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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Wiles' proof of Fermat's Last Theorem is a proof of the modularity theorem for semistable elliptic curves, which, together with Ribet's theorem, provides a proof for Fermat's Last Theorem. While first announced in June 1993 in a version that was soon recognized as having a serious gap, the widely accepted version of the proof was released by Andrew Wiles in September 1994, and published in 1995. The proof uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th century techniques not available to Fermat.