Sophie Germain offered much to the mathematical world in the areas of number theory and elasticity theory. That same world would offer her, a middle class woman in the time of the French revolution, very little in return. The Bastille fell when Sophie was only 13. She was from a middle class family of merchants that protected her through the revolution. As a result, she spent many hours in her father's library where she learned of the story of Archimedes. She was fascinated with his passion for geometry and immediately scoured the library for every book on the subject.
From the onset her parents opposed her interest. They deemed her enthusiasm so inappropriate for a young woman that they denied her heat and light to prevent her from studying. They even confiscated her clothing at night, but she wrapped herself in blankets and used a hidden supply of candles to read from. Such was her passion that her parents finally conceded. She continued, tutorless. In 1794 Ecole Polytechnique opened, and as no women were allowed, she acquired the notes from the classes to learn from. At the end of one term she offered some observations that she made to Lagrange under the name of M. LeBlanc. He was impressed, found her, and praised her talents.
In 1801 Carl Freidrich Gauss presented a complicated treatise on number theory, Disquisitiones Arithmeticae. Sophie was inspired by this work and began a correspondence with Gauss in 1804, again under the name M. LeBlanc. Her identity was revealed when she sent a message through an army commander friend of hers to Gauss. Napolean had conquered most of Prussia and she was concerned for his safety.
In 1808, she shared with Gauss one of her greatest results in number theory. If x, y, z, are integers such that x5 + y5 = z5 then either x, y, or z are divisible by 5. This was a good stepping stone to the proof of Fermat's last theorem for n = 5.
She then began a shift from number theory to the experiments of Ernst Chladni, a German physicist investigating the vibration of elastic plates. A search was on to find the equations governing the actions in the experiments. Sophie took up this challenge. Her works earned her a First Class Honourable mention by the French Academy of Sciences in 1813. This prize elevated her mathematical status considerably. She published Memoir on the Vibrations of Elastic Plates which became well known. She also published works on the nature, bounds and extent of elastic surfaces, and the principles of analysis used in the solution of the problem of elastic surfaces. She was the first woman, not a wife of a member, to attend sessions of the Academy of Sciences.
Gauss was so impressed by her work, he recommended to the faculty of the University of Gottingen that they grant her an Honourary Doctoral Degree in 1830. Though she was deserving, she never received one. She died in 1831 after a two-year battle with breast cancer.
Sophie lacked many of the advantages that other women in math have had. She was not born into a mathematical family, nor one in aristocratic intellectual circles. She yearned for professional training, but was continually denied. Yet, she had determination and an undistracted passion for mathematics. She continually strove for excellence amidst prejudice. She offers an excellent model for us to follow.
Marni Mishna
mjmishna@undergrad.math.uwaterloo.ca
Copyright © mathNEWS 1997.