Auguste Eugene Leray painted this portrait (on the left) of Germain at 14. She had started studying mathematics a year earlier, despite her family's efforts to discourage her. A friend noted in her obituary that she studied "by getting up at night in a room so cold that the ink often froze in its well, working enveloped with covers by the light of a lamp even when, in order to force her to rest, her parents had put out the fire and removed her clothes and a candle from the room." Left picture and caption taken from Science News Online article referred to below. Right picture taken from Science article referred to below.

Links for Sophie Germain
1776-1831
Thank You, Sophie, and I'm Sorry, Scientific American article by Evelyn Lamb, 2017
"I'm sorry, Sophie, that the world was not ready to recognize or nurture your genius. I'm sorry you were never Professor Germain. I'm sorry that medicine could not heal you or ease your pain at the end. And I'm sorry for the thousands of other women just as bright as you who never got to share their gifts with the world."
"Voici ce que j'ai trouve [Here is what I have found]:" Sophie Germain's grand plan to prove Fermat's Last Theorem, 2010.
Seventy-five page article by Reinhard Laubenbacher and David Pengelley on Germain's recently discovered work on number theory.
"A study of Sophie Germain's extensive manuscripts on Fermat's Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a full-fledged, highly developed, sophisticated plan of attack on Fermat's Last Theorem. The supporting algorithms she invented for this plan are based on ideas and results discovered independently only much later by others, and her methods are quite different from any of Legendre's. In addition to her program for proving Fermat's Last Theorem in its entirety, Germain also made major efforts at proofs for particular families of exponents. The isolation Germain worked in, due in substantial part to her difficult position as a woman, was perhaps sufficient that much of this extensive and impressive work may never have been studied and understood by anyone."
An Attack on Fermat, two part article in Science News Online, February 23 and March 1, 2008.
Sophie Germain was the first to propose a realistic plan to prove Fermat's Last Theorem.
"The mathematician who developed the approach was respected by luminaries like Carl Friedrich Gauss, Adrien-Marie Legendre, and Joseph-Louis Lagrange, but was marginal in the mathematical community, with no formal training or university position. That's because the mathematician was a woman, indeed, the first woman to do significant research in mathematics."
A Woman Who Counted by Barry Cipra, article in the February 2008 issue of Science.
"Sophie Germain was one of the great mathematicians of the early 19th century. Number theorists laud her for 'Sophie Germain's theorem,' an insight into Fermat's famous equation xn + yn = zn aimed at establishing its lack of solutions (in positive integers) for certain exponents. Oddly, Germain's fame for her theorem stems not from anything she herself published but from a footnote in a treatise by her fellow Parisian Adrien-Marie Legendre, in which he proved Fermat's Last Theorem for the exponent n = 5. Now, two mathematicians have found that Germain did far more work in number theory than she has ever been given credit for.
Poring over long-neglected manuscripts and correspondence, David Pengelley of New Mexico State University in Las Cruces and Reinhard Laubenbacher of Virginia Polytechnic Institute and State University in Blacksburg have discovered that Germain had an ambitious strategy and many results aimed at proving not just special cases of Fermat's Last Theorem but the whole enchilada. 'What we thought we knew [of her work in number theory] is actually only the tip of the iceberg,' Pengelley said at a session on the history of mathematics. "
Wikipedia article
Includes an excerpt from Gauss' letter to her after learning that she was a woman,
and explains how she blew her cover in order to save his life.
"But how to describe to you my admiration and astonishment at seeing my esteemed correspondent Monsieur Le Blanc metamorphose himself into this illustrious personage who gives such a brilliant example of what I would find it difficult to believe. A taste for the abstract sciences in general and above all the mysteries of numbers is excessively rare: one is not astonished at it: the enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But 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 superior genius. Indeed nothing could prove to me in so flattering and less equivocal manner that the attractions of this science, which has enriched my life with so many joys, are not chimerical, [than] the predilection with which you have honored it."
Math's hidden woman from the PBS documentary on Fermat's Last Theorem, The Proof.
Its assertion that she stopped working on FLT after 1808 is incorrect. She worked much more on it and made some important discoveries that were never published. See the next link below.
"Germain's contribution would have been forever wrongly attributed to the mysterious Monsieur Le Blanc were it not for the Emperor Napoleon. In 1806, Napoleon was invading Prussia and the French army was storming through one German city after another. Germain feared that the fate that befell Archimedes might also take the life of her other great hero Gauss, so she sent a message to her friend, General Joseph-Marie Pernety, asking that he guarantee Gauss's safety. The general was not a scientist, but even he was aware of the world's greatest mathematician, and, as requested, he took special care of Gauss, explaining to him that he owed his life to Mademoiselle Germain. Gauss was grateful but surprised, for he had never heard of Sophie Germain. "
Sophie Germain and Fermat's Last Theorem
Sophie's long known work on Fermat's Last Theorem.
"We now know, of course, that Fermat's Last Theorem is true for every value of n > 2 thanks to the crowning work of Andrew Wiles, first described in 1993 and then published in 1995. But as L.E. Dickson wrote in 1917,

This challenge problem has received attention of many mathematicians of the highest ability, including Euler, Legendre, Gauss, Abel, Sophie Germain, Dirichlet, Kummer and Cauchy."
Encylopedia Britannica article
"As a girl Germain read widely in her fathers library and then later, using the pseudonym of M. Le Blanc, managed to obtain lecture notes for courses from the newly organized École Polytechnique in Paris. It was through the École Polytechnique that she met the mathematician Joseph-Louis Lagrange, who remained a strong source of support and encouragement to her for several years..."
St. Andrews biography
"At the age of thirteen, Sophie read an account of the death of Archimedes at the hands of a Roman soldier. She was moved by this story and decided that she too must become a mathematician..."
Sophie Germain: Revolutionary Mathematician
"On the establishment in 1795 of the Ecole Polytechnique, which women could not attend, Germain befriended students and obtained their lecture notes. She submitted a memoir to the mathematician J. L. Lagrange under a male student's name. Lagrange saw talent in the work, sought out the author, and was bowled over to discover it had been written by a woman. She continued to study, corresponding with leading mathematicians of the day...."
“Voici ce que j´ai trouv´e:” Sophie Germain’s grand plan to prove Fermat’s Last Theorem, 2010, (76 pages)
by Reinhard Laubenbacher and David Pengelley
A study of Sophie Germain’s extensive manuscripts on Fermat’s Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a fully-fledged, highly developed, sophisticated plan of attack on Fermat’s Last Theorem. The supporting algorithms she invented for this plan are based on ideas and results discovered independently only much later by others, and her methods are quite different from any of Legendre’s. In addition to her program for proving Fermat’s Last Theorem in its entirety, Germain also made major efforts at proofs for particular families of exponents. The isolation Germain worked in, due in substantial part to her difficult position as a woman, was perhaps sufficient that much of this extensive and impressive work may never have been studied and understood by anyone.
Top 10 Early Female Mathematicians
A list that includes Sophie Germain, Ada Lovelace (Augusta Byron, Countess of Lovelace) (1815-1852)
and Amalie Emmy Noether (1882-1935).

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