Wiles' path to proving Fermat's Last Theorem, by way of proving the modularity theorem for the special case of semistable elliptic curves, established powerful modularity lifting techniques and opened up entire new approaches to numerous other problems. John Coates described the proof as one of the highest achievements of number theory, and John Conway called it the proof of the century. Together, the two papers which contain the proof are 129 pages long, and consumed over seven years of Wiles's research time.

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