(April 1, 1776 - June 27, 1831)
Sophie Germain was born in an era
of revolution. In the year of her birth, the American Revolution
began. Thirteen years later the French Revolution began in her
own country. In many ways Sophie embodied the spirit of
revolution into which she was born. She was a middle class
female who went against the wishes of her family and the social
prejudices of the time to become a highly recognized
mathematician. Like the member of a revolution, her life was
full of perseverance and hard work. It took a long time for her
to be recognized and appreciated for her contributions to the
field of mathematics, but she did not give up. Even today, it is
felt that she was never given as much credit as she was due for
the contributions she made in number theory and mathematical
physics because she was a woman.
Sophie Germain was born in Paris on
April 1, 1776 to Ambroise-Francois and Marie Germain. Her family
was quite wealthy. Her father was a merchant and later became a
director of the Bank of France.
Sophie's interest in mathematics
began during the French Revolution when she was 13 years old and
confined to her home due to the danger caused by revolts in
Paris. She spent a great deal of time in her father's library,
and one day she ran across a book in which the legend of
Archimede's death was recounted. Legend has it that "during the
invasion of his city by the Romans Archimedes was so engrossed
in the study of a geometric figure in the sand that he failed to
respond to the questioning of a Roman soldier. As a result he
was speared to death" (Perl 64). This sparked Sophie's interest.
If someone could be so engrossed in a problem as to ignore a
soldier and then die for it, the subject must be interesting!
Thus she began her study of mathematics.
Sophie began teaching herself
mathematics using the books in her father's library. Her parents
felt that her interest was inappropriate for a female (the
common belief of the middle-class in the 19th century) and did
all that they could to discourage her. She began studying at
night to escape them, but they went to such measures as taking
away her clothes once she was in bed and depriving her of heat
and light to make her stay in her bed at night instead of
studying. Sophie's parents' efforts failed. She would wrap
herself in quilts and use candles she had hidden in order to
study at night. Finally her parents realized that Sophie's
passion for mathematics was "incurable," and they let her learn.
Thus Sophie "spent the years of the Reign of Terror studying
differential calculus" (Osen 85) without the aid of a tutor!
In 1794, when Sophie was 18, the
Ecole Polytechnique was founded in Paris. It was an academy
founded to "train mathematicians and scientists for the country"
(Perl 64). Women were not allowed to enroll in the academy, but
Sophie was able to obtain the lecture notes for several of the
courses and study from them. This gave her the opportunity to
learn from many of the prominent mathematicians of the day.
Sophie was particularly interested in the teachings of J. L.
Lagrange. Under the pseudonym of M. LeBlanc ( a former student
of Lagrange's), Sophie submitted a paper on analysis to Lagrange
at the end of the term. He was quite impressed with the work and
wanted to meet the student who had written it. Lagrange was
amazed that the author of the work was actually a female, but he
recognized her abilities and became her mentor. With a male to
introduce her, Sophie could enter the circle of scientists and
mathematicians that she never before could. Up until this point
not only had her gender been a hindrance to her, but her social
status had been too. It was socially acceptable for aristocratic
women to be taught the sciences and mathematics so that they
could talk about it casually with friends. Sophie was of the
middle class so this opportunity had passed her by.
In 1804, Sophie began corresponding
with the German mathematician, Carl Friedrich Gauss. She was
intrigued with his work in number theory and sent him some of
the results of her work in number theory. Again she used her
pseudonym to disguise her true identity. It was not until 1807
that he found out who M. LeBlanc truly was. He was thrilled to
find that his "pen pal" was a very gifted woman. In 1808 Germain
sent Gauss a letter describing some of her work in number
theory. Sophie never heard from him about her last
correspondence because he had stopped his work in number theory
after taking a job as professor of astronomy at the University
of Gottingen. About 12 years later, however, she wrote to the
mathematician Legendre about what would be her most important
work in number theory. "Germain proved that if x, y, and z are
integers and if x^5 + y^5 = z^5 then either x, y, or z must be
divisible by 5. Germain's theorem is a major step toward proving
Fermat's last theorem for the case where n equals 5"
(Dalmedico 119). Fermat's last theorem says that if x, y, z, and
n are integers then x^n + y^n = z^n cannot be solved for any n
greater than 2.
Gauss had guided Sophie's research,
so now she began to search for a new mentor. At about this time
the French Academy of Sciences announced a contest to explain
the "underlying mathematical law" of a German physicist's study
on the vibration of elastic surfaces. Sophie was fascinated and
set out to explain the law underlying Chladni's study. The
Academy set a two year deadline, and in 1811 Sophie submitted
the only entry in the contest. Her lack of formal education was
evident in the anonymous paper she submitted, and thus she was
not awarded the prize. She still had much to learn in the area.
Lagrange was able to correct her errors and two years later she
again entered the contest which had been extended. She received
honorable mention this time. Finally in 1816, she entered the
contest for the third time and won with her paper Memoir on the
Vibrations of Elastic Plates. Upon earning the prize, the judges
did relate that there were some serious shortcomings in her
explanation. These shortcomings would not be corrected for
decades. After winning the contest, Sophie continued her work on
the theory of elasticity publishing several more memoirs. The
most important of these deals with the "nature, bounds, and
extent of elastic surfaces" (Osen 90). Her work in the theory of
elasticity would prove to be very important to the field.
The prize from the Academy, however,
was of immediate importance because it introduced her into the
ranks of the prominent mathematicians of the time. She became
the first woman who was not a wife of a member to attend the
Academy of Sciences' sessions with the help of Jean-Baptiste-Joseph
Fourier. She was praised by the Institut de France and was
invited to attend their sessions. This was "the highest honor
that this famous body ever conferred on a woman" (Osen 90).
Sophie worked with a well-known male mathematician in the 1820s
as an "equal collaborator" (Dalmedico 122) to refine her proofs
and work in number theory.
Sophie Germain died at the age of
55, on June 27, 1831, after a battle with breast cancer. Shortly
before this Gauss, one of her earliest mentors, had convinced
the University of Gottengen to give Sophie an honorary degree.
She died before she could receive it.
Sophie Germain was a revolutionary.
She battled against the social prejudices of the era and a lack
of formal training in order to become a celebrated mathematician.
She is best known for her work in number theory, but her work in
the theory of elasticity is also very important to mathematics.
