84 4. WOMEN MATHEMATICIANSis less than 100.^10 Gauss also praised her work very highly. He did not learn her
identity until 1806, when French troops occupied his homeland of Braunschweig.
Remembering the death of Archimedes, Sophie Germain wrote to some friends,
asking them to take care that Gauss came to no harm. Gauss' opinion of her,
expressed in a letter to her the following year, is often quoted:
But how to describe to you my admiration and astonishment at
seeing my esteemed correspondent Monsieur LeBlanc metamor-
phose himself into this illustrious personage who gives such a bril-
liant example of what I would find it difficult to believe. The
enchanting charms of this sublime science reveal themselves only
to those who have the courage to go deeply into it. But when
a woman, who because of her sex and our prejudices encounters
infinitely more obstacles than a man in familiarizing herself with
complicated problems, succeeds nevertheless in surmounting these
obstacles and penetrating the most obscure parts of them, with-
out doubt she must have the noblest courage, quite extraordinary
talents and superior genius.
Remembering that Sophie Germain was completely self-taught in mathematics
and had little time to learn physics, which was increasingly developing its own
considerable body of theory, we can only marvel that she had the courage to enter
a prize competition in 1811 for the best paper on the vibration of an elastic plate.
She had to start from zero in this enterprise, and Lagrange had warned that the
necessary mathematics simply did not yet exist. According to Dahan-Dalmedico
(1987, p. 351), she had learned mechanics from Lagrange's treatise and from some
papers of Euler "painfully translated" from Latin. It is not surprising that her
paper contained errors and that she did not win the prize. Actually, no one did;
she was the only one who ventured to enter. Even so, her paper contained valuable
insights, in the form of modeling assumptions that allowed the aged Lagrange to
derive the correct differential equations for the displacement of the middle plane of
the plate. She then set to work on these equations and in 1816 was awarded a prize
for her work. This work became fundamental in the development of the theory of
elasticity during the nineteenth century.
Perhaps because of the inevitable deficiencies resulting from her inadequate
education, but more likely because she was a woman, Sophie Germain never received
the respect she obviously deserved from the French Academy of her time. Prominent
academicians seem to have given her papers the minimum possible attention. In
their defense, it should be said that they were a galaxy of brilliant stars—Cauchy,
Poisson, Fourier, and others—and it is unfortunate that their occasional neglect of
geniuses such as Sophie Germain and Niels Henrik Abel stand out so prominently.
Like the Marquise du Chatelet, Sophie Germain had a strong interest in phi-
losophy and published her own philosophical works. She continued to work in
mathematics right up to the end of her life, writing papers on number theory and
(^10) The divisibility hypothesis makes for a nice theorem, since it is obviously impossible to satisfy
if ç = 1 or ç = 2. It seems to explain why those cases are exceptions. However, we now know
that it is not a necessary hypothesis.