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Tuesday, August 8, 2017

Women Mathematicians

By Kristy McCaffrey

As early as the 1700s, women were drawn to scientific fields but society excluded them from receiving proper training and the same employment opportunities as their male counterparts. However, that didn’t stop the following women from educating themselves and making important breakthroughs during their lifetimes.

Sophie Germain
Sophie Germain was born in Paris, France, in 1776. Her father was a wealthy merchant and when Sophie was 13 years old she began to read books on mathematics and physics in her father’s library. Her parents disapproved of this interest and would often deny her warm clothes and a fire in her bedroom to keep her from studying. When they finally realized her serious intent, they secretly supported her. When Sophie was 18, the Ecole Polytechnique opened but women were not allowed. However, notes from the classes were made public and she was able to obtain the material and study along with the male students. She submitted her work under a man’s name and when Joseph Louis Lagrange, a faculty member, requested a meeting, he didn’t turn her away when he learned she was a woman. Instead, he became her mentor. She is known as one of the pioneers of elasticity theory, and she won the grand prize from the Paris Academy of Sciences for her essay on the subject, the first woman to do so. She also contributed foundational work on Fermat’s Last Theorem, ideas that were central to other mathematicians works for over two hundred years. She died at the age of 55 from breast cancer.

Ada Lovelace

Ada Lovelace was born in London, England, in 1815. She is best known for her work on a proposed mechanical general-purpose computer known as the Analytical Engine. She created the first algorithm and is often credited as the first computer programmer. Lovelace was the only legitimate daughter of the poet Lord Byron and his wife Anne. (His other children were born out of wedlock with other women.) Byron left Anne only a month after Ada was born and died when Ada was 8 years old. Anne remained bitter toward her husband and encouraged Ada’s love of mathematics and logic in an effort to subvert the madness that had seemed to grip Byron. Never close with her mother, she was raised by her grandmother and led a fairly scandalous adult life, with numerous purported affairs and a love of gambling. One project that never reached fruition was her desire to create a mathematical model for how the brain gives rise to thoughts and nerves to feelings, a ‘calculus of the nervous system’. Her interest in the brain came from an obsessive focus on the potential madness she may have inherited from her father. Ada died at the age of 36, most likely from uterine cancer.

Sofia Kovalevskaya

Sofia Kovalevskaya was born in Moscow, Russia, in 1850. Her military father, along with her mother, provided a good education. When Sofia showed an aptitude for math, they hired a tutor to teach her calculus. In order to study abroad, she needed permission from her father or a husband, so she contracted a ‘fictitious’ marriage with Vladimir Kovalevskij, a young paleontology student who later became famous for collaborating with Charles Darwin. In 1869, she attended the University of Heidelberg in Germany by auditing classes. After two years, she moved to Berlin where she took private lessons since the university wouldn’t even allow auditing. In 1874, she presented a doctoral dissertation at the University of Gottingen with three papers—one on partial differential equations, one on the dynamics of Saturn’s rings, and one on elliptic integrals. With the support of her private tutor, she was awarded her doctorate in mathematics summa cum laude, becoming the first woman in Europe to hold such a degree. Although Sofia and Vladimir had a fake marriage, for a short time it became real and together they had a daughter. However, much of their married life was spent apart. Vladimir, who suffered mental problems, eventually committed suicide. Sofia later settled in Sweden where she secured a teaching position and died at the age of 41 from influenza. She made noteworthy contributions to analysis, partial differential equations, and mechanics.

Emmy Noether

Emmy Noether was born in Erlangen, Germany, in 1882. Inspired by her mathematician father, she sought to follow in his footsteps but German universities didn’t admit women. She circumvented this obstacle by auditing classes and eventually proved herself so adept at the curriculum that she earned an undergraduate degree. In 1904, she was permitted to enroll in a doctoral program at the University of Erlangen and received a Ph.D. in 1907. For over eight years she worked for no pay, relying on her family to financially support her. It wasn’t until 1922 that she became an untenured associate math professor at the University of Gottingen, where she earned a modest salary. Noether is well-known in the physics community for two theorems she proved. The first dealt with a problem in Einstein’s theory of general relativity in relation to conservation of energy. She resolved the issue by showing that while energy may not be conserved ‘locally’, it is conserved if the space considered is sufficiently large. The other theorem uncovered a link between conservation laws and the symmetries of nature. Today, our grasp of everything from subatomic particles to black holes draws heavily from this theorem, known as Noether’s theorem. When Hitler came to power, she was forced to leave Germany and came to the United States to teach at Bryn Mawr College. Noether never married and died at 53 from complications stemming from a pelvic tumor.

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  1. Great posts. I so enjoy learning about women who beat the odds and were able to pursue intellectual activities considered inappropriate for women in their time. Today, educators are begging for more women to study math and science. It is also a shame to learn these women died so young, most without producing children who could have potentially inherited their abilities for mathematics.

    1. I was surprised the women died so young, and most without children.

  2. Thank you for finding and sharing the story of these pioneering and determined women, Kristy. What one can do when you set your mind to it. Doris

  3. It always astounds me how society would rather get all gender stupid and deny the right for women of intelligence to contribute the knowledge of society.
    This was a wonderful and well researched article, Kristy. Thank you.

    1. Well, it's easier to control a population if they have few skills. :-( But a lot of these women had mentors who thankfully stepped in to help them.

  4. Kristy,

    I particularly enjoyed your article, because it took me back a few of years to when I helped my teacher-daughter in her master's program (secondary math). I helped her research (and then edited) one of her papers about female mathematicians in history. I learned a great deal then, and I learned even more from you.

    It's a travesty that the female contributions to the areas of science and math aren't given as much credence as is warranted or deserved.

    1. I agree. My background is in engineering and I'd never heard of these women. It's rather shocking, considering all the classes I took and textbooks I read and math equations I did. And there are certainly more women than these 4. It's actually heartening to know that they didn't give up on their passion.