# Prominent Mathematician: Marie-Sophie Germain

During the time of the uprising in French, a great mathematician by the name Marie-Sophie Germain was born in Paris on April 1, 1776. Even though at this time when revolution was taking place in French, unfortunately, this rebellion never favored women who were eager to venture into the competitive and male-dominated field of mathematics. Sophie Germain faced opposition from her father and male scholars who discouraged her from pursuing mathematics. At some point, polytechnics were built as part of education reforms, but still, females were denied opportunities to join. This did not deter Sophie Germain from pursuing mathematics. She posed as a male student and thereby obtaining lecture notes from male students. Despite all of these challenges, she pressed on and later emerged as one of the major contributors to developing mathematical concepts.

Sophie Germain was inspired by great scientists like Archimedes and Carl Friedrich Gauss. She spent most of her time around her father’s library, which may have influenced her reading culture. While reading at her father’s library, she came across an article talking about a great physicist called Archimedes who was accidentally killed when failed to respond to the instructions of a Roman soldier; this is because he was absorbed in his geometric drawings. Archimedes challenged her from that point she chose to pursue her interests in mathematics. We see circumstances that led to Archimedes death as being the major inspiration of her journey to being a great female mathematician in a male-dominated field. She goes ahead to overcome the language barrier by studying Greek and Latin to enable her to study early arithmetical works.

It is evident Sophie Germain was both influenced and challenged to nurture her talent in mathematics. For example, by posing as “M. Antoine August LeBlanc,” she submitted a paper on analysis to a great mathematician, Joseph-Louis Lagrange. Joseph-Louis classified it as exceptional and later introduced her to a club of mathematicians which she may have benefited in one way or another but she declined to join. This can be one reason why never achieved her full potential. We see that her work was never honored as a result of being unsystematic and aimless. By sticking to the club of mathematicians, Sophie Germain could have achieved much.

Other mathematicians such as Carl Friedrich Gauss contributed to her raising either directly or indirectly. By actively commenting on the topic “Disquisitiones Arithmeticae,” she drew the attention of Carl Friedrich Gauss who broadcasted her contribution to fellow mathematicians even though under a pen as “M. LeBlanc.” According to The Bridgeman Art Library (n.d, p.4), Gauss congratulated her verifications and spoke greatly of M. LeBlanc’s achievements in correspondences to other mathematicians. As it is known, positive feedback will always motivate an individual and Sophie Germain was no exception. We see later Gauss praising more Sophie Germain after he learnt that indeed, she was a woman and not a man claimed in her letters to him commenting on his formulas.

It is not easy to pinpoint, which field of mathematics did Sophie Germain specialized in. However, her quote says much about her passion for Algebra, “algebra is but written geometry and geometry is but figured algebra” (Germain, n.d, p.4). This is evident when she came up with an algebraic equation commonly referred to as “Germain primes” that was acknowledged by Adrien-Marie Legendre in his book. By the fact that Adrien-Marie Legendre acknowledged her work, may have challenged her to work even harder and contribute in this area of mathematics. Sophie Germain’s first theorem, now commonly referred to as Germain’s Theorem, states that “in the case when *n *is equal to certain prime numbers, now called *Germain primes*, the equation xn + yn = zn probably has no solutions. Germain primes satisfy the condition that if *n *is prime, then 2*n *+ 1 must also be a prime” (Franklin, 1981, p.7).

Germain went ahead and proved that if n is a prime number, then one of the digits represented by z, y, or x should be a multiple or manifold of n. By putting those conditions, she restricted possible results of the equation. Again, here we can see her breakthrough in algebra. By coming up with that equation, she successfully separated Fermat’s Last Theorem those that had a solution, and those that never had a solution such as when n is either 5 or 7.

A major achievement that might have made Sophie Germain be known is when she was the only one who “formulated a mathematical theory of elastic surfaces and indicated how it agreed with empirical evidence” (Germain, 2009, p.4). Even though her work had some flaws, she was the only one to offer an explanation when all other great mathematicians were defeated. This is a great achievement. Poor organization skills and lack of formal education was her major setback since she could not organize well her work and

link up physics and mathematic to explain phenomena that were being contested. In the same contest, after her third attempt, judges decided that her work was worth a prize. Unfortunately, she declined to attend the event when she felt that her work was not being given the credit it deserved and general disrespect of her contribution to mathematics by other scientists.

In short, Sophie Germain’s achievements that made her be known among mathematicians include: 1) explaining phenomena, which defeated all the great mathematicians of that time using mathematics and physics concepts.2) formulating a theorem that distinguished prime numbers with 5 and 7 lacking a solution. We see that even after repeated undermining of her effort to explain a physics phenomena, she continued working at her death in the year 1831. Just when she was at the top of her scientific career at the age of 55, it is when she died. Since she died before the honorary doctorate award organized by Gauss could be awarded to her, we can say that her achievements became well known in the mathematics community after her death. Up to date even after centuries of her departure, her work is still recognized.

Key challenges that might have challenged her to contribute were the fact that science was considered as a field of men only. We see that she used to hide her identity as a woman and only disclosed it only after receiving a compliment for the work. With a positive comment, she felt challenged to even work more and make a difference as a woman. We see again this when she was the only contender who submitted an explanation to a phenomenon and after three attempts she was finally recognized. More so, we see that the entire community never supports child girl education even after the revolution. This greatly hampered her success, as she could not connect mathematics and physics. Additionally, her lack of formal education was another reason why her work lacked organization skills and was a reason for rejection of her work.

Sophie Germain was a great mathematician whose contribution has gone a long way to shape mathematics centuries after her death. She is well known for her theory called “Germain’s Theorem” which is still applicable in modern days. After major contributions in the field of mathematics and specifically algebra, she was awarded a doctorate even after her death. Some of the challenges she faced included her work being undermined since was a woman and lacked formal education. More so, we see that the entire community never supported girl child education even after the revolution. This greatly hampered her success, as she could not connect mathematics and physics due to lack of formal education which may have offered her some required skills. Secondly, contrary to what we expected, her father also discouraged her and never took her to school to study. He does this to an extent that he took away her clothes, light, and fire that she was using to study. Sophie Germain goes and uses dim light coming through the window.

Several factors influenced her passion for mathematics and these include Archimedes’ love for science that he was killed when he failed to obey orders, positive comment from other mathematicians such as Gauss and Joseph-Louis Lagrange. They described her as a generous and courageous person with an amazing endowment.

## References

Franklin, C. (1981). Sophie Germain: unknown mathematicians. *Century AWM*, 11(3), 7-11.

Germain, R. (2009). *Biographies of women mathematicians*. New York, NY: Prentice Hall.

Germain, (n.d). “Marie-Sophie Germain,”. Web.

The Brigdement Art Library. (n.d). “Finding one inspiration.” Web.