, there was a remarkable connection between Einstein and Hilbert.