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Summary Article: Germain, Sophie (Marie) (1776-1831)
from The Hutchinson Dictionary of Scientific Biography

Place: France

Subject: biography, physics

French mathematician who developed the modern theory of elasticity (the mathematical theory of the stress and strain that a material can sustain and still return to its original form) and made major contributions to numbers theory and acoustics.

Germain was born on 1 April 1776 in Paris, the second of three daughters of a prosperous silk merchant. She grew up in Paris at the time of the fall of the Bastille and the Reign of Terror and her home was a meeting place for liberal reformers. Germain was used to intellectual discussion from a young age.

Germain studied alone in her father's library from childhood. When she was 13 she was moved by the story of the death of Archimedes at the hands of a Roman soldier and became fascinated by geometry. She was determined to become a mathematician and taught herself Greek and Latin and read the works of Isaac Newton and Leonhard Euler during the night. Out of concern for her health her parents doused the fire in her bedroom and took away her clothes and her light to try to prevent this but she still came downstairs and worked secretly by firelight wrapped in a quilt.

The Ecole Polytechnique opened in Paris in 1794 and although women were not admitted, she managed to obtain professors' lecture notes for several courses. Inspired by the work of Joseph Lagrange on analysis and using the pseudonym M le Blanc she sent him a paper. Impressed by her originality he sought her out, and out of respect for her work, became her sponsor and mathematical counsellor, in spite of her gender and lack of formal education.

Germain then entered into a long correspondence with Adrien Legendre and he included some of her discoveries in his writings. But her most productive and best known correspondence, in the guise of M. le Blanc, was with the German mathematician Karl Gauss, who did not suspect her identity for several years. Between 1801-09, she wrote to him outlining her number theory proofs and he praised her highly, eulogizing her to his colleagues. When the French occupied his home town of Braunschweig in 1806, she feared for his safety and interceded on his behalf through a family friend who was a French commander. When Gauss discovered her true identity he was even more full of praise for her. Germain also worked on Pierre de Fermat's last theorem at this time and proved that his equation does not hold for the case in which n is equal to 5. She wrote to Gauss explaining this but he failed to reply to her letter. She produced a theorem that has become known as Germain's theorem. Gauss later recommended her for an honorary doctorate from the University of Göttingen, but she died before it could awarded.

In 1809 Germain began work on the theory of the patterns formed by sand on vibrating plates. The German physicist Ernst Chladni had demonstrated the phenomenon to Napoleon in 1808 and the emperor had been so impressed that he had offered a gold medal weighing 1 kg/2.2 lb to the first person to explain ‘Chladni's figures’. Germain submitted the only entry in 1811 to the competition, but because of her lack of formal knowledge of analysis and the calculus of variation it was flawed. It was at her third attempt in 1815, again as the only entrant, that she finally won the award. To public disappointment, however, she did not appear at the presentation ceremony. She published her work privately in 1821 as Rechèrches sur la theorie des surfaces élastiques. She published memoirs on the theory of numbers and others on the theory of elasticity and her paper ‘Considerations sur l'etat des sciences et des lettres aux differentes époques de leur culture’ was a philosophical essay on the theme of unity of thought.

Germain was, probably quite rightly, of the opinion that she was not being taken seriously by the scientific community and when others from more privileged educational backgrounds took up the work she had begun on elasticity she was simply ignored, as was a subsequent paper she submitted to the Institut de France in 1825. When the Eiffel Tower was built in 1889 using in part her groundbreaking work on elasticity, she failed to receive a mention among the 72 contributors in the inscription.

Germain never married and was never offered a position in a university or fellowship of any society. Her father supported her financially throughout her life. She was diagnosed as having breast cancer in 1829 but continued working, completing papers on numbers theory and the curvature of surfaces before her death on 27 June 1831, in Paris.

© RM, 2018. All rights reserved.

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