About Sophie Germain, the unsung hero of France

About the 18th century mathematician who managed to tackle the most difficult problems in mathematics in a society where women were not even allowed to study

(This article is taken from the programMaking history!', a bi-weekly podcast about the history of science and technology. )

In 212 BC, the forces of the Roman general Marcus Marcellus invaded the city of Syracuse (Syracuse) in Sicily. Syracuse was a Greek settlement, and the most famous of its sons was the philosopher Archimedes. Archimedes' name went before him in Rome as one of the greatest mathematicians, and General Marcus sought to protect him from the dangers of war. He sent one of his soldiers to bring Archimedes to him.

No one knows for sure what happened in the fateful meeting between Archimedes and the Roman messenger. It is a fact that Archimedes met his death. Legend has it that the Roman soldier found Archimedes engrossed in solving a complicated geometric problem. He demanded that Archimedes come with him, but he replied: "Don't disturb my circuits." The soldier got mad at Archimedes and killed him.

Almost two thousand years later, in 1789, a young Parisian girl rummaged through her father's bookshelves and found a book about the history of mathematics. She read it eagerly, and was especially fascinated by the story of Archimedes. If a person can be so engrossed in a mathematical problem that he is willing to risk his life to solve it, then mathematics must be a particularly interesting pursuit! From that moment the girl decided to dedicate her life to the science of numbers.

The young woman's name was Sophie Germain, and the decision she made at the age of thirteen went against all social conventions. A woman in eighteenth-century France was not supposed to be educated. At most, women from the upper class, the aristocracy, were allowed to acquire a little general knowledge so that they could have a fluent conversation with their husbands.

Her parents anxiously followed their daughter's new hobby. Out of desperation, they tried to force Sophie to abandon mathematics. When Sophie stayed up at night to read books, her father confiscated all the candles in the house. When she sneaked into the library, he took all her clothes so she couldn't leave the room. Sophie did not give up. She hid makeshift candles in drawers, and continued to read math books under the blanket in the freezing Parisian cold. Finally the parents had to give up. They realized that the mathematical bug was incurable, and decided to support their daughter.

After devouring all the math books she could find, Sophie realized that if she hopes to one day become a real scientist, she must acquire an education. In Paris, right near it, a prestigious science school was recently opened: the Polytechnic. The mathematics lecturer at the Polytechnic was none other than Joseph Louis-Lagrange, one of the greatest analytical minds of all time, a genius of stature.

For Sophie, the polytechnic could also have been in another country. This respectable institution was locked and closed to women - she had no chance of being admitted to it. To be accepted...in acceptable ways, that is.

One of Sophie Germain's acquaintances was Antoine LeBlanc, a boy of her age. Sophie, who had a passion for mathematics, couldn't even get into the Polytechnic but LeBlanc, who was a walking accident when it came to numbers and arithmetic, was a full-fledged student by virtue of being 'Monsieur'. For one reason or another, Antoine decided to leave the polytechnic - but for some reason the school's secretariat did not receive the notification about this. Sophie noticed the bureaucratic confusion, and realized that she had fallen into her hands a gift from heaven.

Elegantly and without arousing suspicion, Sophie stepped into Antoine's (small, intellectually speaking) shoes. She received the summaries of the lectures and exercises that were intended for him, and submitted the homework on his behalf. This arrangement was perfect for her: she enrolled in the lectures of the great Joseph Lagrange and expanded her mathematical knowledge immeasurably - and no one at the Polytechnic noticed her - Blanc stopped coming to classes.
I mean - almost no one. In circumstances we do not know, Lagrange managed to reveal Sophie's secret, and remove the mask of 'Monsieur Le Blanc' from her face. But Lagrange was not angry with Sophie. He supported her, continued to teach and advise her and even introduced her to important scientists and intellectuals.
Sophie was encouraged by Lagrange's support and recognition of her skills. She knew that as a woman, she had to succeed in a big way to gain the attention of the other French scientists. Sophie decided to aim high, very high - and try to solve the greatest mathematical puzzle of all: Fermat's last theorem.

The Pythagorean theorem is one of the most well-known and basic laws of mathematics: X2+Y2=Z2. This equation has many solutions - that is, three numbers (X, Y and Z) that satisfy the equation. For example: 3^2+4^2=5^2. Pierre de Ferme was a mathematician who lived one hundred and fifty years before Sophie. Fermat examined equations of similar form to the Pythagorean equation, but with different powers than 2: for example, X3+Y3=Z3 or X4+Y4=Z4. Despite the obvious resemblance to the Pythagorean theorem, Fermat claimed that all these equations had no solution. That is to say, no matter what power is chosen, for example - X10+Y10=Z10, there is no group of three numbers that satisfies it. In the days of Sophie Germain, after countless efforts, mathematicians managed to prove the theorem only for the third and fourth powers. The solution to this puzzle is not even in sight. When Sophie was 25 years old, the book 'Arrhythmic Studies' by Carl Friedrich Gauss was published. The book ignited in her mind possible ideas for solving Fermat's Last Theorem, and she asked to share them with Gauss.

