Andrew Wiles’ proof of Fermat’s Last Theorem relied on some very heavy machinery in algebraic geometry. What I had not realized (this is not at all my field) was that this machinery (built by Grothendieck in the middle of the 20th century) involved an additional axiom beyond those of ordinary set theory. Thus Wiles’ proof FLT relied on an axiom well beyond those needed to state the theorem. This is disconcerting.
Colin McLarty of Case Western Reserve University has just shown that Grothendieck’s work (or maybe just that part needed for FLT, I’m not sure) could in fact be built on a more familiar, standard set of axioms, meaning that the proof of FLT is a little more concerting (which should be the opposite of disconcerting, n’est-ce pas?).