Leah Leddin
History of Mathematics
Biography
Sophie Germain
(1776-1831)
‘An 18th-century woman who assumed a man’s identity in order to pursue her passion –
attempting to prove Fermat’s Last Theorem.’i
Many women in mathematics are not given enough credit as they are due for their
contributions to the studies just because they are women. The women that are
acknowledged work long and hard to be recognized and appreciated for their
contributions to the field of mathematics. But not many women can say that they not only
overcame the social prejudices but also the turmoil of the revolution to become a highly
recognized mathematician. Sophie Germain’s life was just that way, overcome by the
chaos of the French Revolution yet still destined for mathematical greatness.
Marie-Sophie Germain was born on April 1, 1776 in Paris, France. She was the
middle daughter of three girls, Marie-Madeleine and Angelique-Ambroise. Her father
was Ambroise-Francois Germain, a thriving middle class silk merchant who later became
a director of the Bank of France. Her mother was Marie-Madeleine. She was known as
Sophie to distinguish herself from all the Maries in the family.
At the age of thirteen, her parents kept her isolated in their home due to the
danger caused by the French Revolution in Paris. During this time Sophie kept herself
occupied by reading her father’s extensive library collection. While going through her
father’s books she came across one that gave an account of the death of Archimedes of
Singh, Simon. “Math’s Hidden Woman,” in FERMAT’S ENIGMA: The Epic Quest to Solve the World’s
Greatest Mathematical Problem. Walker and Company.
http://www.pbs.org/wgbh/nova/proof/germain.html
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Syracuse. The story is told 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.” ii
She was so affected by the story that she decided she too must study this subject a person
could be so captivated by that it resulted in their own death. She thought mathematics
must be an interesting subject.
Sophie pursued her desire to study mathematics. She once again turned to her
father’s library, now for her mathematical teaching material. Sophie began teaching
herself mathematics. She also taught herself Latin and Greek so she could read certain
math books. She read late into the night to study the works of Newton and Euler. Her
mother and father felt as though her interest in mathematics was inappropriate for a
woman, following the usual belief of the times that women were not suited to do
mathematics and they did all they could to discourage her from furthering her studies.
This just caused her to study at night while they were sleeping. Her parents even got to
the point where they were hiding her books, taking away the fire, her light, and taking her
clothes from her once she got into bed to force her to not study at night. All the effort
they put into keeping her away from mathematics, she found ways around it. She hid
candles and wrapped herself in bedding in order to continue her studies at night. Her
parents either got tired of trying or they realized she was determined to study
mathematics because they finally gave in to desire, even allowing her to remain at home
her entire life and support her financially since she never got married.
Perl, Teri. “Math Equals: Biographies of Women in Mathematics + Related Activities.” Menlo Park :
Addison-Wesley Publishing, 1978, p. 64.
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History of Mathematics
Biography
In 1794, the École Polytechnique opened in Paris. It was an academy ‘of
excellence’ to teach mathematicians and scientists. Though Sophie was not allowed to
enroll in the academy, men were only accepted, she was some how able to get the lecture
notes from several of the courses being taught and teach herself from the notes and
problems. This allowed her to continue her studies in mathematics with the opportunity to
learn from some of the most influential mathematicians of the time.
Instead of participating in lectures, she had the practice of sending back ideas and
insights to the professors and some times including her work on mathematical problems
along with them. When sending these she took the name of a former student of the
academy, Monsieur Antoine-August LeBlanc. She some how was able to intercept what
was intended for LeBlanc and she continued to submit her insights to the problems under
her false name. She took on this male name so she would be taken seriously, as many
females of the time did.
Sophie had a particular interest in the lecture notes of Joseph-Louis Lagrange.
After studying Lagrange’s lecture on analysis she submitted a paper to Lagrange.
‘LeBlanc’s’ insight into the subject impressed him so much, in part due to the change in
skills from this previously average student of his, that he wanted to arrange a meeting
with the person that wrote it. This request forced Sophie to reveal that a woman was the
actual writer behind the paper. Lagrange looked beyond her gender and saw the brilliance
of the work itself. He saw her abilities and became her mentor and friend. Though Sophie
never had the formal education she would have liked, she now had a teacher who could
help her take her skills to another level and inspire her. He remained a strong support and
source of guidance to her for several years. He also introduced her to various French
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History of Mathematics
Biography
mathematicians and scientists. This was important due to the fact that Sophie was not
able to acquire these contacts on her own because of her gender.
