Sophie Germain; Mathematician against all the Odds

Sophie Germain was a French girl born on 1 April 1776, at a time when scientific pursuits for girls were not encouraged (that's a euphemism for forbidden). When she was 13 (the same year the Bastille was stormed and the French revolution got under way) she came across a History of Mathematics, and was enthralled by the life of the great Greek mathematician Archimedes - but even more by his manner of death.

She read that when the mighty Romans finally broke through the brave defences and invaded his home city of Syracuse, the troops were ordered to spare the life of the famous man who had kept the invaders at bay with his ingenious `engines of war'. However, when a Roman soldier came upon Archimedes, he was, characteristically, engrossed with a geometrical diagram in the sand. He totally ignored the challenge of the soldier, who thereupon speared him to death in anger. Sophie figured that any subject which could hold a person in so much concentrated fascination must be worth studying, and she decided to teach herself maths - in particular number theory and calculus.

She would study late into the night the (difficult!) works of Newton and Euler, which worried her parents so much (after all, she was a GIRL) that they confiscated her candles and removed all heating from her room. That way she'd have to go to bed. She responded by building up a secret hoard of candles and then sitting at her table wrapped in blankets. Her parents wisely relented and funded her studies for the rest of her life.

Finding a school where she could be taught was a big problem since only males were admitted. Sophie, undaunted, found a student who was leaving Paris, Antoine-August Le Blanc, and secretly took his place, using his name to send and receive material from the recently opened Ecole Polytechnic. Joseph-Louis Lagrange was her supervisor and was astonished that this student could have improved so much - from a terrible student to one whose weekly assignments (sent of course by post) were the finest in the class. He asked to meet Mr Le Blanc and was astonished to find that the Mr was now a Miss! Unlike her previous tutors though, he was very pleased with her ambitions and became her personal guide and friend. She gained fame in Paris, and became one of the greatest number theorists of her time.

She decided to write to the great German mathematician Carl Friedrich Gauss about a possible breakthrough in her work on Fermat's Last Theorem. Fearing his response if he knew she was a woman, Sophie again called herself Mr Le Blanc. She was very nervous and respectful:

`Unfortunately, the depth of my intellect does not equal the keenness of my desire, and I feel a kind of temerity in troubling a man of genius...'

Gauss, impressed with her work, responded graciously: `I am delighted that arithmetic has found in you so able a friend.'

In 1806 the French Emperor Napoleon invaded Prussia and, fearing that her mentor Gauss might suffer the same fate as her hero Archimedes, she wrote to a friend who happened to be the General in charge of the advancing French forces, begging him to take care of Gauss. This he did, and told Gauss that he owed his life to the lady Sophie Germain. Gauss, of course had no idea who she could be, and Sophie felt obliged to reveal her true identity. Gauss, like Lagrange, was not at all displeased at the deception, and expressed his delight to her:

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 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 themselves only to those who have the courage to go deeply into it. But when a person of the sex which, according to all 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.

Sadly, when Gauss was appointed Professor of Astronomy at the University of Göttingen , his interests shifted to more applied maths, and he stopped replying to Sophie's letters on number theory. A year or so later she also moved away from pure maths, but made brilliant contributions to physics, helping to found the theory of elasticity with a paper called `Memoir on the Vibrations of Elastic Plates'. Gauss did not forget her - he persuaded the University of Göttingen to award her an honorary degree, but tragically, Sophie Germain died of breast cancer before this honour could be conferred upon her.

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