In the middle of the eighteenth century, change was in the air. New ideas about independence, how people should work and govern themselves, were spreading. Colonists in North America were fighting a revolution against British rule. In England, factories were popping up along river banks, where huge mill-wheels used the energy of the rushing water to power machines. France had factories too, but it also had philosophy, art and fashions that people around the world imitated. But there was one thing that this fast-changing world was not ready for: Sophie Germain.
Sophie was born in Paris, France, in the same year that the Americans signed their Declaration of Independence from Britain: 1776. Before Sophie grew up, revolution would come to France too, and it would change her life, shaping her into the person she would become. A person that didn’t fit the mold. A woman who thought and worked tirelessly on a subject women weren’t supposed to be interested in.
Sophie’s family included father, Ambroise-François; her mother, Marie-Madeline, and two sisters: an older one also named Marie-Madeline, and younger one named Angélique-Ambroise. Sophie’s father was a wealthy silk merchant and politician, so the family always had what they needed. But sometimes things happen that we just can’t avoid. When Sophie was 13, One of these unavoidable things happened. The French revolution started, spurred on by an economic crisis that caused many people to suffer. The common people wanted more rights, and angry people were marching through the streets.
It was too dangerous for Sophie to leave the house, so she looked for things to do inside. She spent much of her time in father’s library. She was especially drawn to books about mathematics. In one book, she found the story of a famous Greek mathematician and engineer, Archimedes. Archimedes invented many ingenious contraptions. They moved things up and down with pulleys, counted the miles carts had traveled, and even plucked enemy ships out of the water. But the story that captivated Sophie had to do with a simple drawing in the sand. Roman forces had invaded Archimedes’ home island of Syracuse. As the soldiers stormed the island, Archimedes was lost in thought over a geometric diagram he’d drawn in the sand, and didn’t run to safety, so he was killed by the invading Roman forces. Wanting to honor her mathematical hero, Sophie taught herself all the math she could.
At first her parents discouraged her. They refused to light fire in her room or let her have warm clothes at night, thinking this would keep her from late-night study sessions. But Sophie found a way. When she was sure her parents were in bed, she lit candles, bundled herself in blankets, and took out the math books she’d hidden. She teased out patterns in the numbers and worked through equations. Maybe she even traced diagrams with her finger in the ash of that cold fireplace in her room, imagining Archimedes with his sand. She taught herself Latin so she could read famous mathematical works by Isaac Newton and Leonard Euler. At one point, a famous mathematician named Jaques Antoine-Joseph Cousin visited Sophie’s father at their house. Meeting him inspired Sophie to study even harder. Eventually, Sophie’s mother saw that her daughter was not going to give up, and secretly supported her studies.
As she grew into a young woman, Sophie wished she could study and work with other mathematicians. But women could not attend universities in France at the time. Still, Sophie found a way. A new university opened in Paris, which promised to send lecture notes to anyone who wanted them. Sophie took advantage, requesting, then carefully studying, the notes of another famous mathematician, Joseph Louis Lagrange. But just keeping up with advances in math wasn’t enough for Sophie. She wanted to be a part of those advances. She wanted to contribute.
But again, Sophie had to find a way. She began writing to Lagrange about his work, using a false name M. LeBlanc to hide the fact that she was a woman. After a few letters, Lagrange was impressed. In fact, he wanted to meet this M. LeBlanc in person. Of course, this would blow her cover! But there was no way around it. Sophie reluctantly agreed. Fortunately, Lagrange wasn’t upset. He saw that Sophie was a talented, hard-working mathematician, He encouraged her to keep up her studies.
The type of math that Sophie was most interested in is called number theory. She had read a book about it by Adrien Marie Legendre, and was hooked. Number theory is all about finding patterns in numbers and seeing how they relate to each other. If you know that all even numbers can be divided by two, and odd numbers can’t, then you know something about number theory. Number theorists also study things like prime numbers, which can only be divided by themself and 1, and square numbers, which you get by multiplying any number by itself.
