Immediately after earning his laurea in 1925, he became the assistant of Mauro Picone, who in that year was called to the University of Naples, where he remained until 1932.

During the following five years, Caccioppoli published about 30 works on topics developed in the complete autonomy provided by a ministerial award for mathematics in 1931, a competition he won at the age of 27 and the chair of algebraic analysis at the University of Padova.

In the years from 1947 to 1957, he directed, together with Carlo Miranda, the journal Giornale di Matematiche, founded by Giuseppe Battaglini.

Together with his companion Sara Mancuso, he had the French national anthem played by an orchestra, after which he began to speak against fascism and Nazism in the presence of OVRA agents.

He was again arrested, but his aunt, Maria Bakunin, who at the time was a professor of chemistry at the University of Naples, succeeded in having him released by convincing the authorities that her nephew was non compos mentis.

Between 1933 and 1938 he applied his results to elliptic equations, establishing the majorizing limits for their solutions, generalizing the two-dimensional case of Felix Bernstein.

In 1992 his tormented personality inspired the plot of a film directed by Mario Martone, The Death of a Neapolitan Mathematician (Morte di un matematico napoletano), in which he was portrayed by Carlo Cecchi.