Sophie Germain, Hidden Math

Etxebeste Aduriz, Egoitz

Elhuyar Zientzia

Ed. Manu Ortega

Paris, 1789. As the revolution erupts in the streets, the 13-year-old Sophie has been without leaving her home for days. He is in his father's library, reading a book.

When the Roman soldier arrived, Archimedes focused on a problem with a diagram drawn in the sand. The soldier asked him to surrender, but Archimedes ignored him, the problem was more important. "Don't spoil my circles," he said. Then the soldier killed Archimedes with sword.

Sophie was fascinated by the account of the death of Archimedes. If mathematics aroused such a passion in Archimedes, until forgetting the reality of its surroundings, it should be really interesting. Since then, Sophie Germain began to swallow all the mathematics books she found.

The parents did not like the new love of their daughter. A girl learning mathematics, was not adequate. And his daughter was forbidden to read these books. But he already had the thread of mathematics within. Trying to escape the prohibition of his parents, he began reading at night. When they heard of it, after putting the young man in bed, they began to remove clothes and light so that he would not rise. He also faced it; by harassing his parents, in the light of velitas he kept with blankets and hidden, Sophie continued to satisfy his passion.

One morning, when they found their daughter asleep on their desk, wrapped in the blanket, with the ink frozen in the inkwell and the notebook full of calculations, they realized that their daughter's passion was real and they began to yield.

In 1794, when Mademoiselle Germain was 18, they opened the École Polytechnique in Paris. For Germain it would have been a perfect place to study mathematics, but of course it was only for men. In that academy you could ask for notes without having to go to class and send in writing the results of the problems, etc. Germain takes the name of a student who left the academy: Monsieur Antoine-August Le Blanc. He obtained notes and wrote to École Polytechnique by signing with the name of Monsieur Le Blanc.

One of the professors of the Academy, Joseph Louis Lagrange, appropriated the brilliant work of Le Blanc and wanted to meet that young man. Germain could not hide his true identity. Lagrange was surprised to learn that she was a woman, but did not receive her badly, even more, it would help Germain to advance in the world of mathematics.

Little by little, Germain went from school problems to real research. He was interested in the theory of numbers and began to work with Fermat's last theorem. After several years, he needed to show his work to someone expert in number theory. And he decided to write to the best, the German Carl Friedrich Gauss.

For fear that Gauss would not take a woman seriously, he resigned the letter with the name of Le Blanc. In the same letter you can see the respect he made to Gaus: "Unfortunately my mind does not equal my enormous appetite, and I feel a kind of fear of disturbing a genius, when I have nothing to draw his attention, rather than an admiration I share with all his readers." But in fact he had much more than admiration to offer it and Gauss replied: "I am glad that arithmetic has found in you such a skilled friend." They continued to write letters.

Around 1807 the Napoleonic troops were occupying the German city of Braunschweig, where Gauss lived. Germain, thinking that Gauss could end up as Archimedes, wrote to General Pernety, a family friend, to ask him to ensure the safety of the mathematician. This was what the general did and told Gauss that he lived thanks to Sophie Germain. Gauss was surprised because he had never heard the name.

In the following letter, Germain confesses the truth to Gauss with suspicion. Gauss was fascinated: "How to describe my admiration and fascination by seeing the metamorphosis of my dear Monsieur Le Blanc... The fascinating charm of this supreme science only appears to those who have the mood to dive thoroughly into it. But when a woman, for being of this sex, for our customs and prejudices, has millions of difficulties to form in these thorny investigations that men, manages to overcome those barriers and reach the most hidden parts, then there is no doubt that she has the most noble courage and the unique talent; and that we are before a great genius."

Germain made important contributions to Fermat's last theorem. And then he abandoned pure mathematics and approached physics. It had much to do with an exhibition of the German physicist Ernst Chladni in 1808 in Paris. Chladnik, a sheet of metal containing a little sand, was driven by a violin bow, and the resonances so generated made the remains strange figures. Faced with this phenomenon, the Paris Academy of Sciences gave a special prize to those who "provided the mathematical theory of vibration of elastic surfaces and compared theory with experimental evidence".

Only Germain presented a work. He did not win the prize because he had some mistakes, it was evident that he did not have formal training. But the approach was direct. And with the help of Lagrange, he corrected errors and after presenting two other works, he finally won the prize.

The most important part of winning this prize was to open the circle of the best mathematicians. At first, however, he was not allowed to attend the Academy sessions, as women were forbidden to enter unless they were the women of their peers. Seven years later this tradition was broken: Germain became a friend of Joseph Fourier and as secretary of the Fourier Academy managed to open those doors to Germain.

Germain continued to work in mathematics and philosophy until in June 1831 he died affected by breast cancer. In his death certificate they put him rentière, not mathematical or scientific, rentista.

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