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In the summer of 1986, Ken Ribet proved that Fermat's Last Theorem is a special case of the [[Taniyama–Shimura Conjecture]].

In the summer of 1986, Ken Ribet proved that Fermat's Last Theorem is a special case of the [[Taniyama–Shimura Conjecture]].

In a series of lectures in 1993, mathematician [[Andrew Wiles]] announced a proof using techniques in algebraic geometry, relying on the nonconstructive [[Axiom of Choice]].<ref name="Occam">http://www.occampress.com/fermat.pdf Page 5</ref>  A flaw was found before publication, and Wiles spent a year on fixing the flaw. Then, in September 1994, he and Richard Taylor announced a new version of the proof.  However, criticism does continue on the internet.<ref name="Occam" /> Further criticism came from [[Marilyn vos Savant]], known for her very high [[IQ]] and commentary on [[mathematics]], in her column and book.<ref>Ask Marilyn ® by Marilyn vos Savant, Parade Magazine. November 21, 1993</ref><ref>''The World's Most Famous Math Problem: The Proof of Fermat's Last Theorem and Other Mathematical Mysteries'', Marilyn vos Savant. St. Martin's Griffin, 1993</ref> She questioned the use of [[Non-Euclidean geometry]] and the Axiom of Choice, among other points.

In a series of lectures in 1993, mathematician [[Andrew Wiles]] announced a proof using techniques in algebraic geometry, relying on the nonconstructive [[Axiom of Choice]].<ref name="Occam">http://www.occampress.com/fermat.pdf Page 5</ref>  A flaw was found before publication, and Wiles spent a year on fixing the flaw. Then, in September 1994, he and Richard Taylor announced a new version of the proof.  However, criticism does continue on the internet.<ref name="Occam" /> Further criticism came from [[Marilyn vos Savant]], known for her very high [[IQ]] and commentary on [[mathematics]], in her column and book.<ref>Ask Marilyn ® by Marilyn vos Savant, Parade Magazine. November 21, 1993</ref><ref>''The World's Most Famous Math Problem: The Proof of Fermat's Last Theorem and Other Mathematical Mysteries'', Marilyn vos Savant. St. Martin's Griffin, 1993</ref> She questioned the use of [[Non-Euclidean geometry]] and the Axiom of Choice, among other points. In 1996 she retracted her argument in a 1995 addendum to the book.

== References ==

== References ==