**Question Corner and Discussion Area**

Has a complete proof of fermat's last theorem been published? If so when was it published and has it stood up to scrutiny?Yes, a complete proof of Fermat's Last Theorem has been published. The original proof announced by Andrew Wiles had a gap, but that gap was closed in joint work by Wiles and Richard Taylor.

The complete proof consists of two papers:

*Modular elliptic curves and Fermat's Last Theorem*, by Andrew Wiles.*Ring theoretic properties of certain Hecke algebras*, by Richard Taylor and Andrew Wiles.

Both papers were published in the May 1995 issue of the journal
*Annals of Mathematics*. The second paper (much shorter than the
first) contains the corrected
proof of the step in the argument where Wiles's original work
was flawed. The first paper contains the rest of the argument. Together
they constitute a complete proof of Fermat's Last Theorem, which
has stood up to the scrutiny of every expert in the field. In fact,
other people upon reading the proofs have come up with generalizations and
simplifications of much of it.

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