Wiles's proof of Fermat's Last Theorem is a proof by the British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves, which together with Ribet's theorem supplies a proof of Fermat's Last Theorem itself. Both Fermat's Last Theorem and the modularity theorem had been considered beyond proof with existing techniques by almost every mathematician of the time. Wiles first announced his proof on 23 June 1993 in a Cambridge lecture titled Modular Forms, Elliptic Curves and Galois Representations, but by September 1993 the proof was found to contain an error.
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StatementWiles proved the modularity theorem for semistable elliptic curves, from which Fermat's Last Theorem follows by proof by contradiction. 1 Classification
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Source Wiles's proof of Fermat's Last Theorem - Wikipedia
Source Wiles's proof of Fermat's Last Theorem - Wikipedia
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Source Wiles's proof of Fermat's Last Theorem - Wikipedia
Sources
1. Wiles's proof of Fermat's Last Theorem - Wikipedia
Summary of Wiles's proof section
Wiles proved the modularity theorem for semistable elliptic curves, from which Fermat's last theorem follows using proof by contradiction.
Lead section
One year later on 19 September 1994, in what he would call "the most important moment of [his] working life", Wiles stumbled upon a revelation that allowed him to correct the proof to the satisfaction of the mathematical community.
Proved By: Andrew Wiles, Lead
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves.
In Branch: Algebraic Geometry, Lead paragraph
The proof uses many techniques from algebraic geometry and number theory and has many ramifications in these branches of mathematics.
In Branch: Number Theory, Lead paragraph
The proof uses many techniques from algebraic geometry and number theory and has many ramifications in these branches of mathematics.
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