Controversy Regarding Fermat's Last Theorem
A few months after the announcement by Andrew Wiles that he had proved Fermat's Last Theorem, vos Savant published her book The World's Most Famous Math Problem in October 1993. The book surveys the history of Fermat's last theorem as well as other mathematical mysteries. Controversy came from the book's criticism of Wiles' proof; vos Savant was accused of misunderstanding mathematical induction, proof by contradiction, and imaginary numbers.
Her assertion that Wiles' proof should be rejected for its use of non-Euclidean geometry was especially contested. Specifically, she argued that because "the chain of proof is based in hyperbolic (Lobachevskian) geometry", and because squaring the circle is considered a "famous impossibility" despite being possible in hyperbolic geometry, then "if we reject a hyperbolic method of squaring the circle, we should also reject a hyperbolic proof of Fermat's last theorem."
Mathematicians pointed to differences between the two cases, distinguishing the use of hyperbolic geometry as a tool for proving Fermat's last theorem and from its use as a setting for squaring the circle: squaring the circle in hyperbolic geometry is a different problem from that of squaring it in Euclidean geometry. She was criticized for rejecting hyperbolic geometry as a satisfactory basis for Wiles' proof, with critics pointing out that axiomatic set theory (rather than Euclidean geometry) is now the accepted foundation of mathematical proofs and that set theory is sufficiently robust to encompass both Euclidean and non-Euclidean geometry as well as geometry and adding numbers.
In a July 1995 addendum to the book, vos Savant retracts the argument, writing that she had viewed the theorem as "an intellectual challenge – 'to find a proof with Fermat's tools.'" Fermat claimed to have a proof he couldn't fit in the margins where he wrote his theorem. If he really had a proof, it would presumably be Euclidean. Therefore, Wiles may have proven the theorem but Fermat's proof remains undiscovered, if it ever really existed. She is now willing to agree that there are no restrictions on what tools may be used.
Read more about this topic: Marilyn Vos Savant
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