Born in
Naples, he was the son of Giuseppe Caccioppoli (1852–1947), a
surgeon, and his second wife Sofia Bakunin (1870–1956), daughter of the Russian revolutionary
Mikhail Bakunin. After earning his high-school diploma in 1921, he enrolled in the Department of engineering to swap to mathematics in November 1923. 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. Picone immediately discovered Caccioppoli's brilliance and pointed him towards research in
mathematical analysis. 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 Padua. In 1934 he returned to Naples to accept the chair in
group theory; later he took the chair of superior analysis, and from 1943 onwards, the chair in mathematical analysis. In 1931 he became a correspondent member of the Academy of Physical and Mathematical Sciences of Naples, becoming an ordinary member in 1938. In 1944 he became an ordinary member of the
Accademia Pontaniana, and in 1947 a correspondent member of the
Accademia Nazionale dei Lincei, and a national member in 1958. He was also a correspondent member of the
Paduan Academy of Sciences, Letters, and Arts. In the years from 1947 to 1957, he directed, together with
Carlo Miranda, the journal
Giornale di Matematiche, founded by
Giuseppe Battaglini. In 1948 he became a member of the editing committee of
Annali di Matematica, and starting in 1952 he was also a member of the editing committee of
Ricerche di Matematica. In 1953 the Academia dei Lincei bestowed on him the national prize of physical, mathematical, and natural sciences. He was an excellent
pianist, noted as well for his nonconformist temperament. He tried out the vagrant life, and was arrested for begging. In May 1938 he gave a speech against
Adolf Hitler and
Benito Mussolini, when the latter was visiting Naples. 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. Thus Caccioppoli was interned, but he continued his studies in mathematics, and playing the piano. In his last years, the disappointments of
politics and his wife's desertion, together perhaps with the weakening of his mathematical vein, pushed him into
alcoholism. His growing instability had sharpened his "strangenesses", to the point that the news of his suicide on May 8, 1959, by a headshot did not surprise those who knew him. He died at his home in
Palazzo Cellamare. ==Work==