Probability theory
He graduated in mathematics in 1935 and immediately undertook a university career. In 1942 he was lecturer in geometry (he had studied algebraic geometry under the guidance of Federigo Enriques and other Roman mathematicians). After an interruption for military service and a long period of imprisonment, in 1948 Pompilj won the competition for the chair in geometry. He taught geometry and probability theory at the Faculty of Statistical Sciences, University of Rome. Probability theory became the main topic of his interests and he taught this discipline until his premature death.