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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 Taniyama-Shimura 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 peer-reviewed for the conjecture to be put entirelyto rest.