Sophie was a very good mathematician and Agrange was one of the best - but Gauss was something else. He was a genius the likes of which only appear once every few hundred years. No wonder, then, that Sophie adored the ground upon which Gauss's foot had trod. She didn't want to take the risk of Gauss rejecting her letters due to her being a woman, so she went back to assuming the identity of good old Monsieur LeBlanc. The German genius was very impressed by the understanding and originality demonstrated by the young Frenchman, Monsieur LeBlanc, and wrote to her - "I am happy that mathematics has found such a talented friend in you."

Gauss and Sophie corresponded back and forth. He encouraged her to continue trying to prove Fermat's theorem, and wrote to her that her ideas were in the right direction. Gauss's support was of immense importance to Sophie. But in 1806 this friendship was in danger. Napoleon Bonaparte fought the Prussians to expand his French empire and Brunswick - Gauss's city - was occupied by the French army.

Well, there might be a little unnecessary drama here. After all, the French army is not the most terrifying army in the world. Bureau-Disney is said to have banned the use of fireworks because every time a firework is fired, the French army tries to surrender. It is also said that a French tank has four gears for traveling in reverse and one gear for traveling forward, in case the enemy attacks from behind. The only reason the French won the French Revolution is probably because they fought other Frenchmen.

And yet, when Sophie heard about the events on the war front, she was filled with anxiety. She feared that the story of Archimedes would repeat itself again - and this time, Gauss in the role of the Greek genius and a French soldier in the role of the Roman legionnaire. One of the family's friends was a general in the French army, and Sophie sent him a telegram in Hall asking him to take care of Gauss's well-being.

When the officer arrived at the front, he approached Gauss's house, and showed him the letter that Sophie wrote in which she asked to protect his life. Gauss was confused. He was grateful for the unexpected assistance...but who is Mademoiselle Germaine? He did not know any French mathematician. The only French mathematician that Gauss knew was… Monsieur… Le Blanc!

When the realization dawned on Gauss, he wasn't angry at Sophie for cheating on him. On the contrary: "I cannot describe to you," Gauss wrote to Sophie, "I was surprised when I realized the true identity of Monsieur LeBlanc... The love for the abstract sciences and the mysteries of numbers is extremely rare, and the charms of this science reveal themselves only to those who have the courage to dive to their depths. But when a woman succeeds, despite the formidable difficulties arising from prejudices and cultural customs in your country, to overcome these obstacles... then without a doubt she must be brave and noble, possessing exceptional skills and a clear genius."

Sophie and Gauss continued to exchange letters for several months, until their relationship faded and died. Gauss was appointed to an official position at one of the universities and the academic load, combined with the fact that his interests wandered from the world of numbers to other fields, caused him to lose interest in Sophie's research but she continued, nevertheless, to work on Fermat's last theorem. She managed to show that every possible solution must be a huge number, thirty digits long or more, and greatly strengthened the feeling among researchers that Fermat's last theorem is true.

Gauss was not the only German who had a profound influence on Sophie's life. Ernst Chaldani was a physicist and musician who performed a very interesting experiment. He took metal beams, sprinkled fine sand on them - and played them with a violin bow. The pull of the bow caused the beams to vibrate and shake, and as a result the white sand on the beams arranged itself in strange and fascinating patterns. These forms were named 'Chaldeni patterns'.

While visiting Paris, Cialdani performed the experiment for Napoleon, who was very impressed by this interesting phenomenon. The French emperor offered a respectable reward - a whole kilogram of pure gold - to whoever could explain the results of Chaldani's experiment. The French Academy of Sciences picked up the gauntlet, and organized a competition between the scientists: the first to give a physical and mathematical explanation for Chaldani's experiment, will win the gold.

Sophie worked for two years on the explanation of the 'Chaldani patterns', and in 1811 she submitted her work to the prize committee. It turned out that Sophie was not only the first to submit a proposal for a solution - she was the only one! Unfortunately, there were flaws in Sophie's proposal - errors that stemmed mainly from a lack of formal education and too weak a background in physics. The committee decided not to award her the award. Personal disagreements between Sophie Germain and Simeon Poisson, one of the members of the committee who was a well-known and influential mathematician, also contributed to this decision.

The committee decided to extend the competition for another two years. In 1813, Sophie submitted another proposal to the committee - and again she was the only contender for the prize. But there were still errors and deficiencies in her work, and she was denied the prize.

The competition was extended for two more years, and Sophie submitted a third solution proposal - still the only competitor. This time the committee approved the solution, and Sophie finally won the long-awaited gold. Angry and resentful of the many rejections she received, Sophie refused to come to the award ceremony and boycotted it.

When Sophie was 53, she was diagnosed with breast cancer. After two years of stubborn struggle, Sophie passed away in 1831. She never married and had no children. Sophie published very few articles during her lifetime. Her important result about Fermat's Last Theorem, for example, appears only as a brief footnote in a paper by another mathematician with whom she worked.

Sophie Germain's story is a source of inspiration for many young women around the world. Her fight against discrimination and the narrow horizons of her male colleagues became a symbol of the victory of merit over cultural chains. And in the words of the historian Mozens:

"Looking back, Sophie Germain was probably the most intellectual woman France has ever produced...and yet, strange as it sounds, on her death certificate she appears as 'a woman without a profession' and not a 'mathematician'...was she pushed aside for the same reason that Bettia was not Was she entitled to be considered a full member of the French Academy of Sciences? If so, those responsible for this should be ashamed of themselves for forcing kindness against someone who has contributed so much to science, and whose achievements have earned her a place of honor in the hall of fame."