Finessing Fermat, Again; February 1995; Scientific American Magazine; by Leutwyler; 2 Page(s)

When Andrew J. Wiles of Princeton University announced in December 1993 that his proof of Fermat's Last Theorem was incomplete, some mathematicians predicted that it could take years to finish. Only 10 short months later Wiles seemingly proved them wrong and Fermat right. He has now simplified his proof of Pierre de Fermat's proposal--which the French mathematician scribbled in a book margin in the late 1630s--that the equation xn + yn = zn has no integer solutions if the exponent is greater than 2. Most experts now say the new argument looks solid.

Four scholars deemed Wiles's second proof incontestable last October. He then sent E-mail messages to some 20 colleagues, telling them a surprise package was on its way. Each received two manuscripts via express mail: Modular Elliptic Curves and Fermat's Last Theorem, offering the revised proof, and Ring Theoretic Properties of Certain Hecke Algebras, which validates an assumption used in the proof. Wiles devised the work in the latter text with a former student, Richard L. Taylor of the University of Cambridge. Both papers have been submitted to the Annals of Mathematics. "People are quite confident that this proof works," reports Henri R. Darmon of McGill University. "All the concepts involved have been studied at length, and what he's added is small."