More than just a footnote
Every time I see this list of the greatest mathematicians of all time, I get all worked up. It is not like official or anything, and there is definitely going to be some disagreement among mathematicians in the rankings, but I do feel like overall it accurately reflects how history remembers the contributions to mathematics. So why do I get all worked up? There are almost no women on the entire list.
The field of mathematics is still dominated by men, but historically, it was even worse. Many of the biggest developments in mathematics were made at a time when women weren’t just forbidden from studying math, but forbidden from attending school at all. Only a handful of women in all of recorded history have been remembered for their contributions to mathematics. Emmy Noether, #28, is the only woman to make the top 100. Sofia Kovalevskaya (also known as Sonia Kovalevsky) made it to the list of “spares”, and Sophie Germain appears as a footnote.
Sophie Germain was born in 1776 in France. When she was a teenager, she became fascinated with mathematics through books belonging to her father, but was not permitted to study formally because she was a girl. The École Polytechnique opened when she was a young woman, but she was not allowed to attend. She was, however, permitted to obtain lecture notes from the classes held at the school, and with these notes, she continued her studies on her own.
Eventually, she began a correspondence with a professor at the school, and he became impressed with her ideas. They arranged a meeting, and while he was surprised to discover that she was a woman, he continued to correspond with her and became her mentor. His responsibilities as a professor and his own work in mathematics prevented him from spending much time with her, but he was a source of encouragement and support.
Several years later, she began writing to a German mathematician, and the two of them discussed some theories on Fermat’s Last Theorem through correspondence. He was also shocked when he learned she was a woman, and said this in a letter to her about her knowledge of mathematics:
“But when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarizing herself with their 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.”
She went on to prove a special case of Fermat’s Last Theorem and her work was instrumental in moving the work on the theorem forward.
In 1816, she became the first woman to win a prize from the Paris Academy of Sciences, but was not permitted to attend, because the only women allowed were wives of the male members. Modern mathematicians say that her work exhibits extraordinary mathematical talent but contains mistakes, is often based on weak assumptions, and lacks mathematical rigor. She never studied mathematics formally, never took a class, never learned from a professor, never had anyone to guide her, to challenge her, to review her work. The professor who became her mentor was Joseph-Louis Lagrange, number eight on the list. And the German mathematician who called her a superior genius was Carl Gauss, number three. I have no doubt that if Sophie Germain hadn’t been faced with the ridiculous notion that women were unfit to study mathematics, she would have made contributions to the field equal to theirs.
Sophie Germain was an incredible woman and an incredible mathematician and she deserves to be remembered as more than just a footnote.