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"Beyond the Last Theorem," by Dorian Goldfeld. The Sciences, March/April1996, pages 34-40.
Fermat's Last Theorem is an incidental consequence of the work of Andrew Wilesand Richard Taylor, and the author uses the enormous interest in FLT as astarting point to explain some profound mathematical ideas. First he discussesDiophantine equations and the Shimura-Taniyama-Weil Conjecture. By measuredsteps the reader arrives at a workable understanding of what it means for anelliptic curve to be modular and why the STW Conjecture is so fundamentallyimportant. Finally, Goldfeld offers a glimpse of the treasures in store shouldthe ABC conjecture be solved and describes some recent progress in thisdirection.