  A study of Sophie Germain's extensive manuscripts on Fermat's Last Theorem
calls for a reassessment of her work in number theory. There is much in these
manuscripts beyond the single theorem for Case 1 for which she is known from a
published footnote by Legendre. Germain had a fully-fledged, highly developed,
sophisticated plan of attack on Fermat's Last Theorem. The supporting
algorithms she invented for this plan are based on ideas and results discovered
independently only much later by others, and her methods are quite different
from any of Legendre's. In addition to her program for proving Fermat's Last
Theorem in its entirety, Germain also made major efforts at proofs for
particular families of exponents. The isolation Germain worked in, due in
substantial part to her difficult position as a woman, was perhaps sufficient
that much of this extensive and impressive work may never have been studied and
understood by anyone.
