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Any connection between this story and the life and death of the actual mathematician Renato Caccioppoli, whose name and life-setting are used in this film is, according to the knowledgeable (including reviewers and the director himself) only incidental.
Instead, the last days of a highly eccentric academic and mathematical wunderkind are evoked in a way which also paints a portrait of Naples in the 1950s. The mathematician, an alcoholic, has driven away those who were closest to him, except for a sympathetic and kindly old priest who attends concerts with him at the Opera.
One of his students who did not do well in his classes, is, on the other hand, full of condemnation for the tormented man, who eventually kills himself.