With the support of her mentor she grew in confidence, not only solving problems
in her studies but also exploring areas of mathematics not many had done. Her early work
was in number theory. This was motivated by the 1789 work of Andrien-Marie
Legendre’s Théorie des Nombres. Sophie wrote to Legendre about problems suggested in
his work. By then Legendre must have known that she was a woman because he was also
a professor at the École and Lagrange’s colleague. This started a chain of communication
that became a type of partnership. Legendre included some of Sophie’s discoveries in a
supplement to the second edition of the Théorie.iii Her method of Fermat’s Last Theorem
formed the basis for his proof of the theorem for the case n = 5. But how did she get
involved in such a famous problem?
Through Sophie’s interest in number theory, she came across Fermat’s Last
Theorem; xn + yn = zn has no positive integer solutions for x, y, z when n  2. She worked
on this for several years and when she got to the point where she thought she had a major
breakthrough she needed the insight of someone who knew the subject very well. In
1804, Sophie began consulting the top number theorist, Carl Friedrich Gauss. Her work
on Fermat’s Last Theorem, called Germain’s Theorem, is known as her greatest
contribution to mathematics but she was not initially given the credit she deserved for her
work. She was still very young, in her 20’s, when she wrote to Gauss and even though
she was known in Paris for her work, she did not think she would be taken seriously by
Gauss due to her gender.
iii
Osen, Lynn M. “Women in Mathematics.” Cambridge, Mass. : MIT Press, 1977, c1974.
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History of Mathematics
Biography
She began writing him, under her male name, concerning his work of 1801,
Disquisitiones Arithmeticae. He was quite impressed with the work he was receiving and
many times told of this to colleagues. Sophie’s work on Fermat’s Last Theorem was
more general than other work Gauss had seen. She looked at the broader spectrum of the
problem, looking at several equations rather than trying to figure out just one equation.
‘In her letter to Gauss she outlined a calculation which focused on those equations in
which n is equal to a particular type of prime number.
Prime numbers are those numbers which have no divisors. For example, 11 is a
prime number because 11 has no divisors, i.e. nothing will divide into 11 without leaving
a remainder (except for 11 and 1). On the other hand, 12 is not a prime number because
several numbers will divide into 12, i.e., 2, 3, 4, and 6. Germain was interested in those
prime numbers p such that 2p + 1 is also a prime number. Germain’s list of primes, now
known as the Sophie Germain prime, includes 5, because 11 (2 × 5 +1) is also prime, but
it does not include 13, because 27 (2 × 13 + 1) is not prime.
For values of n equal to these Germain primes, she could show that there were
probably no solutions to the equation: xn + yn = zn. By “probably” Germain meant that it
was unlikely that any solutions existed, because if there was a solution, then either x, y,
or z would be a multiple of n. this put a very tight restriction on any solutions. Her
colleagues examined her list of primes one by one, trying to prove that x, y, or z could
not be a multiple of n, therefore showing that for that particular value of n there could be
no solutions.’iv This proof was significant in the study of mathematics due to the fact that
it restricted the possible solutions to Fermat’s Last Theorem. Before her, the only proofs
Singh, Simon. “Math’s Hidden Woman,” in FERMAT’S ENIGMA: The Epic Quest to Solve the World’s
Greatest Mathematical Problem. Walker and Company.
iv
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History of Mathematics
Biography
had been for specific cases of n. For prime exponents less than 100, she showed there
could be no solutions relatively prime to the exponent. The first few Sophie Germain
primes are. 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, and 131.v One of her other well known
mathematical identities was ‘commonly known as Sophie Germain’s Identity, which
states that for any two numbers x and y:’vi
x4 + 4y4 = (x2 + 2y2 + 2xy)(x2 + 2y2 – 2xy)
Though not much is mentioned about it when reading about Sophie, we use this today in
factorizing certain equations.
It was not until Sophie feared that Gauss’ life may be in danger that Gauss learned
of her true identity. Due to the French occupation of Gauss’ hometown of Braunschweig,
Sophie asked French commander General Joseph-Marie Pernety, a friend of her family,
to ensure Gauss’ safety.vii Even though Pernety was not a mathematician or scientist, he
knew of the greatest mathematician and took particular care of Gauss. When hearing that
Sophie Germain made the request of his safety Gauss was confused due to the fact that he
did not know of this name. Sophie wrote another letter to him when she heard this.
