Mathematical Digest
Short Summaries of Articles about Mathematics in the Popular Press"Fermat's Last Theorem Extended," by Dana Mackenzie. Science, 9 July1999, page 178. Five years ago, when Wiles' proof of Fermat's Last Theorem rocked the math world,mathematicians believed that the TaniyamaShimura conjecture would be leveledin the aftershock. Now Brian Conrad of Harvard University and a group ofcollaborators believe to have a proof this prominent unsolved problem. Though the conjecture is only 40 years old ("only" as compared with Fermat'sLast Theorem), its solution applies to a broad class of problems. Terselystated, the conjecture says that all elliptic curves are modular andultimately gives a geometrical strategy to solve certain algebraic problems.The proof still needs to be peerreviewed for the conjecture to be put entirelyto rest.  Benjamin Stein
