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"Fermat's Last Theorem Extended," by Dana Mackenzie. Science, 9 July 1999, 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 leveled in the aftershock. Now Brian Conrad of Harvard University and a group of collaborators believe to have a proof this prominent unsolved problem.
Though the conjecture is only 40 years old ("only" as compared with Fermat's Last Theorem), its solution applies to a broad class of problems. Tersely stated, the conjecture says that all elliptic curves are modular and ultimately gives a geometrical strategy to solve certain algebraic problems. The proof still needs to be peer-reviewed for the conjecture to be put entirely to rest.
--- Benjamin Stein
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