“In describing the honourable mission I charged him with, M. Pernety informed
me that he made my name known to you. This leads me to confess that I am not as
completely unknown to you as you might believe, but that fearing the ridicule attached to
a female scientist, I have previously taken the name of M. LeBlanc in communicating to
“Sophie Germain prime.” http://www.answers.com/topic/sophie-germain-prime
Osen, Lynn M. “Women in Mathematics.” Cambridge, Mass. : MIT Press, 1977, c1974.
vii
Katz, Victor J. “A History of Mathematics: An Introduction.” Reading, Mass. : Addison-Wesley, c1998,
p. 656.
v
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History of Mathematics
Biography
you those notes that, no doubt, do not deserve the indulgence with which you have
responded.”viii
When hearing that the brilliant person he was in touch with was a woman he was
taken back and he gave her even more respect as a mathematician.
“When a person of the sex which, according to our customs and prejudices, must
encounter infinitely more difficulties than men to familiarize herself with these thorny
researches, succeeds nevertheless in surmounting these obstacles and penetrating the
most obscure parts of them, then without doubt she must have the noblest courage, quite
extraordinary talents, and a superior genius.”ix
Her interaction with Gauss inspired much of her work in number theory. But in
1808 the letters stopped coming from Gauss. He had received the position of professor of
astronomy at the University of Göttingen and his interest in number theory also stopped.
Now that Sophie was without the guidance of Gauss she was in search of something new.
She turned to the work of a physicist.
Around this time the French Academy of Sciences was offering a prize for a
contest to explain the mathematical account of German physicist Ernst F.F. Chladni’s
study of patterns produced by vibration. “Formulate a mathematical theory of elastic
surfaces and indicate just how it agrees with the empirical evidence.”x Sophie accepted
the challenge and spent the next two years trying to derive a theory of elasticity. In 1811
she entered an anonymous paper into the contest. Her paper was the only one submitted.
Errors were found and it was evident that she had no formal education, but that did not
“A quotation by Sophie Germain.” http://www-history.mcs.st-andrews.ac.uk/Quotations/Germain.html
Edwards, Harold M. “Fermat’s Last Theorem: A Genetic Introduction to Algebraic Number Theory.”
New York : Springer-Verlag, c1977, p. 61.
x
O’Connor, J J and E F Robertson. “Marie-Sophie Germain.” December 1996. http://www-groups.dcs.stand.ac.uk/~history/Biographies/Germain.html
viii
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History of Mathematics
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stop her from moving forward in the subject. Lagrange, being one of the judge’s of the
contest, was able to make the corrections in Sophie’s paper. But she was not awarded the
prize. The contest was extended two years later and again she was the only one who
entered it. Her paper this time was better showing the corrections she missed that last
time but she was still not able to fulfill the requirements from the physical principles.
Again, she was not awarded the prize but she was given an honorable mention. And again
the contest was extended.
Sophie submitted a paper titled “Memoir on the Vibrations of Elastic Plates” and
was finally awarded the prize of a medal of one kilogram of gold in 1816. Her paper laid
the foundations for the modern theory of elasticity and was published privately in 1821,
though she received word that there were still some insufficiencies in her work. ‘What
should have been Sophie’s greatest achievement and source of pride, however, turned
into a bittersweet victory. She received a laconic response from Siméon Denis Poisson,
one of the judges and chief rival on the theory of elasticity, who wrote that her analysis
still contained deficiencies and lacked mathematical rigor.’xi
Even though her work had earned her the prize, she did not go to the award
ceremony. She felt that the judges and the community didn't really respect her work.
“Although it was Germain who first attempted to solve a difficult problem, when others
of more training, ability, and contact built upon her work, and elasticity became an
important scientific topic, she was closed out. Women were simply not taken
Musielak, Dora. “Sophie Germain’s Biography” in Sophie’s Diary: A Historical Fiction Book.
http://www.sophiesdiary.net/id2.html
xi
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seriously.”xii But she did continue to study in the field of the theory of elasticity and
published several additional works. Her work in the theory of elasticity is important today
as it is used in the construction of skyscrapers and the applied mathematics associated
with them.
Sophie met Jean-Baotiste-Joseph Fourier, well known mathematician of heat
conduction and Secretary to the mathematical section of the Académie des Sciences, they
became friends and he had quite a few goods words to say about her. As a result of her
work on the theory of elasticity and Fermat’s Last Theorem, Sophie received honors from
the Institut de France and was invited to attend lectures there. She was even allowed to
attend meetings at the Académie des Sciences, with the help of her good friend Joseph
Fourier. She was the first woman not related by marriage to have the privilege to be able
to do so.
