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A revolutionary mathematician

Name: Marie-Sophie Germain
Nationality: French
Lived: 1776-1831
Fields: Mathematics and physics
Claim to fame: Made progress on finding a proof for Fermat’s Last Theorem

Despite the French Revolution‘s claim to have abolished the class system, Sophie Germain‘s (1776-1831) status as an upper-middle-class woman meant that mathematics was
considered an unsuitable occupation. Through determination and the adoption of an alias, Germain overcame social prejudices to become celebrated in the field of number theory and mathematical physics.

Finding refuge in books

The daughter of a wealthy middle-class silk merchant, Marie-Sophie Germain was born in Paris on 1 April 1776, the second of three daughters. Following the storming of the Bastille in July 1789, in order to avoid the mayhem engulfing the streets of Paris, Sophie was forbidden from leaving the house. Escaping the boredom of being housebound, she delved into her father’s extensive library. Her interest in mathematics was piqued upon reading the tale of how the Ancient Greek mathematician Archimedes was killed whilst engrossed in a geometric conundrum during the Roman invasion of Syracuse. A subject that could so distract someone must be truly fascinating, Germain thought, and she decided to devote herself to the study of mathematics.

Studying under the covers

Alongside her mathematical enquiries, Germain also taught herself Latin and Greek so that she could read classical texts on the subject. Germain’s parents were disapproving of their daughter’s new-found interest so, to avoid their censure, she began to study at night. Upon discovering this, her parents did everything they could think of to stop it: removing her candles, forbidding fires at night, even taking away her clothes. However, nothing could deter the young mathematician, who found ways to continue her nocturnal learning, such as smuggling in candles and wrapping herself in her bedclothes. Eventually, her parents gave in to their daughter’s obvious determination.
Germain never married and continued to live in the family home, supported financially by her father, throughout her career.

The mysterious Monsieur le Blanc

Having exhausted the mathematical knowledge in her father’s collection of books, Germain craved ways of furthering her education. The problem was that, in 18th century France, women were not normally accepted by universities, including the famous École Polytechnique, founded in 1894 to educate middle-class boys in ‘practical’ knowledge, such as natural sciences and engineering.
To overcome this obstacle, Germain assumed the identity of a former student of the École Polytechnique who had left Paris. Under the name of M. le Blanc, she was able to get hold of the lecture notes of the mathematician Joseph-Louis Lagrange and began to send comments to the professors, including her own original notes on mathematical problems. Lagrange was so amazed by the remarkable observations of this M. le Blanc that he requested to meet with “him”. Germain was thus forced to reveal her true identity. Lagrange was astonished, but impressed, and went on to become her mentor and friend.

Quite extraordinary talents

Fascinated by number theory, Germain had also begun to correspond with the German Carl Friedrich Gauss, the greatest mathematician of the day. She put to him her novel approach to finding a proof for Fermat’s Last Theorem, which had troubled mathematicians for more than a century. Although Germain’s proposal did not lead to a defi nitive solution to the problem, it was the greatest breakthrough made on the subject until the 1960s.
Gauss, of course, believed that the idea had been that of M. le Blanc and it might have gone done in history as such, had it not been for the Napoleonic Wars. When the Emperor’s army invaded Prussia in 1806, Germain feared that Gauss might meet a similar fate as Archimedes. She sent a message to a family friend, General Joseph-Marie Pernety, asking him to guarantee Gauss’ safety. This he did, explaining to Gauss that he owed his safety to Mademoiselle Germain. Gauss was understandably confused, having never heard of Germain, but in her next letter she reluctantly revealed her identity. Gauss was delighted, saying that to overcome the difficulties of being a woman “she must have the noblest courage, quite extraordinary talents and superior genius”.

Good vibrations

The correspondence between Gauss and Germain ended abruptly in 1808 when he became a Professor of Astronomy and turned his interests away from number theory. Germain too changed her field of study to focus on physics, becoming particularly interested in so-called Chladni figures – the patterns produced by vibrations of elastic surfaces.
In 1811, the Académie des Sciences launched a competition on the mathematical law underlying Chladni’s study on vibrations of elastic surfaces. By the deadline in 1813, Germain’s was the only paper to have been entered. The judges found errors and it was clear that the paper’s author lacked a formal scientific education, so they extended the closing date. With the help of Lagrange, Germain reworked her thesis and was fi nally awarded the prize on 8 January 1816. The prize catapulted Germain into the ranks of the day’s prominent mathematicians and she continued to work on the elasticity theory. The Académie des
Sciences allowed her to be the first woman not related to a member to attend its sessions, and she was praised by the Académie’s over-arching body, the Institut de France, whose members invited her to their meetings.

Scientific achievements

Germain is best remembered for her advances in number theory, particularly the progress she made on finding a proof for Fermat’s Last Theorem. Her work on Chladni numbers laid the foundations for the applied mathematics used today in the construction of tall buildings, and which proved important at the time in the new field of mathematical physics, especially the study of acoustics and elasticity.
Once her true identity had been revealed, Germain found acceptance in the scientific community and was granted access to the world of academia that no French woman had previously achieved. Shortly before her death in 1831, Gauss (with whom she had regained contact) convinced the University of Göttingen to award Germain an honorary degree. Sadly, she died before she could accept it.


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