Studied in Roma with G. Castelnuovo -who was his supervisor- and F. Severi, and he graduated in1910; he was mainly interested in differential and projective-differential geometry; he also was interested in the geometrical theory of differential equations.

He taught in Milano (1922-23), Bologna (1923-26) and Roma from 1926 till 1964, when he retired. He was a member of the Accademia Nazionale dei Lincei and editor of the Rendiconti di Matematica e due applicazioni (1940-1959). His reviews of many of the most important mathematical books of his times show deep and different cultural interests.

Among his students we may cite F. Conforto.

His selected papers have been published by the Unione Matematica Italiana (U.M.I.) in three volumes, with beginning in 1978.

His main commemoration has been written by B. Segre, Rend. di Mat. e delle sue applicazioni , 1976; republished in vol. I of his selected papers, I-XVII..