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Giuseppe Vitali graduated from the Scuola Normale Superiore in Pisa in 1899. He assisted Dini for 2 years from 1899 then left mathematics. His move away from mathematics was probably due to financial problems and he taught in schools.
From 1904 until 1923 he taught at the Liceo C Colombo in Genoa where he became involved in politics becoming a Socialist councillor. However, when the Fascists came to power in 1922, they dissolved the Socialist Party. His political career at an end, Vitali returned to mathematics.
First Vitali was appointed to a chair in Modena. This was as a result of him winning a competition for the chair of infinitesimal analysis in 1923. Then the following year Vitali was appointed to the chair of mathematics at Padua and finally, in 1930, to the chair of mathematics at the University of Bologna.
His significant mathematical discoveries include a theorem on set-covering, the notion of an absolutely continuous functions and a criteria for the closure of a system of orthogonal functions. Since he worked very much on his own, his work involves some rediscovering of known results but also some remarkably original discoveries.
From 1926 he developed a serious illness and he could no longer write. Nevertheless about half his research papers were written in the last four years of his life after the illness struck. In his last years he worked on a new absolute differential calculus and a geometry of Hilbert spaces. These topics were not followed up by later mathematicians.
After his death his work Moderna teoria delle funzoni d variabile reale was completed and published in 1935.
Article by: J J O'Connor and E F Robertson
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