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She was so in love with learning that her parents worried about her health. She wanted to read rather than sleep. Her parents would remove all her clothes and douse the fire in her bedroom to force her to sleep. She would sneak out of the bedroom late at night to spend the hours wrapped in a blanket reading by firelight. She taught herself basic mathematics, learning Latin and Greek so she could read important works by Sir Isaac Newton and the mathematician Leonhard Euler. She became an outstanding mathematician. Sophie Germain prime numbers are the result of her work in number theory. She proved that the first case of Fermat's last theorem is true for certain prime numbers - when both p and 2p + 1 are prime, then p is called a Sophie Germain prime, and the theorem is true. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131
She sent one of her papers to the mathematician Lagrange who was so overwhelmed by it that he offered himself as her mentor. She even impressed the rather gruff mathematician Karl Friedrich Gauss (one of the rare true geniuses in mathematics) who said about her:
"But, when a person of the sex, which according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and a superior genius."
She helped to develop the modern theory of elasticity. Elasticity is the mathematical representation of stress and strain in materials such as steel beams. Modern construction would be impossible without her original works on the subject, including the Eiffel Tower in Paris, France. Her compatriots dubbed her the Hypatia of the 18th century.
More information may be found here for Sophia Germain