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He founded the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics. He edited the journal of the Istituto from 1930 to 1958 during which time it became one of the leading journals in its field.
From 1931 Cantelli was professor at the University of Rome.
His first papers were on problems in astronomy and celestial mechanics and he wrote on Lagrange's method of studying perturbations of the planets. His later work is all on probability, frequency distributions, actuarial science and applications of probability theory.
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