Studied in Padova (where he graduated in 1886) with G. Veronese, in Roma with L. Cremona, in Torino with E. D'Ovidio and C. Segre. He taught projective and analytical geometry in Roma since 1891. He was also a member (and also president) of the Accademia Nazionale dei Lincei.

Castelnuovo, with Enriques and Severi, was one of the most prominent mathematicians of the "golden age" of Italian algebraic geometry. Besides to algebraic geometry he devoted himself to educational issues (he was president of the association "Mathesis" from 1911 to 1914), to the philosophical implications of the theory of relativity and to historical studies. He may also be considered, together with F. P. Cantelli the founder and the main propagator of Italian studies in the calculus of probability.

Among his many students we may cite G. Fano, F. Conforto, L. Campedelli and O. Zariski .

Selected papers have been published by U.M.I. in 1937 ( Memorie Scelte , Zanichelli, Bologna ).

Main commemorations and studies: F. Conforto, Rend. di Mat. e sue applicazioni , (5), 11, 1952, I-III; A. Terracini, Atti dell'Acc. delle Scienze di Torino , 86, 1951-52, 366-377; G. Fano, Rend. della R. Acc. Nazionale dei Lincei , fascicolo speciale, 1953; L. Campedelli, Boll. dell' Unione Mat. Ital. , (3), 7, 1952, 241-246; E. Carruccio, in Dictionary of scientific biographies , 3, 117.