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"Beyond the Last Theorem," by Dorian Goldfeld. The Sciences, March/April 1996, pages 34-40.
Fermat's Last Theorem is an incidental consequence of the work of Andrew Wiles and Richard Taylor, and the author uses the enormous interest in FLT as a starting point to explain some profound mathematical ideas. First he discusses Diophantine equations and the Shimura-Taniyama-Weil Conjecture. By measured steps the reader arrives at a workable understanding of what it means for an elliptic curve to be modular and why the STW Conjecture is so fundamentally important. Finally, Goldfeld offers a glimpse of the treasures in store should the ABC conjecture be solved and describes some recent progress in this direction.
-Allyn Jackson
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