Though Sophie was privileged in being able to attend these functions, people tend
to think that during this time she was still isolated from the educational aspect of
mathematics. Most say it was still on account of her gender, she was discouraged, and
though there were new steps in the discovery of the theory of elasticity, she did not
advance her own work in the subject.
Towards the end of Sophie’s life she continued her work on her own and got back
in touch with Gauss, who convinced the University of Göttingen to award Sophie with an
honorary doctorate for her work in mathematics. Unfortunately the university was not
able to award her with the degree. Sophie died before she was able to receive it. Sophie
O’Connor, J J and E F Robertson. “Marie-Sophie Germain.” December 1996. http://www-groups.dcs.stand.ac.uk/~history/Biographies/Germain.html
xii
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History of Mathematics
Biography
Germain died at the age of 55, on June 27, 1831, after a few years battle with breast
cancer.
Historian H. J. Mozans stated of Sophie: “All things considered, she was probably
the most profoundly intellectual woman that France has ever produced. And yet, strange
as it may seem, when the state official came to make out her death certificate, he
designated her as a ‘rentière-annuitant’ (a single woman with no profession) – not as a
‘mathématicienne.’ Nor is this all. When the Eiffel Tower was erected, there was
inscribed on this lofty structure the names of seventy-two savants. But one will not find
in this list the name of that daughter of genius, whose researches contributed so much
toward establishing the theory of the elasticity of metals – Sophie Germain. Was she
excluded from this list for the same reason she was ineligible for membership in the
French Academy – because she was a woman? If such, indeed, was the case, more is the
shame for those who were responsible for such ingratitude toward one who had deserved
so well of science, and who by her achievements had won an enviable place in the hall of
fame.”xiii Sophie Germain’s death certificate listed her not as a mathematician or scientist,
but as a rentier (property holder).
Since her death, Sophie has been honored in many different ways. The house with
which she passed away in has been designated as a historical landmark. In Paris there is a
street, Rue Sophie Germain, that has been named in honor of her and there is a statue of
her that is in the courtyard of the Ecole Sophie Germain School.xiv Marie-Sophie
Singh, Simon. “Math’s Hidden Woman,” in FERMAT’S ENIGMA: The Epic Quest to Solve the World’s
Greatest Mathematical Problem. Walker and Company.
xiv
“Sophie Germain.” http://womenshistory.about.com/library/bio/blbio_sophie_germain.html
xiii
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History of Mathematics
Biography
Germain made a major contribution to number theory, acoustics and elasticity. She may
be given more credit after her death than during her life, but she is given the credit.
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History of Mathematics
Biography
Bibliography
1.
Singh, Simon. “Math’s Hidden Woman,” in FERMAT’S ENIGMA: The Epic
Quest to Solve the World’s Greatest Mathematical Problem. Walker and
Company. http://www.pbs.org/wgbh/nova/proof/germain.html
2.
Katz, Victor J. “A History of Mathematics: An Introduction.” Reading, Mass. :
Addison-Wesley, c1998, pp. 655-656.
3.
Swift, Amanda. “Sophie Germain.”
www.agnesscott.edu/lriddle/women/germain.htm
4.
Perl, Teri. “Math Equals: Biographies of Women Mathematicians + Related
Activities.” Menlo Park : Addison-Wesley Publishing, 1978.
5.
“Sophie Germain prime.” http://www.answers.com/topic/sophie-germain-prime
6.
Edwards, Harold M. “Fermat's Last Theorem: A Genetic Introduction to
Algebraic Number Theory.” New York : Springer-Verlag, c1977, p. 61.
7.
O’Connor, J J and E F Robertson. “Marie-Sophie Germain.” December 1996.
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Germain.html
8.
Osen, Lynn M. “Women in Mathematics.” Cambridge, Mass. : MIT Press, 1977,
c1974.
9.
“A quotation by Sophie Germain.” http://www-history.mcs.standrews.ac.uk/Quotations/Germain.html
10. Musielak, Dora. “Sophie Germain’s Biography” in Sophie’s Diary: A Historical
Fiction Book. http://www.sophiesdiary.net/id2.html
11. “Women in Science.” Detroit : Macmillan Reference USA, c2001.
12. “Celebrating Women in Mathematics and Science.” Edited by Miriam P.
Cooney. Reston, Va. : National Council of Teachers of Mathematics, c1996.
13. “Sophie Germain.”
http://womenshistory.about.com/library/bio/blbio_sophie_germain.html
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