Lagrange wasn’t Sophie’s only pen-pal. Later, she began writing to another famous mathematician, Carl Friedrich Gauss, Gauss had also worked on number theory. Again, Sophie used the pen name M. LeBlanc to disguise her gender. Gauss was also impressed with the work of “Monsieur LeBlanc,” and even raved to his friends about it.
But Sophie became worried when she learned that Gauss was living in an area of Germany that was occupied by French soldiers. She wanted to make sure he was safe. She used her father’s connections to contact someone in the French army there, and a soldier was sent to check on Gauss. He was fine, but confused. He didn’t know why this mysterious young woman called Mademoiselle Germain would be concerned. He told the officer that he didn’t know anyone by that name!
Sophie later wrote to clear up his confusion, revealing that he knew the mysterious Mademoiselle Germain as “Monsieur Leblanc.” Gauss, like Lagrange, was not angered by the revelation that the person he’d been writing turned out to be a femme-savant or “knowledgable woman.” He continued writing to Sophie, and gave her credit for inspiring some of his ideas in number theory.
Though Sophie had found some supporters in the math world, she still had few chances to prove to the wider world that she was just as capable as any male mathematician. Finally, an opportunity arose when the Paris Academy of Sciences decided to put on a competition. A visiting professor named Ernst Chladni had recently put on an intriguing demonstration in Paris. He had sprinkled a layer of sand onto metal plates of many different shapes, then rubbed a violin bow across the edge of each plate. A different tone sounded from each plate, and the sand on the plates would jump and shift, making beautiful waves, whorls, and starbursts that were unique to each shape.
The Academy asked mathematicians to explain what was happening using mathematical formulas. This was a hard problem, but like Archimedes, Sophie got to work, studying the patterns in the sand. She submitted her entry anonymously in 1811. She was the only entrant, so you might think she’d automatically get the prize. But some contests don’t have a winner. The judges decided her entry didn’t quite explain the problem well enough.
The Academy re-opened the contest in 1813, giving Sophie a chance to show the progress she’d made. Again, she was the only entrant, and again no prize was awarded. But Sophie kept going, working on the problem, correcting the errors in her formulas, and experimenting with the metal plates. Luckily for her, the Academy had kept the contest going, and still no one else had entered! By this time, Sophie had been working on this problem for more than three years. She entered (again, the only person to do so) and finally won!
Even though she’d won a prize for her work, and many male mathematicians praised her abilities, Sophie would never get a job as a mathematician. They simply weren’t available for women at the time. Some male mathematicians even used her work without giving her credit. But she continued to toil away at math for the rest of her life. She was able to publish a few papers, including one about her work on the metal plates. She worked on Fermat’s last theorem–a famous and very difficult math problem, finding new ways to solve parts of it. Adrien Legendre, whose book had drawn her to number theory, would give her credit for this work when he finally solved it.
Sophie even continued working on math after she discovered she had cancer in 1829. She continued working when revolution again broke out in France in 1830. She found a way until she finally passed away at home in 1831.
Many people have paid tribute to Sophie in other ways though. Gauss asked the University of Gottingen to give her an honorary degree, though they didn’t grant it until 1837, after her death. Some of her work would turn out to be important in the design of the Eiffel Tower. There’s a street named after her in Paris, and, fittingly, later mathematicians named a new type of prime number after her. The Paris Academy of Sciences named an annual math prize after her, honoring the time and care she took in working on the contest she entered three times before she finally won.
Sophie did not have the opportunities she deserved during her life. Though she was clearly talented, she might have been a much greater mathematician if others had taken her more seriously. Still, Sophie helped change people’s minds about what women could do. She worked hard and refused to be ignored. Because of Sophie and other female scientists of her time, future generations of women could enter math and science as themselves. They no longer had to sign their letters with fake names, or hide under layers of blankets late at night to study. They were free to claim their own work and study near an open window, the sun shining on their faces.
Sources
https://byjus.com/maths/number-theory/
https://interestingengineering.com/7-amazing-inventions-from-archimedes
https://en.wikipedia.org/wiki/Sophie_Germain
Campbell, Paul J; Grinstein, Louise S (1987) Women of Mathematics: A Bibliographic Source Book. Greenwood Press, New York.