Sophie Germain: French Mathematician Extraordinaire

Mathematician extraordinaire Sophie Germain was born on 1 April 1776 in Paris, France, to a wealthy silk merchant (or perhaps a goldsmith) named Ambroise-François Germain and a woman named Marie-Madeline Gruguelu. Thirteen years later, in 1789, the French Revolution broke out, and it was during this time that Sophie became interested in mathematics.

Her interest in mathematics began after her parents confined her to her home. That was because there were many revolts and a lot of danger when outside. Stuck indoors, Sophie began to explore her father’s library and one day found a book about the legend of Archimedes’s death. According to legend, when Roman soldiers invaded Archimedes’s city, he was “so engrossed in the study of a geometric figure in the sand that he failed to respond to the questioning of a Roman soldier. As a result he was speared to death.”[1]* Archimedes’s story so impressed Sophie, she decided mathematics must be a very interesting subject and immediately began devoting herself to its study.

When Sophie’s parents learned she was studying mathematics, they felt it was an inappropriate subject for their daughter. One person wrote:

“Her family were alarmed at so much ardor, and endeavored to turn her attention to more ladylike pursuits. They tried the plan of putting out her fire and taking away her clothes at night, but she found in the morning wrapped up in blankets, absorbed in her studies in a room so cold that the ink was frozen in the inkstand.”[2]

Sophie Germain could not be dissuaded from mathematics. Her family finally realized that she was determined and they saw that her desire was so strong they yielded, “and she was allowed to dispose of her time and her talents at her pleasure.”[3] When the École Polytechnique was founded, as it was not open to women,

“Sophie … was … anxious to profit by so valuable a means of instruction, she procured for herself students’ note-books specially of the courses in chemistry of Fourcroy, and in analysis of Lagrange. She did more. The students were in the habit of handing in to the professors [such as Lagrange, Prony, Fourcroy, and others], at the end of a course, their observations in writing on the lectures … under the supposed name of a student, Le Blanc, she sent her note-books to Lagrange. He noticed them, publicly praised them, found out their real author, and, having made her acquaintance, became the friend and counselor of the young mathematician.”[4]

Several years later when the German mathematician Carl Friedrich Gauss produced “Theory of Numbers,” Sophie Germain examined it and sent Gauss (under the name of Le Blanc) her notes. She wrote that she hoped “he will not disdain to enlighten with his advice an enthusiastic amateur of that science which he cultivates with such brilliant success.”[5] However, Sophie was no amateur and Gauss knew it. He answered Le Blanc and a correspondence between the two ensued, and Gauss did not discover it was Sophie writing him for several years.

Sophie in the meantime continued to study and learn. Then Napoleon decided to offer an extraordinary prize to explain the theory of elastic surfaces, with the prize being presented through the Institut de France. Sophie was the only person to enter in 1808. She did not win, but she was on the correct path. Two years later she sent a second memoir and this one received an honorable mention. Undeterred, Sophie tried a third time on 8 January 1816. This time she won the prize. The Institute praised her and invited her to attend their sessions as this was “the highest honor that this famous body ever conferred on a woman.”[6] However, the world at large either briefly noted her achievement or ignored her achievement altogether.

In 1894, it was stated of Sophie’s abilities in this field that

“[Sophie’s] equation for elastic plates is still the fundamental equation of the theory. [However,] her boundary-equations have not stood the test of time; Poisson, fourteen years later, gave a different set of boundary-equations based upon a different hypothesis, and Kirchoff, in 1850, show that neither hypothesis was tenable, and that neither set of equations was correct.”[7]

Sophie Germain continued to study after winning the Institut’s prize. She also attended sessions at the Academy of Sciences and stayed abreast of research conducted by her contemporaries. She then contributed to the “Annales de Physique et de Chimie,” which related to the laws of movement of elastic solids. However, Sophie’s best work was in number theory, and her most significant contribution to number theory dealt with Fermat’s Last Theorem. In an unpublished manuscript entitled “Remarque sur l’impossibilité de satisfaire en nombres entiers a l’équation xp + yp = zp,” Sophie demonstrated that any counterexamples to Fermat’s theorem for p>5 must be numbers around 40 digits long. Her brilliant theorem is known only because of a footnote in Legendre’s treatise on number theory, where he used it to prove Fermat’s Last Theorem for p = 5. In addition, Sophie proved or nearly proved several results that were erroneously attributed to Lagrange.

Besides Sophie’s superb mathematical abilities, she was amazing in other ways. One person noted:

“There are many testimonials to the charm of her character and of her conversation. She was imbued with a pure love of science, and she was remarkably indifferent to her own fame. She rejoiced when ideas which she had let fall in conversation were appropriated by others. It made no difference, she said, from whom an idea came; it was only of consequence that is should be true and useful. … Virtue she looked upon as a sense of order … Her conversation as full of gaiety and freshness, and bore constant marks of originality of thinking, and of a poetic handling of her thoughts.”[8]

In 1829, Sophie Germain learned she had breast cancer, just like Eliza de Feuillide‘s mother. Before her death Gauss had convinced the University of Gottingen to give her an honorary degree. Unfortunately, Sophie died at the age of fifty-five on 27 June 1831. She was buried at France’s famous Père Lachaise Cemetery.

Sophie’s memory and her amazing accomplishments have been memorialized in France in several ways since her death. First, a state girl’s school was established and named after her (École Sophie Germain), second, a street (Rue Sophie Germain) exists, and, lastly, the Sophie Germain prize, an annual award was established in 2003 by the Foundation Sophie Germain. This Academy of Science in Paris confers the award in honor of a French mathematician for his or her research in the foundations of mathematics.

*Either the history book or Sophie’s conclusion about Archimedes was wrong as Archimedes did not die because of his focus on geometry. Rather he was the “brains” behind Syracuse’s defenses as it was his idea to build catapults and create a mirrored system that caused the sails of the Roman ships to catch fire.

References:

• [1] Pickover, Clifford A., Wonders of Numbers, 2003, p. 71.
• [2] The Century, Volume 48, 1894, p. 947.
• [3] Ibid.
• [4] Ibid.
• [5] Ibid, 948.
• [6] Osen, Lynn M., Women in Mathematics, 1992, p. 90.
• [7] The Century, p. 968.
• [8] Ibid.