Sophie Germain – Hero’s Journey
The Mundane World
Born into a wealthy family just prior to the French Revolution, Sophie Germain would find her childhood a lonely one. Danger from the violence and revolts of the revolution forced Sophie to remain confined to her parent’s home. With little or no contact with other children her age Sophie was forced to find ways to amuse and entertain herself. This often brought her to her father’s library.
The Call To Adventure
It was during one of these forays into the library that Sophie came across a book which contained an account of Archimedes’s death. According to legend Archimedes was so engrossed in the study of a geometrical figure traced in the sand that he failed to answer the questions of a Roman guard and was speared to death for that failure. This must have made quite an impression upon the young Sophie for at the age of thirteen she decided to devote her life to the study of mathematics.
Crossing The Threshold
A woman studying mathematics in the mid eighteenth century was virtually unthinkable. This decision absolutely mortified her parents who forbid such a pursuit for her. Sophie would have to study on her own with out the benefit of tutors. Using the books in her father’s library Sophie began to teach herself geometry, she additionally had to teach herself Greek and Latin in order to read the texts. Her parents did everything they could to stop her and convince Sophie to take up pursuits more becoming of a lady. When Sophie started reading at night her parents started taking away her fire wood, candles and clothes. Sophie continued her studies by wrapping in her bed sheets and using candles she had smuggled into her room. Eventually Sophie’s parents gave up and deemed her passion for mathematics incurable. Sophie continued her studies unhindered but on her own. While the Reign Terror raged across France, Sophie taught herself differential calculus.
The Path of Trials
Ecole Polytechnique was founded in Paris in 1794. It was an academy founded to train mathematicians and scientists for the country. Women were not allowed to enroll in the academy but that did not stop 18 year old Sophie. Obtaining the notes and lectures for several courses Sophie was able to study from a number of prominent mathematicians of the day. One who particularly interested Sophie was J. L. Lagrange. Near the end of the course Sophie submitted a paper on analysis to him using the pseudonym “M. Le Blanc”. Lagrange wanted to meet the person who had submitted the paper to him and was quite surprised to find it was a woman. He was however quite impressed with her skills and became Sophie’s mentor. This enabled Sophie to enter circles that would have been forbidden to her as a middle class woman. Up to this point Sophie had been barred from the pursuit of scientific study by both gender and social status. Had she been a member of the aristocracy she would have been afforded the opportunity to study mathematics.
By 1804 Sophie had become interested in number theory and began to correspond with a German mathematician by the name of Carl Friedrich Gauss. Again she had to conceal her gender and use the pseudonym “M. Le Blanc”. In 1807 Gauss finally found out the identity of “M. Le Blanc” and was excited to find out he had been corresponding with a woman. Gauss eventually moved on to studies other then number theory but the correspondence he had with Sophie greatly influenced and guided her own studies. In 1811 Sophie’s greatest work in number theory came with her Germain Theorem. Germain proved that if x, y, and z are integers and if x^5 + y^5 = z^5 then either x, y, or z must be divisible by 5. Germain’s theorem is a major step toward proving Fermat’s last theorem for the case where n equals 5. Fermat’s last theorem says that if x, y, z, and n are integers then x n + yn = zn cannot be solved for any n greater than 2.
It was also in 1811 that Sophie began looking for a new mentor. She became interested in Chaldni Figures several years earlier when the French Academy of Sciences announced a prize to be awarded for explaining the underlying mathematical law in Chaldni’s study on the vibration of elastic surfaces, Sophie ultimately submitted three entries for the prize. The first was in 1811 and was the only entry submitted. The anonymous paper was promptly rejected as her lack of formal training was evident. Sophie sought out the aid of Lagrange who helped her fix the errors and resubmitted it in 1813. This time the paper received an honorable mention though it still had problems. In 1816 she submitted for the third and final time and was awarded the prize though the submission had serious short comings. These short comings wouldn’t be rectified for another two decades.
Master of Two Worlds
Winning the prize gave Sophie the credibility she was due. It allowed her access to areas never before open to women. She became the first woman who was not a wife of a member to attend the Academy of Sciences. She was honored by the Institut de France and was asked to attend their sessions. In 1820 Sophie worked with a male mathematician as an equal collaborator. Sophie’s relentless determination to the science of mathematics not only provided substantial contributions to that science but also advanced the cause of women’s rights all over the world.
Submitted by: Charles Leibrand