As we all know, Fermat has stated his theorem at the corner of a book. That is far from the standard way of representing a theorem. He said he had a proof which we never saw. So before it was proven true by Andrew Wiles was it assumed that Fermat actually had a proof and thus its a THEOREM or it was called a CONJECTURE till it was proved by Andrew Wiles.
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2$\begingroup$ I highly doubt that people thought Fermi had a proof of the theorem... $\endgroup$– Najib IdrissiCommented May 30, 2016 at 11:09
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Mathematicians speculate that Fermat may have made a subtle error in a proposed "proof" such as for example the error of assuming unique factorisation of algebraic integers which was the basis for a 19th century incorrect proof apparently by Lamé.
It is considered unlikely that Fermat had a correct proof. The odds are against it, given the number of people who have worked on the problem and continue to do so :-)
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2$\begingroup$ Another argument against the likelihood of Fermat having a proof: he never mentioned it in public. $\endgroup$ Commented May 31, 2016 at 22:04