Bompiani received his Ph.D. (laurea) in 1910 under
Guido Castelnuovo at the
Sapienza University of Rome with thesis
Spazio rigato a quattro dimensioni e spazio cerchiato ordinario. Until 1913 he remained in Rome as an assistant to
Guido Castelnuovo and then, from 16 October 1913 to 30 October 1915, he was at the
University of Pavia as an assistant to
Francesco Gerbaldi. In December 1915 he became a docent lecturing on analytic geometry at the Sapienza University of Rome, where in 1922 he became an assistant professor (
professore incaricato). In 1922 he won a competition for a professorial chair at the
University of Milan, where he taught in 1922–1923. From 1923 to 1926 he was a professor at the
University of Bologna. Near the end of 1926 he returned to Rome to become a professor for
descriptive geometry (and then differential geometry and higher mathematical analysis) at the Sapienza University of Rome, remaining in this capacity until his retirement as professor emeritus in 1964. From 1939 to 1959 he was the director of the Mathematical Institute of the University of the Rome. and in 1928 at Bologna. He was a visiting professor at the University of Chicago, the University of Missouri–Kansas City, and the University of Pittsburgh. Bompiani wrote textbooks on projective, analytic, descriptive, and
non-Euclidean geometry. == Honors and awards ==