A century after the trailblazing French mathematician Émilie du Châtelet popularized Newton and paved the path for women in science, and a few decades before the word “scientist” was coined for the Scottish mathematician Mary Somerville, Sophie Germain
(April 1, 1776–June 27, 1831) gave herself an education using her
father’s books and became a brilliant mathematician, physicist, and
astronomer, who pioneered elasticity theory and made significant
contributions to number theory.
In lieu of a formal education, unavailable to women until more than a century later,
Germain supplemented her reading and her natural gift for science by
exchanging letters with some of the era’s most prominent mathematicians.
Among her famous correspondents was Carl Friedrich Gauss, considered by
many scholars the greatest mathematician who ever lived. Writing under
the male pseudonym M. LeBlanc — “fearing the ridicule attached to a
female scientist,” as she herself later explained — Germain began
sharing with Gauss some of her theorem proofs in response to his magnum
opus Disquisitiones Arithmeticae.
Sophie Germain
Their correspondence began in 1804, at the peak of the French
occupation of Prussia. In 1806, Germain received news that Napoleon’s
troops were about to enter Gauss’s Prussian hometown of Brunswick.
Terrified that her faraway mentor might suffer the fate of Archimedes,
who was killed when Roman forces conquered Syracuse after a two-year
siege, she called on a family friend — the French military chief M.
Pernety — to find Gauss in Brunswick and ensure his safety. Pernety
tasked one of his battalion commanders with traveling two hundred miles
to the occupied Brunswick in order to carry out the rescue mission.
Just arrived in this town and have bruised myself with
your errand. I have asked several persons for the address of Gauss, at
whose residence I was to gather some news on your and Sophie Germain’s
behalf. M. Gauss replied that he did not have the honor of knowing you
or Mlle. Germain… After I had spoken of the different points contained
in your order, he seemed a little confused and asked me to convey his
thanks for your consideration on his behalf.
Carl Friedrich Gauss (Portrait by Jensen)
Upon receiving the comforting if somewhat comical news, Germain felt
obliged to write to Gauss and clear his confusion about his would-be
savior’s identity. After coming out as the woman behind the M. LeBlanc
persona in a letter from February 20 of 1807, she tells Gauss:
The appreciation I owe you for the encouragement you have
given me, in showing me that you count me among the lovers of sublime
arithmetic whose mysteries you have developed, was my particular
motivation for finding out news of you at a time when the troubles of
the war caused me to fear for your safety; and I have learned with
complete satisfaction that you have remained in your house as
undisturbed as circumstances would permit. I hope, however, that these
events will not keep you too long from your astronomical and especially
your arithmetical researches, because this part of science has a
particular attraction for me, and I always admire with new pleasure the
linkages between truths exposed in your book.
Gauss responds a few weeks later:
Mademoiselle,
Your letter … was for me the source of as much pleasure as surprise.
How pleasant and heartwarming to acquire a friend so flattering and
precious. The lively interest that you have taken in me during this war
deserves the most sincere appreciation. Your letter to General Pernety
would have been most useful to me, if I had needed special protection on
the part of the French government.
Happily, the events and consequences of war have not affected me so
much up until now, although I am convinced that they will have a large
influence on the future course of my life. But how I can describe my
astonishment and admiration on seeing my esteemed correspondent M.
LeBlanc metamorphosed into this celebrated person, yielding a copy so
brilliant it is hard to believe? The taste for the abstract sciences in
general and, above all, for the mysteries of numbers, is very rare: this
is not surprising, since the charms of this sublime science in all
their beauty reveal themselves only to those who have the courage to
fathom them. But when a woman, because of her sex, our customs and
prejudices, encounters infinitely more obstacles than men in
familiarizing herself with their knotty problems, yet overcomes these
fetters and penetrates that which is most hidden, she doubtless has the
most noble courage, extraordinary talent, and superior genius. Nothing
could prove me in a more flattering and less equivocal way that the
attractions of that science, which have added so much joy to my life,
are not chimerical, than the favor with which you have honored it.
The scientific notes which your letters are so richly filled have
given me a thousand pleasures. I have studied them with attention, and I
admire the ease with which you penetrate all branches of arithmetic,
and the wisdom with which you generalize and perfect. I ask you to take
it as proof of my attention if I dare to add a remark to your last
letter.
With this, Gauss extends the gift of constructive criticism on some
mathematical solutions Germain had shared with him — the same gift which
trailblazing feminist Margaret Fuller bestowed upon Thoreau,
which shaped his career. Although Gauss eventually disengaged from the
exchange, choosing to focus on his scientific work rather than on
correspondence, he remained an admirer of Germain’s genius. He advocated
for the University of Gottingen to award her a posthumous honorary
degree, for she had accomplished, despite being a woman and therefore
ineligible for actually attending the University, “something worthwhile
in the most rigorous and abstract of sciences.”
She was never awarded the degree.
Red fish pond in front of the girls’ school named after Germain
After the end of their correspondence, Germain heard that the Paris Academy of Sciences had announced a prix extraordinaire
— a gold medal valued at 3,000 francs, roughly $600 then or about
$11,000 now — awarded to whoever could explain an exciting new physical
phenomenon scientists had found in the vibration of thin elastic
surfaces. The winning contestant would have to “give the mathematical
theory of the vibration of an elastic surface and to compare the theory
to experimental evidence.”
The problem appeared so difficult that it discouraged all other
mathematicians except Germain and the esteemed Denis Poisson from
tackling it. But Poisson was elected to the Academy shortly after the
award was announced and therefore had to withdraw from competing. Only
Germain remained willing to brave the problem. She began work on it in
1809 and submitted her paper in the autumn of 1811. Despite being the
only entrant, she lost — the jurors ruled that her proofs were
unconvincing.
Germain persisted — because no solution had been accepted, the
Academy extended the competition by two years, and she submitted a new
paper, anonymously, in 1813. It was again rejected. She decided to try a
third time and shared her thinking with Poisson, hoping he would
contribute some useful insight. Instead, he borrowed heavily from her
ideas and published his own work on elasticity, giving Germain no
credit. Since he was the editor of the Academy’s journal, his paper was
accepted and printed in 1814.
Still, Germain persisted. On January 8, 1816, she submitted a third
paper under her own name. Her solution was still imperfect, but the
jurors decided that it was as good as it gets given the complexity of
the problem and awarded her the prize, which made her the first woman to
win an accolade from the Paris Academy of Sciences.
But even with the prize in tow, Germain was not allowed to attend
lectures at the Academy — the only women permitted to audit were the
wives of members. She decided to self-publish her winning essay, in
large part in order to expose Poisson’s theft and point out errors in
his proof. She went on to do foundational mathematical work on
elasticity, as well as work in philosophy and psychology a century
before the latter was a formal discipline. Like Rachel Carson,
Germain continued to work as she was dying of breast cancer. A paper
she published shortly before her terminal diagnosis precipitated the
discovery the laws of movement and equilibrium of elastic solids.
