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.

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.

But Gauss, it turned out, was unscathed by the war. In a letter from November 27 of 1806, included in the altogether fascinating Sophie Germain: An Essay in the History of the Theory of Elasticity (public library), the somewhat irate battalion commander reports to his chief:

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.

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.

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.

Her unusual life and enduring scientific legacy are discussed in great detail in the biography Sophie Germain. Complement it with the stories of how Ada Lovelace became the world’s first computer programmer, how physicist Lise Meitner discovered nuclear fission, was denied the Nobel Prize, but led the way for women in science anyway, and how Harvard’s unsung 19th-century female astronomers revolutionized our understanding of the universe decades before women could vote.