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A study of Sophie Germain's extensive manuscripts on Fermat's Last Theoremcalls for a reassessment of her work in number theory. There is much in thesemanuscripts beyond the single theorem for Case 1 for which she is known from apublished footnote by Legendre. Germain had a fully-fledged, highly developed,sophisticated plan of attack on Fermat's Last Theorem. The supportingalgorithms she invented for this plan are based on ideas and results discoveredindependently only much later by others, and her methods are quite differentfrom any of Legendre's. In addition to her program for proving Fermat's LastTheorem in its entirety, Germain also made major efforts at proofs forparticular families of exponents. The isolation Germain worked in, due insubstantial part to her difficult position as a woman, was perhaps sufficientthat much of this extensive and impressive work may never have been studied andunderstood by anyone.

"Voici ce que j'ai trouve": Sophie Germain's grand plan to prove Fermat's Last Theorem