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Line 35: − The highly publicized proof of [[Fermat's Last Theorem]] relies on the Axiom of Choice, which was one of the points of criticism by [[Marilyn vos Savant]] 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> − − Interestingly, it has been proven that any theorem of [[number theory]] which uses the Axiom of Choice may be proven in a different way unaided by the axiom.<ref>http://www.occampress.com/fermat.pdf Page 5</ref>
to the best of my knowledge this is simply not true. the citation of vos savant's book is telling, since she later more or less retracted the entire thing because it was so full of nonsense
The Axiom of Choice can also be used to prove the apparently absurd existence of subsets of the real line which do not have a well-defined Lebesgue measure.<ref>However, it is also possible to construct such a subset without using the Axiom of Choice. See [http://matwbn.icm.edu.pl/ksiazki/fm/fm138/fm13812.pdf "The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set"]</ref>
The Axiom of Choice can also be used to prove the apparently absurd existence of subsets of the real line which do not have a well-defined Lebesgue measure.<ref>However, it is also possible to construct such a subset without using the Axiom of Choice. See [http://matwbn.icm.edu.pl/ksiazki/fm/fm138/fm13812.pdf "The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set"]</ref>
== Controversy ==
== Controversy ==