Sophie Germain: Mathematical Genius Emerging from the French Revolution

The Storming of the Bastille, artist unknown (source)

The Storming of the Bastille, artist unknown (source)

Born on April 1, 1776 in Paris, Sophie Germain grew up during a turbulent time. She was 13 years old in 1789 when the Bastille fell and life on the streets became very dangerous. Her parents, Ambroise-Franҫois and Marie-Madeline Germain, were wealthy. Ambroise was a merchant (some sources say silk, some say goldsmith) and elected as a deputy to the Estates-General. Sophie and her sisters would surely have heard intelligent conversation in their home, especially politics and philosophy.

The Germains were able to keep their daughters safe, but it did require remaining indoors most of the time. To keep herself occupied, Sophie turned to her father’s library. It wasn’t long before she ran across the story of the death of Archimedes in a book called The History of Mathematics by Jean-Étienne Montucla. Legend has it that Archimedes was so engrossed in a geometry problem that he didn’t realize Roman soldiers were about to kill him. Sophie thought that geometry must be very fascinating to cause Archimedes to ignore a threat to his life, so she decided to study math. This idea, however, didn’t please her parents.

Sophie Germain (source)

Sophie Germain (source)

Studying math and science wasn’t thought appropriate for women and girls except among the aristocrats. There wasn’t a need for it and some thought it harmful to a girls mind. Her parents did everything they could think of to discourage Sophie. When they forbid her to study these subjects, she appeared to comply, but waited until they went to sleep and studied by candlelight. When they discovered what she was doing, they took away her candles, put out her fire, and took away her clothes after she went to bed, so that she would sleep. She simply kept a stash of hidden candles, wrapped herself in quilts and continued. Even when it was cold enough to freeze the ink in the inkwell, they would find her asleep over her books. Finally, they gave in and let her choose her subjects.

Sophie studied philosophy, classics and math, even learning Latin and Greek to be able to read Newton, Euler and Virgil. She worked through all the math books she found in her father’s library eventually moving on to differential calculus.

The École Polytechnique opened in 1794, when Sophie was 18. Because she was a woman, she couldn’t attend lectures, but she borrowed lecture notes from friends. She also began to submit her work to Joseph Lagrange under the name Monsieur Le Blanc. When Lagrange found out her true identity, he supported her and encouraged her to correspond with other mathematicians.

Historic building of the École Polytechnique by Juan Antonio Cordero (source)

Historic building of the École Polytechnique by Juan Antonio Cordero (source)

Probably the most famous and accomplished mathematician with whom Sophie corresponded was Karl Friedrich Gauss, considered by many to be the “greatest mathematician since antiquity.” Again, she chose to use the name M. Le Blanc and Gauss was impressed with her work in number theory. They corresponded for several years and then Sophie became concerned with Gauss’s safety. He lived in a German town which was soon to be occupied by French troops. Knowing his devotion to mathematics and thinking of Archimedes, she contacted a family friend in the French army and asked him to ensure Gauss’s safety. He did, but Gauss was confused because he didn’t know Sophie Germain by her real name.

Karl Friedrich Gauss c. 1887 by Gottlieb Biermann (source)

Karl Friedrich Gauss c. 1887 by Gottlieb Biermann (source)

The confusion was soon sorted out via correspondence, and much to Sophie’s pleasure and surprise, Gauss was delighted. “How can I describe my astonishment and admiration on seeing my esteemed correspondent M LeBlanc metamorphosed into this celebrated person. . . when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarising herself with knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius.” (emphasis mine)

Sophie contributed significantly to number theory including the foundation 20th century mathematicians would build on in attempting to solve Fermat’s Last Theorem, but she also became interested in physics. In 1808, Ernst Chaldni gave a demonstration before the Paris Academy of Sciences on vibrating surfaces. The experimental results were intriguing and caught the attention of Napoléon. He convinced the Academy to run a contest to “give the mathematical theory of the vibration of an elastic surface and to compare the theory to experimental evidence.” Sophie decided to enter.

One of Sophie’s challenges was her lack of rigor in her mathematics, probably due to her lack of formal education in the field. This was part of the problem that caused the rejection of her submission to the contest in 1811. But Sophie didn’t give up. The contest was extended and Sophie submitted another paper in 1813. This time she was awarded an honorable mention, although there were still problems with her calculations.

Finally, in 1816, Sophie submitted a paper under her own name which won the prize. She was the first woman to win a prize from the Academy, but was still unable to attend its sessions. (The only women admitted were the wives of the members!) However, now she was allowed to attend lectures at the École Polytechnique. Sophie continued her work on elasticity, publishing her results in 1821 and a refined version in 1826.

Although Sophie’s work was always affected by her lack of formal education, she was seen  as ingenious and earned the respect of many of her colleagues. Gauss was sufficiently impressed to recommend to the University of Göttingen that she be awarded an honorary degree. Sadly, she died before this could happen.

In 1829, Sophie learned that she had breast cancer. Although some of her philosophical works were published posthumously, she ironically finished her last mathematical publication to the sounds of the Second French Revolution in the summer of 1830. On June 27, 1831, Sophie Germain died at her home in Paris.

Sophie Germain's headstone, photo by Miek Messerschmidt (source)

Sophie Germain’s headstone, photo by Miek Messerschmidt (source)

Read about other Famous Women Mathematicians and Scientists.

Celebrating Women in Mathematics and Science by The National Council of Teachers of Mathematics (NCTM)
“Sophie Germain” by Mary Gray in Complexities: Women in Mathematics, ed. Bettye Anne Case and Anne M. Leggett
Women in Mathematics by Lynn Osen
Women in Science by H. J. Mozans
Women in Science: Antiquity Through the Nineteenth Century : a Biographical Dictionary with Annotated Bibliography by Marilyn Bailey Ogilvie

4 thoughts on “Sophie Germain: Mathematical Genius Emerging from the French Revolution

  1. Thank you so much for this! I did not know about her until now; however, I have an abiding interest in women who were able to stretch themselves into mathematics and science against the “rules” of the day. I suffered from math-phobia a long time ago when a bratty girl in my grade used to deliberately mark my papers wrong. Then the teacher would support her because there would be a few erasures while I had been doing the problem. Needless to say, I became very anxious and would blank out on how to do various operations. It was a nightmare (ie, quadratic equations — I still can’t do them). They are all heroines to me.

    • I’m so glad you enjoyed it Julia! So sorry you had a bad math experience though. These women are the ones I started writing about. In many ways they are heroines to me as well. Because I did study math in college, I know it’s not easy and have great admiration for these women who did so much of it on their own.

  2. Thanks for this website Susan Ozmore! I was studying her in class so I could do BIG presentation o n her and this helped me a lot. Also I do have some bad experiences in math also, when a girl named Alyssa ripped my math papers so it would count as missing….I want to be an engineer but I feel like with

    her getting in the way of many good grades that will never happen (ever since then I felt like I wasn’t able to do those problems anymore)

    • Sara. Please don’t give up. I don’t know your circumstances, but I know Alyssa can’t rip up what is in your head! One girl can’t stand in the way of a determined young woman. You want to be an engineer – Go For It! Good luck!

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