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For 358 years it produced whole fields of mathematics as by-products, from Kummer's ideal numbers onward. The end came indirectly. Frey, Serre and Ribet showed that a counterexample would give an elliptic curve that could not be modular. Wiles then proved enough of the modularity conjecture to rule that curve out. The theorem itself was a corollary of a much larger structure.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 1637, Pierre de Fermat, in a margin. Closed 1995, Andrew Wiles, with Richard Taylor.
Related problems
- Progress here drew on Modularity theorem, whose resolution the original curation lists as unlocking it; the argument for the link has not been written yet.