What Does it Take to Prove Fermat's Last Theorem? Grothendieck and the Logic of Number Theory | Bulletin of Symbolic Logic | Cambridge CoreThis paper explores the set theoretic assumptions used in the current published proof of Fermat's Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.
If it is necessary to use assumptions, or perhaps Unproven Axioms, why then we can not take the Fermat's Theorem as fact? Like was taken as fact the Darwin's Evolution? Just call Fermat's Theorem an Axiom. Like the 5-th postulate of Euclid.