to all of pure mathematics, could hold such fascination for Archimedes, it was a subject worthy of study. So she pored over every book on mathematics in her father's library, even teaching herself Latin and Greek, so she could read works like those of Sir Isaac Newton and Leonhard Euler. She also enjoyed by Étienne Bézout and by Jacques Antoine-Joseph Cousin. Later, Cousin visited Germain at home, encouraging her in her studies. Germain's parents did not at all approve of her sudden fascination with mathematics, which was then thought inappropriate for a woman. When night came, they would deny her warm clothes and a fire for her bedroom to try to keep her from studying, but after they left, she would take out candles, wrap herself in quilts and do mathematics. After some time, her mother even secretly supported her. École Polytechnique In 1794, when Germain was 18, the École Polytechnique opened. As a woman, Germain was barred from attending, but the new system of education made the "lecture notes available to all who asked". The new method also required the students to "submit written observations". Germain obtained the lecture notes and began sending her work to Joseph Louis Lagrange, a faculty member. She used the name of a former student Monsieur Antoine-Auguste Le Blanc, "fearing", as she later explained to Gauss, "the ridicule attached to a female scientist". When Lagrange saw the intelligence of M. Le Blanc, he requested a meeting, and thus Sophie was forced to disclose her true identity. Fortunately, Lagrange did not mind that Germain was a woman, and he became her mentor. Early work in number theory Correspondence with Legendre Germain first became interested in number theory in 1798 when Adrien-Marie Legendre published . After studying the work, she opened correspondence with him on number theory, and later, elasticity. Legendre included some of Germain's work in the to his second edition of the , where he calls it ("very ingenious"). See also Her work on Fermat's Last Theorem below. Correspondence with Gauss Germain's interest in number theory was renewed when she read Carl Friedrich Gauss' monumental work . After three years of working through the exercises and trying her own proofs for some of the theorems, she wrote, again under the pseudonym of M. Le Blanc, to the author himself, who was one year younger than she. The first letter, dated 21 November 1804, discussed