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This volume brings to the forefront some of the proponents of the mathematics of the twentieth century who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present impressive and passionate people.

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Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between soul and precision.

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Preface.- Hilbert s Problems. A Research Program for Future Generations: U.Bottazzini.-The Way We Were. The Protagonists of the Italian Spring in the First Decades of the Twentieth Century: G.Bolondi et al.- Intermezzo: Verlaine and Poincaré from Etudes littéraires : P.Valéry.- B.Russell. Paradoxes and Other Enigmas: G.Rigamonti.- G.H.Hardy. A Brilliant Mind: R.Lucchetti.- E.Noether. The Mother of Algebra: A.Brigaglia.- Intermezzo: Carciopholus romanus from Furor mathematicus: L.Sinisgalli.- P.A.M.Dirac. The Search for Mathematical Beauty: F.La Teana.- The Theoretical Intelligence and Pratic Vision of J. von Neumann: R.Lucchetti.- K.Gödel. Completeness and Incompleteness: P.Odifreddi.- Intermezzo: In Homage to Gödel: H.M.Enzensberger.- R.Musil. The Audacity of Intelligence: C.Bartocci.- The Life, Death and Miracles of Alan Mathison Turing: S.Termini.- R.Caccioppoli. Naples, Fascism and the Post-War Period: A.Guerraggio.- B. de Finetti. The Foundations of Probability: D.M.Cifarelli.- A Committed Mathematician: G.I.Bischi.- A.N.Kolmogorov. The Basis of Probability, and More...: G.Boffetta et al.- Bourbaki. A Mathematician from Poldavia: G.Bolondi.- Writing and Mathematics in the work of R.Queneau: A.Ferraro.- J.F.Nash, Jr.. The Myth of Icarus: R.Lucchetti.- E.De Giorgi. Intuition and Rigour: G.Dal Maso.- L.Schwartz. Political Commitment and Mathematical Rigour: A.Guerraggio.- R.Thom. Conflict and Genesis of Forms: R.Betti.- Intermezzo: The Dream: J.L.Borges.- A.Grothendick: Enthusiasm and Creativity. A New Language at the Service of Imagination: L.Barbieri Viale.- G.-C.Rota. Mathematician and Philosopher: D.Senato.- S.Smale. Mathematics and Civil Protest: A.Guerraggio.- M.F. Atiyah. The Deep Reasons for Mathematics: C.Bartocci.- V.I.Arnol d: M.Pedroni.- Enrico Bombieri: C.Bartocci et al.- M.Gardner: E.Peres.- Intermezzo: The Door of Miracles from Le Modulor: Le Corbusier.- F.W.Lawvere: R.Betti.- An Interview with A.Wiles: C.Bartocci

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