# Germain, Sophie

### gauss theorem mathematician conjecture

[zhairmî] (1776–1831) France’s greatest female mathematician.

Born into a liberal, educated, merchant family, Sophie Germain did not share their interest in money and politics. She retreated to her father’s library and taught herself mathematics, to the dismay of her parents, who did their best to thwart her. There followed a battle of wills, which she won. She spent the years of the Terror (1793–4) teaching herself differential calculus. Unable to attend the newly opened École Polytechnique (1795) because of her sex, she obtained notes for many of the courses, including analysis given by . Using a pseudonym she submitted work to Lagrange and started a correspondence with , discussing ‘last theorem’ (his conjecture that *x n* + *y n* = *z n* has no positive integral solutions if *n* is an integer greater than 2).

In 1808 she wrote to Gauss describing what was to be her most important work in number theory. She proved that Fermat’s conjecture is true if *x* , *y* and *z* are prime to one another and to *n* , if *n* is any prime less than 100. However, Gauss had become professor of astronomy at the University of Göttingen and did not respond. Germain’s theorem remained largely unknown, although A-M Legendre (1752–1833) mentions it in a paper of 1823. Germain’s theorem was the most important result related to Fermat’s last theorem from 1738 to the work of E E Kummer (1810–93) in 1840.

Sophie Germain was a talented mathematician without sufficient training to fulfil her potential. She was regarded as a phenomenon rather than a serious mathematician in her time. In 1809 Napoleon urged the First Class of the Institut de France to establish a *prix extraordinaire* for anyone who could devise a theory that explained E F F Chladni’s (1756–1827) experiments (the vibration patterns of elastic plates). There were no outright winners, though Germain was awarded the prize in recognition of her competence. After 1820 Germain began to be accepted by Parisian scientific society. She worked with Legendre and, through friendship with attended the sessions of the Académie des Sciences, the first woman to do so in her own right. She never received a degree; in 1830 Gauss failed to persuade the University of Göttingen to award her an honorary doctorate.

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