Annals of Mathematics, 141(1995),443-552 Modular elliptic curves and Fermat’ s Last theoren By ANDREW JOHN WILES* For Nada. Claire. Kate and Olivia Pierre de fermat Andrew ohn wiles Cubun autem in duos cubos, aut quadratoquadratum in duos quadra toquadratos, et generaliter mullam in infinitum ultra quadratum potestatum in duos ejusdem nominis fas est divider: cujes rei demonstrationem mirabile sane deter. Hanc marginis eaiguitas non capered