Fubini was the son of a mathematics teacher and went to Venice to school. He studied from 1896 at the Scuola Normale Superiore di Pisa among others, Ulisse Dini and Luigi Bianchi, where he received his doctorate in 1900, Clifford parallels in elliptic spaces. From 1901 he taught at the University of Catania and soon after in Genoa. From 1908 he taught both at the Polytechnic in Turin and at the university. In 1939 he emigrated as a Jew with his family to the United States in response to the racist policy has now become Mussolini, who had also meant that he was forced to retire. The main reason for his emigration was the concern about the future of his two sons, who were engineers or physicists. Fubini took advantage of an invitation from the Institute for Advanced Study in 1939 and then taught for several years in New York City, but his health began after (heart problems).
As a mathematician, he studied first with projective differential geometry and later with various fields of analysis such as complex analysis and integral calculus ( Fubini's theorem ). Other areas were group theory and mathematical physics, especially in the time of the First World War, where he worked on mathematical problems from the military application in the artillery, and later out of interest for the field of work his sons, who were engineers.
His son, Eugenio Fubini (1913-1997), a physicist, was under Kennedy 1963-1965 Assistant Secretary of Defense in the U.S. and then from 1965 to 1969 Vice President for Research of IBM.