If one were to apply the laws of probability when considering the life of Sophie Germain, the odds of a French baby girl born in 1776 becoming one of history's most influential mathematicians would be, in a word, astronomical.
Born into the Parisian merchant class, Germain spent her childhood surrounded by political and social turmoil. She turned thirteen the year the Bastille was stormed, the seminal event of the French Revolution. Four years later the Reign of Terror began, with at least 18,000 people executed by guillotine. For safety's sake, her parents confined young Sophie to their home, where she found escape in her father's well-stocked library, consuming knowledge typically denied young women of her time and class.
There young Sophie happened upon an essay on the life and, more precisely, death of the ancient Greek mathematician, Archimedes. As he neared his 80th birthday, Archimedes' tranquil life in Syracuse was shattered by the invading Roman army. It is said that, upon being found and then interrogated by a Roman soldier, he was so engrossed in the study of a geometric figure that he failed to acknowledge the soldier and was speared to death.
If mathematics could be so consuming a passion that it could lead to death, Germain thought, it must be the most wonderful subject one could study. From that moment on she began to teach herself number theory and calculus, and study the works of Euler and Newton.
To put it mildly, her parents were not pleased. When their arguments and edicts failed to dissuade her, they confiscated her candles and clothes and even heat from her bedroom. But still she would not be deterred. Finally, her parents gave in to her determination, and eventually her father even funded her research, becoming the sole light of encouragement in her battle to join the closed community of mathematicians.
The Ecole Polytechnique, a premier academy for the study of math and science, opened in 1794 and would have been the natural place for her higher education...if she had been a man. But again she was not deterred. Germain contrived to receive lecture notes and problems for Monsieur Le Blanc, a former student who had left Paris without informing the academy. She then studied the lectures and submitted answers to the problems using his identity.
Sophie's plan would've succeeded, if Monsieur Le Blanc had been half as gifted as she. But soon it became clear to her teacher, renowned mathematician Joseph-Louis Lagrange, that a previously abysmal student had remarkably transformed into a very promising and creative one. Lagrange requested a meeting and Germain's identity...and gender...were revealed, much to Lagrange's astonishment and pleasure. Sophie had finally found a mentor and friend.
As Germain continued her work in number theory, she encountered Fermat's Last Theorem, the famous mathematical challenge posed by the 17th century French mathematician Pierre de Fermat. After several years, believing she had made an important breakthrough, she wrote to Carl Friedrich Gauss, the greatest number theorist in the world and perhaps the most brilliant mathematician in history. But, to ensure she would be taken seriously, she signed the letter "Monsieur Le Blanc."
Once again the story of Archimedes changed her life. Monsieur Le Blanc would surely have been credited with Germain's work if Napolean had not invaded Prussia in 1806. Remembering Archimedes fate and fearing Gauss might also die by a soldier's hand, Germain wrote General Joseph-Marie Pernety to ask that Gauss' safety be ensured. Pernety later explained to Gauss that he owed his life to Mademoiselle Germain and in their next set of letters, Sophie revealed her true identity. Gauss was delighted to find his correspondent to be a woman of "the noblest courage, quite extraordinary talents and superior genius."
Germain later abandoned pure mathematics for a successful career in physics, publishing a paper that laid the foundation for the modern theory of elasticity in metals, making the building of the Eiffel Tower possible. But it would be Germain's work on Fermat's Last Theorem, her calculations containing what eventually would be called "Germain Primes," that would become her greatest contribution to mathematics.