Sophie Germain: Blazing the Trail for Female Mathematicians

Updated: Nov 25, 2019

This week, I thought it'd be fun to feature a female mathematician. Sophie Germain (1776-1831) was one of the most prolific female mathematicians in history for her ability to achieve high level mathematics and break through barriers. The story I'm about to tell you is constructed from several different sources, and some of it may be legend, but all of it reveals just how resilient Sophie was in pursuing her dreams.


Sophie Germain was born in France, and she was only 13 when the French Revolution broke out. All around her, people were screaming for greater liberty and equality, and that likely influenced Sophie to fight even in a field where she was vastly underrepresented.


But the French Revolution had an even more direct effect on her mathematical skills. Because of the revolts in the street, Sophie was forced to stay in her house to avoid the danger, and she ended up spending her time in her father's library. Her father later became a director of the Bank of France and had many scholarly books on his shelves, including one that included some of the historical legends of the great mathematicians.


Archimedes was killed in the Second Punic War, one of the great wars the Romans fought against the Greeks, by a Roman soldier. Legend has it that he was so captivated by a complex mathematical problem he had drawn in the sand that he did not even fight back as he was killed. His last words were, "Do not disturb my circles," and he was buried with a geometric figure on his tombstone:


Left: Archimedes' tomb as it looks today, Right: A computer rendering of the image that was carved on his grave (a sphere inscribed in a cylinder)


Young Sophie Germain was said to have read this legend and become enraptured by the idea that math was so interesting that somebody could choose it over death. Throughout her teenage years, she explored the subject more and more, despite the fact that her parents thought it was inappropriate for her to study math.


Sophie's parents went as far as to deprive their daughter of heat and light to make her stay in bed at night, but she would wrap herself in quilts and use candles to continue her study of math, including differential calculus.


When the Ecole Polytechnique, a prestigious university, was founded in Paris, though Sophie wasn't allowed to enroll, she managed to find some of the course notes and learn from some very prominent mathematicians, including Joseph-Louis Lagrange:

She disguised her work under the name Monsieur LeBlanc, who was actually a former student of Lagrange, and submitted a paper on analysis to Lagrange. When Lagrange found out the truth, he was outraged but he eventually arranged to mentor Sophie, despite the fact she was a woman, because he was just so impressed by her work.


In a few years' time, Sophie reached out one of the most famous mathematicians of all time, Carl Friedrich Gauss, as well as the number theorist Adrien-Marie Legendre about some recent work she had done in number theory, one of the most sought-after fields in math.


Perhaps you've heard of Fermat's Last Theorem, the most famous problem of the 20th century:

Show that x^n + y^n = z^n has no solutions if all x, y, z and n are integers and n > 2.

What Sophie had done was show that if n = 5, one of x,y and z must be divisible by 5, which was a major step towards the proof of Fermat's Last Theorem. This age old problem was finally solved in 1990 by the English mathematician, Andrew Wiles.

Let me know in the comments if you'd like to see a post on Fermat's Last Theorem! I'd be able to give you some insight into the history and proof of a simple-sounding but absolutely miraculous problem that ties very modern fields together!


Anyway, back to Sophie. Through this work, Sophie put her name down in history as an extremely accomplished mathematician. The problems she had tackled laid the groundwork for the future of number theory.


Sophie also explored physics. The French Academy of Sciences announced a contest to explain the mathematics behind the vibration of elastic surfaces. Though there were many difficulties and she stumbled along the way, Sophie was eventually awarded an Honorable Mention in the contest, and she was inspired to publish several papers on elasticity, completely transforming the field.


Throughout her life, Sophie was able to change the mindsets of many established mathematicians to accept women into their ranks. She was invited to attend sessions at the Institute of France, an award that was proclaimed to be "the highest honor that this famous body ever conferred on a woman," and she also became the first woman to attend the French Academy of Science's sessions. She even received an honorary degree from the University of Gottingen (where Gauss worked) despite not having any formal education.


As a result, Sophie was absolutely essential to math today. Her research on number theory and elasticity has also attached her name to several mathematical objects:

A Germain prime is a prime p where both p and 2p+1 are prime, such as 2,3,5,11,23 and 29.

Sophie Germain's identity is a factorization of the expression a^4 + 4b^4:

Sophie Germain died at the age of 55 of breast cancer, but her legacy holds even today. She was a pioneer for women, changing the shape not only of her field but of her culture, and today, she was one of the most well-known female mathematicians in the world. She even has a street named after her: Rue Sophie Germain. The discrimination of the 1800s unfortunately made a stamp on her history: She was never allowed to become a professor, but we can do what we can to defend her legacy! If you ever visit Paris, make a pilgrimage to Rue Sophie Germain, and simply supporting the community of female mathematicians and/or aspiring to be one is a step directly in support of Sophie's legacy!


Would you like me to continue a series on female mathematicians, scientists and programmers? I would love to feature some of today's recent pioneers, like the first female Fields Medalist, Maryam Mirzakhani, in whose honor I modeled our logo after, the first female member of the United States' team for the International Math Olympiad, Melanie Wood, and the recent Nobel medalist, physicist Donna Strickland. Let me know what you think!


Here are some wonderful sources I used in writing this post, and they're great if you'd like to learn more about Sophie Germain:

https://www.agnesscott.edu/lriddle/women/germain.htm

https://blogs.scientificamerican.com/roots-of-unity/thank-you-sophie-and-im-sorry/

https://scientificwomen.net/women/germain-sophie-39

https://simonsingh.net/books/fermats-last-theorem/sophie-germain/

Here's a video:

And here's a podcast: https://www.listennotes.com/podcasts/women-in-math-the/episode-24-sophie-germain-iQ3hyIBx5b2/

There's also an amazing picture book about her: Nothing Stopped Sophie by Cheryl Bardoe, if you'd like to give it as a gift to any of the younger girls in your life.


That's what I got! Thanks so much for reading this week's blog post! And as always, leave any comments in the comment section with feedback, questions or requests for next week!