Sophie Germain
Do you know how Archimedes died? He died by being speared to death by a Roman soldier. He had ignored the soldier because he was so intrigued by a geometric figure drawn in the sand. If you are like Sophie Germain, you too are wondering what was so interesting about a shape in the sand that you would lose your life over it? This was the story that first inspired Sophie to start studying mathematics.
Germain was born in Paris on April 1, 1776. Her life was surrounded by revolutions. The year she was born the American Revolution started and thirteen years later a revolution started in her own country.
She was thirteen years old and stuck in her home since the revolts around their land made it unsafe to be out. There she started exploring her father's library which was where she found Archimedes story. She continued searching her father's books and began studying mathematics on her own, studying works by Newton and Euler in Latin and Greek. Germain had to study at night by candle light to hide from her parents. Her family was middle class so her education had been limited and on top of that, social norms claimed that the studies Germain was carrying out were inappropriate for females. In an attempt to stop Germain before she got too carried away, her parents tried everything they could to stop her, but she fought back with just as much zeal till her parents decided that it could not be helped, their daughter was going to study mathematics one way or another.
In 1794, when Sophie was about eighteen years old, the Ecole Polytechnique was founded in Paris. It was meant to train mathematicians and scientist for the country but did not accept women to study there. Despite that, Germain was able to get ahold of lecture notes and study the materials taught there. She eventually took the pseudonym M. LeBlanc and sent her work on analysis to a teacher whos lectures she was especially fond of, J.L. Lagrange. Lagrange was so impressed, he insisted on meeting the author of the well done paper. When he found out that M. LeBlanc was really Sophie Germain, he looked past the fact that she was a female and decided to be her mentor, recognizing her capabilities in math. And just like that, with her new escort, she had been introduced into the formal society of mathematics.
Through the years Germain continued to do work with Lagrange and worked with Gauss (who also did not know she was a woman originally) and Jean-Baptiste- Joseph-Fourier and other mathematicians. And eventually, in 1816 on her third attempt, she won a prize from the French Academy of Sciences. She was the only one to have entered the contest originally.
With her paper Memoir on the Vibrations of Elastic Plates she not only won the prize but had been accepted to the Academy of Sciences. She would finally go and study mathematics as an equal collaborator and be able to refine her proofs in number theory.
Sophie Germain died on June 27, 1831 at the age of 55. She had been fighting breast cancer. Before she died, Gauss, an earlier mentor of hers, had petitioned the University of Gottingen to give her an honorary degree. However, she had passed away before they could get it to her. Still, Germain was a revolutionary woman who worked hard to do what she loved despite the obstacles that loomed over her. And she made it! She is now a recognized and appreciated mathematician. Today some of her most important work is recognized in the theory of elasticity and in number theory.
Here is an example of some of the work she accomplished. If both p and $2p+1$ are prime, then $p$ is a Sophie Germain
prime. The first few such primes are $2, 3, 5, 11, 23, 29, 41, 53, 83, 89,
113,$ and $131$. Around 1825 Sophie Germain proved that the first case of Fermat's last theorem is
true for odd Germain primes.
*My favorite quote by Sophie Germain, "Algebra is but written geometry and geometry is but figured algebra."
Thanks bunches,
-Haylee Jo Lau
Works Cited:
Contemporary Abstract Algebra, Joseph A. Gallian, Ninth Edition
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