Her knowledge was already quite extensive in 1794 when the Ecole Polytechnique was founded; she was then able to obtain the notes of Lagrange's course and studied them with profit. It was from their study that her first personal observations took form. She wished to submit them to her master Lagrange and decided to write him; but, as she confessed much later, fearing the "ridicule attached to the name of femme savante," she signed her letter "Le Blanc, pupil at the Ecole Polytechnique." But Lagrange wanted to meet the Polytechnic student with such interesting observations. Astonished and charmed, Lagrange became a valued adviser for Sophie Germain and introduced her to all the French scientists of the time.
She was quickly appreciated in scientific circles, as much for her learning as for the charm of her conversation. Nevertheless, later on, when she wanted to write Gauss, after the publication of his Disquisitiones arithmeticae in 1801, to discuss with him results she had obtained in the theory of numbers, she once more concealed herself under the pseudonym of Le Blanc, Polytechnic student. But Gauss, too, learned the true identity of Le Blanc. It was during the time of the German campaign and French - troops were entering Brunswick, Gauss's city; Sophie Germain, haunted by the memory of Archimedes' death, began to fear for the scholar and wrote to a friend of her father, General Pernety, who was at the very moment in Brunswick, to commend her master to him and to entreat him to watch out for his safety. The latter hastened to reassure Sophie Germain and ... to show her letter to the party concerned, who naturally continued with the young feminine mathematician the epistolary contact begun with the self-styled male Polytechnic student.
Sophie Germain died at the age of 55, after two years of terrible suffering which she bore with an admirable courage and stoicism. Her moral worth was a match for her beautiful intelligence; she loved virtue, it was said, like a geometric truth. She had the great honour in 1816 of receiving from the Paris Academy of Sciences the Grand Prize of the Mathematical Sciences, for a paper on the vibrations of thin elastic plates, a question put up for competition since 1811. It was in the year of her death that her important work on the curvature of surfaces appeared, in which she introduced for the first time the notion - classic today - of mean curvature.
Her arithmetic work is no less important. Attacking the proof of Fermat's last theorem with the help of Legendre's formulas, she supplied an important theorem and its application to the proof of Fermat's theorem up to the hundredth degree.
Finally, aside from her mathematical work, she left a certain number of articles on the history and philosophy of the sciences, articles of a genuine value, which Auguste Comte quoted with praise in his course on positive philosophy.
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