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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 disfavored [[Axiom of Choice]].<ref>http://jimcaprioli.blogspot.com/2005/04/fermats-last-theorem.html</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>http://wiles.coolissues.com/wiles.htm</ref> Further criticism came from [[Marilyn vos Savant]], the woman with the highest [[IQ]], 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 [[Axiom of Choice]].<ref>http://jimcaprioli.blogspot.com/2005/04/fermats-last-theorem.html</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>http://wiles.coolissues.com/wiles.htm</ref> Further criticism came from [[Marilyn vos Savant]], the woman with the highest [[IQ]], 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.

== References ==

== References ==