Sophie Germain ’ s grand plan to prove Fermat ’ s Last Theorem

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 theoretical concepts, ideas and “Here is what I have found:” We owe heartfelt thanks to many people who have helped us tremendously with this project over a long fifteen years: Hélène Barcelo, Louis Bucciarelli, Keith Dennis, Mai Gehrke, Tiziana Giorgi, Catherine Goldstein, Maria Christina Mariani, Pat Penfield, Donato Pineider, and Ed Sandifer, along with Marta Gori of the Biblioteca Moreniana, as well as the Bibliothèque Nationale, New York Public Library, Niedersächsische Staatsund Universitätsbibliothek Göttingen, and the Interlibrary Loan staff of New Mexico State University. Dedicated to the memory of my parents, Daphne and Ted Pengelley, for inspiring my interest in history, and to Pat Penfield, for her talented, dedicated, and invaluable editorial help, love and enthusiasm, and support for this project.