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Fermat's Last Theorem's First Cousin

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Science  04 Feb 2000:
Vol. 287, Issue 5454, pp. 792-793
DOI: 10.1126/science.287.5454.792

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For 30 years, the Langlands conjecture, which posits an equivalence between two different branches of mathematics, has been a driving force in number theory. In 1998, the conjecture was proved for one group of mathematical structures, called local fields; now it has been proven for function fields, leaving only the central problem of number fields unresolved. The conjecture's author says that it is only a matter of time now before that one is solved, too.