Frenkel does a nice job explaining the Langlands program in general. But Buzzard's complaint about Langlands, I believe, refers specifically to the proof of a version of the Geometric Langlands Conjecture by Gaitsgory et al. The proo f is of order thousand pages of mathematical text and builds off of thousands of pages of higher-categorical algebraic geometry by Lurie & others. It's a ripe target for formalization because it's terrifically complicated, not well understood or thoroughly digested yet, and relatively important. A formal proof would be reassuring to mathematicians, whereas Fermat's Last Theorem is relatively unique in that so many mathematicians have examined the proof that it's not very likely to be wrong.