Abstract: A few years ago, I gave a colloquium motivating the Langlands program through examples, mostly taken in chronological order, and used this glossary of examples to formulate the framework of this wide reaching project. Here I will, instead, attempt to start the story closer to the end, with Wiles's proof of Fermat's Last Theorem, and use this as a case study for the power of the Langlands philosophy. We will certainly re-introduce some of the examples from the previous treatment, so there will be some overlap with our earlier talk. I hope, however, those who saw that one will consider this a sequel, while those who did not can find it a suitable introduction.

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