FRANCE: Sophie Germain
John Gehl sends this bio of the French mathematician Sophie Germain (1776-1831), who has been acclaimed as France's greatest female mathematician. In Germain's time, it was almost unheard of for a woman to pursue studies in mathematics. Her contemporaries tended to regard her as a phenomenon more than a serious mathematician. Today historians of mathematics view her as a highly talented mathematician who was denied the
thorough training that would have allowed her to reach her full potential. Her accomplishments, however, were more than sufficient to gain her an honored place in the history of mathematics.
She is best remembered for her work in connection with Fermat's "last theorem" in which he posited that the equation xn + yn = zn has no positive integral solutions if n is an integer greater than 2. Germain 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. She sent her findings for verification to the eminent mathematician Carl Friedrich Gauss, with whom she had been corresponding under the pseudonym M. Leblanc. Unfortunately, Gauss had just become professor of astronomy at the University of Göttingen and did not respond. As a result Germain's theorem remained largely unknown for many years, although it turned out to be the most important result related to Fermat's last theorem until the work of E.E. Kummer in 1840. It was not until 1995 that the English mathematician Andrew Wiles published the full proof of Fermat's last theorem.
Germain was born into a liberal, educated, merchant family. With no real interest in the money-making and political pursuits of her family, Germain spent her time in the family's library, teaching herself mathematics, much to the distress of her parents. Germain ultimately overcame their objections and was allowed to continue her mathematical studies. During the two years of the French Revolution's Terror (1793-4) she succeeded in teaching herself differential calculus, but in 1795 she was refused admission to the newly opened École Polytechnique because of her sex. Undaunted, she obtained notes for many of the courses, including analysis given by Lagrange, and submitted work to him under the pseudonym she also used to correspond with Gauss.
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 experiments on the vibration patterns of elastic plates. There were no outright winners, though Germain was awarded the prize for the excellence of her submission. Beginning in 1820 Germain began to be known and accepted in her own right by the Parisian scientific society. Despite being a woman, she was allowed to attend the sessions of the Académie des Sciences, the first woman accorded the privilege. In 1830 Gauss petitioned the University of Göttingen to award her an honorary doctorate, but she died before the degree could be awarded. Perhaps the fact that she never received academia's highest honors makes her remarkable achievements in acoustics, elasticity and the theory of numbers all the more memorable.
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