Hilbert e i fondamenti della geometria (1891-1902)B

Hilbert's epoch-making Grundlagen der Geometrie (GG) (1899) had a tremendous impact on the development of both logic and axiomatic thought, as discussed by Mangione in vol. 5 of Geymonat's Storia del pensiero scientifico e filosofico. Leaving this on the background, the present paper focuses instead on the origins and development of Hilbert's ideas on the foundations of geometry, and compares them with the contemporary work by Italian mathematicians. In fact, GG was the eventual outcome of a long-term research pursued by Hilbert over a decade, and presented in his courses at Koenigsberg and Goettingen. Eventually, its influence can be recognised in some of his celebrated 'mathemtical problems' (ICM Paris, 1900).