‘Paradoxes, i.e., actual contradic-tions, have always studded and sometimes given impulse to the development of mathematics. They have shown themselves ca-pable of humorously scorning human beings at the most dra-matic moments of the evolution of thought, when the overwhelming power of truth forced mathematicians to confess: ‘We thought …. but instead …’ and to change direction. Though trying to stimulate the visitor’s interest the exhibition has not been conceived simply as a ‘divertissement’ aimed at making clear a number of ab-stract theories. Rather, it proposes a course of both chronolo-gical sequence and conceptual investigation among paradoxes, antinomies and unsolved pro-blems which invest the various branches of mathematics. The paradoxes presented go from the very oldest, that of the liar, right up to the modern antino-my of Russell’s “barber”. Particular stress is put on the fact that the birth of every pa-radox is due to Man’s need to contend (using the instruments at his disposal, which also inclu-de mathematics) with some-thing which lives inside him, but which is greater than him and which surprises him, i.e., the in-finite. And, “paradoxically”, every at-tempt to understand (that is to confine) paradox either leads to an artificial hardening of theo-ries or to the opening up of new prospects. This theory maintains that it is only possible to sense the existence of another world by de-voting oneself with care, atten-tion and above all love to this one.’