Federigo Enriques's Quest to Prove the "Completeness Theorem"

The golden age of the Italian school of algebraic geometry began with Antonio Luigi Gaudenzio Giuseppe Cremona and included among its main contributors Enrico Castelnuovo, Federigo Enriques, and Francesco Severi. The Italian school spanned nearly a century, from the unification of Italy in 1861 to Enriques's posthumously published post- World War II monograph on algebraic surfaces [Enrq 49]. In the 1890s Enriques, a mathematician who once quipped that "intuition is the aristocratic way of discovery, rigour the plebian way" [Hodge 48], and his colleague and future brother-in-law Castelnuovo began their monumental work on the birational theory of algebraic surfaces over the complex numbers C. Severi joined them in this effort a few years later.