SOPHIE GERMAIN’S WORK IN    

                    NUMBER THEORY

        Marie-Sophie Germain ( 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library including ones by Leonhard Euler and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss. One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. 

Renewed interest

Germain's best work was in number theory, and her most significant contribution to number theory dealt with Fermat's Last Theorem. In 1815, after the elasticity contest, the Academy offered a prize for a proof of Fermat's Last Theorem. It reawakened Germain's interest in number theory, and she wrote to Gauss again after ten years of no correspondence.

In the letter, Germain said that number theory was her preferred field, and that it was in her mind all the time she was studying elasticity. She outlined a strategy for a general proof of Fermat's Last Theorem, including a proof for a special case. Germain's letter to Gauss contained her substantial progress toward a proof. She asked Gauss if her approach to the theorem was worth pursuing. Gauss never answered.