No one could have guessed that Marie-Sophie Germain, born in France in 1776 to a wealthy middle class family, would become a world-famous mathematician. However, her work on the subjects of acoustics, elasticity, and the theory of numbers are considered to be important to the history of mathematics even though she suffered from her lack of a formal education her entire career. She struggled from a lack of resources and access due to her gender that kept her from making the mathematical discoveries she otherwise might have.
Sophie's interest in mathematics began when she was thirteen. When the French Revolution started, she turned to her father's library as she had to stay inside. She was fascinated by Archimedes who inspired her to study mathematics. Her parents disapproved and tried to dissuade her, but eventually relented in the face of her determination.
When Sophie was eighteen years old, in 1794, the École Polytéchnique was founded as a school for science and mathematics. Using the name of M. LeBlanc, she obtained notes from lectures since she couldn't attend them herself. She submitted a paper at the end of term about number theory that impressed Professor Joseph-Louis Lagrange. Even after finding out she was a woman, he agreed to mentor her. He introduced her to other scientists and mathematicians including the German Carl Friedrich Gauss who didn't learn that she was female until several years into their correspondence.
In 1809, the French Academy of Sciences held a contest to explain the law about the vibration of elastic surfaces. Sophie's entry was the only essay the first year, but her lack of formal education was too apparent and she was not awarded the prize. Lagrange aided her and she entered again two years later, earning an honorable mention. She entered one last time after three years and finally won with an essay called "Memoir on the Vibrations of Elastic Plates." The committee noted that there were errors in the essay, but those would not be corrected for decades.
In 1816, Sophie befriended Joseph Fourier who managed to get her tickets to attend the Academy of Science's session, a privilege only normally allowed to the wives of members. She was also invited to attend the Institut de France's session, a great honor for a woman. However, her career was cut short at the age of fifty-five when she died of breast cancer on June 27, 1831. She was buried in Père Lachaise Cemetery in Paris.
While she didn't have the opportunities within her lifetime that would have made her name well-remembered after her death, Sophie did receive some recognition. Sophie's nephew published some of her works after her death. She has a prize named after her at the Academy of Sciences, in addition to a street and a girl's school named in her honor. Unfortunately, her gender held her back from achieving what she might have but she still managed to forge a way to become a mathematician despite the odds being against her.
A big thank you to my sister Hannah for introducing me to Sophie Germain!
Source 1, Source 2, Source 3, Source 4