**Sophie Germain** made a major contributions to number theory (in particular, the theory of primes), acoustics and elasticity.

- Sophie was thirteen years old at this time and up until then she had been educated at home.
- Eventually her parents lessened their opposition to her studies, after waking up one morning, seeing Sophie was not in her bed, and finding her asleep in the library which was so cold that the ink had frozen solid in the ink well.
- Sophie Germain was eighteen years old when the École opened and at exactly the right age to begin a university education.
- This did not stop Germain who obtained lecture notes for many courses from École Polytechnique including Antoine-François Fourcroy's chemistry course and Joseph-Louis Lagrange's analysis course.
- Using the pseudonym M LeBlanc, Germain submitted a paper whose originality and insight made Lagrange look for its author.
- Lagrange certainly made his colleagues aware that Germain was a girl with mathematical talent and several of them wrote to her.
- One case was Jérôme Lalande who visited Germain in 1797.
- This "astronomy for ladies" does not contain a single mathematical equation and Germain felt insulted by his suggestion.
- Germain wrote to Legendre about problems suggested by his 1798 Essai sur le Théorie des Nombres Ⓣ(Essay on the theory of numbers), and the subsequent correspondence between the two became virtually a collaboration.
- Several of her letters were later published in her Oeuvres Philosophique de Sophie Germain Ⓣ(Philosophical works of Sophie Germain).
- However, Germain's most famous correspondence was with Gauss.
- Germain's true identity was revealed to Gauss only after the 1806 French occupation of his hometown of Braunschweig.
- Germain, however, spent the next decade attempting to derive a theory of elasticity, competing and collaborating with some of the most eminent mathematicians and physicists.
- In fact, Germain was the only entrant in the contest in 1811, but her work did not win the award.
- Lagrange, who was one of the judges in the contest, corrected the errors in Germain's calculations and came up with an equation that he believed might describe Chladni's patterns.
- The contest deadline was extended by two years, and again Germain submitted the only entry.
- Germain's third attempt in the re-opened contest of 1815 was deemed worthy of the prize of a medal of one kilogram of gold, although deficiencies in its mathematical rigour remained.
- Germain attempted to extend her research, in a paper submitted in 1825 to a commission of the Institut de France, whose members included Poisson, Gaspard de Prony and Laplace.
- Among her work done during this period is work on Fermat's Last Theorem and a theorem which has become known as Germain's Theorem.
- However, as Germain admitted to Gauss, she was unable to establish the existence of an infinite number of auxiliary primes even for a single prime exponent.
- Indeed, Germain's grand plan was doomed to failure as it was later shown that for each odd prime ppp there are only a finite number of auxiliary primes that satisfy the non-consecutive pppth power residue condition.
- Germain continued to work in mathematics and philosophy until her death.
- We should recognise the analogies between the life of Sophie Germain and our own, and they should lead us to strive for excellence in the face of prejudice.
- It is only recently that it has been discovered how distinctly he was anticipated in the main features of his system by Sophie Germain.
- Germain died in June 1831 at 13 rue de Savoie in Paris, which still stands today and has a commemorative plaque.
- Germain was buried at the Cimetière du Père Lachaise.

Born 1 April 1776, Paris, France. Died 27 June 1831, Paris, France.

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Number Theory, Women

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive