Sophie Germain Essay

1 Introduction

Marie-Sophie Germain, more commonly known as Sophie Germain, was born in Rue Saint-Denis in Paris, France on April 1, 1776 to a wealthy French family. Her father, Ambroise-François Germain, was a thriving silk merchant and Sophie grew up lacking for nothing. When the French Revolution began in 1789, Sophie Germain was thirteen years old and the political and social upheaval of the Revolution caused her and her family to remain indoors for much of that time period. In order to entertain herself, Sophie began reading books from her father’s library. Figure 1 shows Sophie as a young teenager [13].

Fig. 1 Sophie Germain

One day she read a book called L 'Histoire des Mathématiques, written by J.E. Montucla, which ignited in her a special interest in mathematics [12]. This book

Sophie also read various works from Carl Friedrich Gauss, a world-famous number theorist, and began corresponding with him, sharing her own proofs to various theorems. Of course, all her correspondence was done using her pseudonym M. LeBlanc.

3.1.1 Germain’s Attempt to Solve Fermat’s Last Theorem (FLT)

The Pythagoras Theorem naturally leads to a number theory problem, which has astounded and baffled mathematicians for over 300 years, and is the problem known as Fermat’s Last Theorem. It was conjectured by mathematician, Pierre de Fermat, in the late 1630s, when he wrote “"It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into two powers of like degree"[10].

If we translate his claim into our modern symbolic notation, we get the following theorem:

x^n+y^n= z^n has no positive integer solutions for x, y, and z when