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modularity-theorem
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An elliptic curve and a modular form are very different objects, and the theorem says they carry the same data. Wiles and Taylor proved the semistable case in 1995, which was enough for Fermat. The full statement followed six years later. It is the template for every later modularity result.
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 1950s–60s, Taniyama, Shimura and Weil. Closed 2001, Breuil, Conrad, Diamond and Taylor, completing Wiles.