"The mathematician who developed the approach was respected by luminaries like Carl Friedrich Gauss, Adrien-Marie Legendre, and Joseph-Louis Lagrange, but was marginal in the mathematical community, with no formal training or university position. That's because the mathematician was a woman, indeed, the first woman to do significant research in mathematics."

"Sophie Germain was one of the great mathematicians of the early 19th century. Number theorists laud her for 'Sophie Germain's theorem,' an insight into Fermat's famous equation xⁿ + yⁿ = zⁿ aimed at establishing its lack of solutions (in positive integers) for certain exponents. Oddly, Germain's fame for her theorem stems not from anything she herself published but from a footnote in a treatise by her fellow Parisian Adrien-Marie Legendre, in which he proved Fermat's Last Theorem for the exponent n = 5. Now, two mathematicians have found that Germain did far more work in number theory than she has ever been given credit for.
Poring over long-neglected manuscripts and correspondence, David Pengelley of New Mexico State University in Las Cruces and Reinhard Laubenbacher of Virginia Polytechnic Institute and State University in Blacksburg have discovered that Germain had an ambitious strategy and many results aimed at proving not just special cases of Fermat's Last Theorem but the whole enchilada. 'What we thought we knew [of her work in number theory] is actually only the tip of the iceberg,' Pengelley said at a session on the history of mathematics. "

"But how to describe to you my admiration and astonishment at seeing my esteemed correspondent Monsieur Le Blanc metamorphose himself into this illustrious personage who gives such a brilliant example of what I would find it difficult to believe. A taste for the abstract sciences in general and above all the mysteries of numbers is excessively rare: one is not astonished at it: the enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. Indeed nothing could prove to me in so flattering and less equivocal manner that the attractions of this science, which has enriched my life with so many joys, are not chimerical, [than] the predilection with which you have honored it."

"Germain's contribution would have been forever wrongly attributed to the mysterious Monsieur Le Blanc were it not for the Emperor Napoleon. In 1806, Napoleon was invading Prussia and the French army was storming through one German city after another. Germain feared that the fate that befell Archimedes might also take the life of her other great hero Gauss, so she sent a message to her friend, General Joseph-Marie Pernety, asking that he guarantee Gauss's safety. The general was not a scientist, but even he was aware of the world's greatest mathematician, and, as requested, he took special care of Gauss, explaining to him that he owed his life to Mademoiselle Germain. Gauss was grateful but surprised, for he had never heard of Sophie Germain. "

"Sophie Germain was the first woman known for important original research in mathematics. While Germain is perhaps best known for her work in mathematical physics, her number theoretic research on Fermat's Last Theorem has been considered by many to be her best mathematics. We will make a substantial reevaluation of her work on the Fermat problem, based on translation and detailed mathematical interpretation of numerous documents in her own hand, heretofore perhaps never seriously analyzed, and will argue that her accomplishments are much broader, deeper, and more significant than has ever been realized.
On the twelfth of May, 1819, Sophie Germain penned a letter from her Parisian home to Carl Friedrich Gauss in Göttingen..."

"We now know, of course, that Fermat's Last Theorem is true for every value of n > 2 thanks to the crowning work of Andrew Wiles, first described in 1993 and then published in 1995. But as L.E. Dickson wrote in 1917,

This challenge problem has received attention of many mathematicians of the highest ability, including Euler, Legendre, Gauss, Abel, Sophie Germain, Dirichlet, Kummer and Cauchy."

"As a girl Germain read widely in her father’s library and then later, using the pseudonym of M. Le Blanc, managed to obtain lecture notes for courses from the newly organized École Polytechnique in Paris. It was through the École Polytechnique that she met the mathematician Joseph-Louis Lagrange, who remained a strong source of support and encouragement to her for several years..."

"At the age of thirteen, Sophie read an account of the death of Archimedes at the hands of a Roman soldier. She was moved by this story and decided that she too must become a mathematician..."

"On the establishment in 1795 of the Ecole Polytechnique, which women could not attend, Germain befriended students and obtained their lecture notes. She submitted a memoir to the mathematician J. L. Lagrange under a male student's name. Lagrange saw talent in the work, sought out the author, and was bowled over to discover it had been written by a woman. She continued to study, corresponding with leading mathematicians of the day...."