Sophie Germain
Learning about women mathematicians and inventors is an instance that presents must scepticism due to the Romanisation that only men in the early years have held interest in math or science. However, there were notable women figures as noted by Osen (1975) in these two fields that have enabled men to understand unfamiliar concepts these women were able to address. One of these women was the Frenchwoman Sophie Germain. Sophie Germain was born to Ambroise Francois and Marie Germain on April 1, 1776. France, in this period, was filled with political conflicts considering the late 18th century France was the beginning of the French Revolution. The Germains were a wealthy family and when Sophie was thirteen, they were able to shed her away from the tension and rebellion happening outside their home. Sophie was also slowly starting to show her extraordinary skills and genius. However, protecting her from the violence made Sophie experience countless hours of solitude in the midst of the books her father had.
It was due to the book “History of Mathematics” by J.E. Montucia, detailing the legend of Archimedes’ death, did she find the wonders of mathematics. For Sophie, Archimedes’ death due to a geometry problem and failing to see his ruthless assailant because of the said problem is intriguing. She believes that if geometry had such impact to the great mathematician to forget everything around him, geometry would present wonders for her to explore and learn. However, her thirst to divulge into mathematics was not immediately accepted by her family. Although they tried to move her away from this interest, it did not stop her from learning through every book she could find in their library. Her parents were concerned that Sophie’s health will deteriorate if she does not venture off in normal girl games or activities. Her parents have also been weary with stories about young, studious girls and feared for the possibilities on Sophie. They denied Sophie of any source of light and heat in her bedroom, even confiscating her clothes when she turned in for the night. Sophie accepted this treatment; however, she would sneak each night to use hidden candles and her quilt to work with the books she has snuck on her bedroom. She would study Etienne Bezout’s “Traite d’Arithmetique” where she learned geometry and algebra. She also taught herself Latin to understand Isaac Newton and Leonhard Euler’s works.
Sophie’s parents only agreed to allow her to study math when they found her sleeping in her desk one morning and saw her slate filled with calculations. Since the Reign of Terror was still on going, Sophie spent the years by studying differential calculus and other advanced mathematical theorems. When Ecole Polytechnique opened in 1794, Sophie collected many lecture notes from various professors as women were not allowed to enter the school. It was through J.L. Lagrange that Sophie was able to present her hypothesis on differential calculus under the alias M. le Blanc. Lagrange was impressed with Sophie’s deduction and analysis, seeking her out to commend her work . Bradley (2006) added that Lagrange visited Sophie and became her mentor. Lagrange also introduced her to European mathematicians such as Adrien-Marie Legendre, writer of “Essai sur le theorie des nombres” and Carl Friedrich Gauss, writer of “Disquisitiones arithmeticae”. Gauss became a correspondent to many of Sophie’s letters under Monsieur Le Blanc and discovered her real identity when Sophie wrote to him in the invasion of the French army in Gauss’ hometown Brunswick and had General Joseph-Marie Pernety to remove him from the warzone. Gauss supported Sophie’s ambition to be a mathematician and became friends despite the fact they did not see each other in person.
Sophie Germain would be known due to two of her analysis, first is the Prime Numbers and her take in the Fermat’s Theorem. With the prime numbers concept, Sophie worked with Legendre and Gauss to develop the number that is greater than 1, but cannot be divided by any positive number except number 1 or itself. An example of a prime number is the number 13 since the only way it can be divided without a remainder is by multiplying it by itself or with the number 1. The first prime numbers discovered by the trio are 2, 3, 5, 7, 11, 13, 17, and 19. A special prime number “p” was also studied by the trio. The special prime number was called the Sophie Germain prime and some examples of the prime are 2 (2x2+1=5), 3 (2x3+1=7) and 5 (2x5+1=11). Sophie Germain’s take on Fermat’s Last Theorem worked hand in hand with her prime numbers discovery. According to the original theory, Pierre de Fermat claimed that there were no integers that would satisfy xn+yn=zn if the exponent n is not greater than 2. Many have tried to break the theorem, however, when Sophie tried it, she believed that n is equal to p-1, where p is a prime number with the form p=8k+7. The proof was not correct, but through Gauss, Sophie persevered in working on the problem. By 1820, she discovered that the two conditions under the first case of the Last Theorem to be true. She noted that the conditions under the first half of the Fermat theorem are applicable to all odd primes less than 100, which is also the same for her Primes. She was awarded for her discovery and enabled Andrew Wiles to prove Fermat’s Last Theorem with her theorem .
As of today, mathematicians are still trying to study many of Sophie Germain’s analysis and dissertations, especially the Sophie Germain primes and her analysis of Fermat’s Last Theorem. Her prime numbers also became the benchmark for computer makers on which computer could discover the largest Sophie Germain prime number in existence. Cryptography also applied Sophie Germain primes to create digital signatures. Many theorists recognize Sophie’s theorem that sufficiently explains the Fermat’s Last Theorem which would remain unproven without her aid. Her perseverance in the world of Mathematics paved the way for other women mathematicians to showcase their talents regarding the subject known to be dominated by men.
Reference
Bradley, M. J. (2006). The Foundations of Mathematics: 1800 to 1900. New York: Infobase Publishing.
Osen, L. (1975). Women in Mathematics. Cambridge: MIT Press.
