Marie-Sophie Germain (French: [maʁi sɔfi ʒɛʁmɛ̃]; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library, including ones by Euler, and from correspondence under the pseudonym of Monsieur Le Blanc with famous mathematicians, such as Lagrange, Legendre, and Gauss. One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On 27 June 1831, she died from breast cancer. Following the publication of a biography in the late 1870s marking the centenary of her life, a street and a girls' school were then named after her. The Academy of Sciences established the Sophie Germain Prize in her honour.
Early life
Family Marie-Sophie Germain was born in a house on Rue Saint-Denis on 1 April 1776, in Paris, France, to Marie-Madeline (née Gruguelin) and Ambroise-François Germain and was baptised the same day. She was from a bourgeois family. According to most sources, her father was a wealthy silk merchant, though some believe he was a goldsmith. In 1789, he was elected as a representative of the bourgeoisie to the États-Généraux, which he saw change into the National Assembly. It has been assumed that Sophie witnessed many discussions between her father and his friends on politics and philosophy. Gray proposes that after his political career, Ambroise-François became the director of a bank. The family remained well-off enough to support Germain throughout her adult life. Marie-Sophie had one older sister, Marie-Madeline and one younger sister, Angélique-Ambroise. Her mother was also named Marie-Madeline, and this plethora of "Maries" may have been the reason she went by Sophie. Germain's nephew Armand-Jacques Lherbette, her sister Marie-Madeline's son, published some of Germain's work after she died (see Work in Philosophy).
Introduction to mathematics When Germain was 13, the Bastille fell, and the revolutionary atmosphere of the city forced her to stay inside. For entertainment, she turned to her father's library. Here she found Jean-Étienne Montucla's L'Histoire des Mathématiques, and his story of the death of Archimedes intrigued her. Germain thought that if the geometry method, which at that time referred to all of pure mathematics, could hold such fascination for Archimedes, it was a subject worthy of study. So she pored over every book on mathematics in her father's library, even teaching herself Latin and Greek, so she could read works like those of Isaac Newton and Leonhard Euler. She also enjoyed Traité d'Arithmétique by Étienne Bézout and Le Calcul Différentiel by Jacques Antoine-Joseph Cousin. Later, Cousin visited Germain at home, encouraging her in her studies. Germain's parents did not at all approve of her sudden fascination with mathematics, which was then thought inappropriate for a woman. When night came, they would deny her warm clothes and a fire for her bedroom to try to keep her from studying, but after they left, she would take out candles, wrap herself in quilts and do mathematics. After some time, her mother secretly supported her.
École Polytechnique
In 1794, when Germain was 18, the École Polytechnique opened in Palaiseau. As a woman, Germain was barred from attending, but the new system of education made the "lecture notes available to all who asked". The new method also required the students to "submit written observations". Germain obtained the lecture notes and began sending her work to Joseph Louis Lagrange, a faculty member. She used the name of a former student Monsieur Antoine-Auguste Le Blanc, "fearing", as she later explained to Gauss, "the ridicule attached to a female scientist". When Lagrange saw the intelligence and originality of M. Le Blanc, he requested a meeting, and thus Sophie was forced to disclose her true identity. Fortunately, Lagrange did not mind that Germain was a woman, and he became her mentor and friend.
Early work in number theory
Correspondence with Legendre Germain first became interested in number theory in 1798 when Adrien-Marie Legendre published Essai sur la théorie des nombres. After studying the work, she opened correspondence with him on number theory, and later, elasticity. Legendre included some of Germain's work in the Supplément to his second edition of the Théorie des Nombres, where he calls it très ingénieuse ("very ingenious"). See also her work on Fermat's Last Theorem below.
Correspondence with Gauss Germain's interest in number theory was renewed when she read Carl Friedrich Gauss's monumental work Disquisitiones Arithmeticae. After three years of working through the exercises and trying her own proofs for some of the theorems, she wrote, again under the pseudonym of M. Le Blanc, to the author himself, who was one year younger than she. Gauss's replies were mailed to the home of Antoine-Isaac, Baron Silvestre De Sacy, who must have understood Germain's reasons for assuming a masculine pseudonym and agreed to help her conceal her identity. The first letter, dated 21 November 1804, discussed Gauss's Disquisitiones and presented some of Germain's work on Fermat's Last Theorem. In the letter, Germain claimed to have proved the theorem for n = p − 1, where p is a prime number of the form p = 8k + 7. However, her proof contained a weak assumption, and Gauss's reply did not comment on Germain's proof. Around 1807 (sources differ), during the Napoleonic wars, the French were occupying the German town of Braunschweig, where Gauss lived. Germain, concerned that he might suffer the fate of Archimedes, wrote to General Pernety (Joseph Marie de Pernety), a family friend, requesting that he ensure Gauss's safety. General Pernety sent the chief of a battalion to meet with Gauss personally to see that he was safe. As it turned out, Gauss was fine, but he was confused by the mention of Sophie's name. Three months after the incident, Germain disclosed her true identity to Gauss. He replied:
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