Number theory sophie germain biography

She continued to study the differential and integral calculus over the following years with the horrific events around her during the Reign of Terror in - 94 only helping her concentrate on her studies. There was no way, however, a girl could become a student. At the end of Lagrange 's lecture course he invited his students to send him their written observations.

Using the pseudonym M LeBlanc, Germain submitted a paper whose originality and insight made Lagrange look for its author. When Lagrange discovered "M LeBlanc" who had submitted a paper to him was a woman, his respect for her work remained and he became her sponsor and mathematical counsellor. Her education was, however, disorganised and haphazard and she never received the professional training which she wanted.

Lagrange certainly made his colleagues aware that Germain was a girl with mathematical talent and several of them wrote to her. Mongefor example, wrote to her about problems associated with a lever when infinitesimal changes in the position of a weight occur. Others discussed certain mathematical paradoxes with her. There was, however, no attempt to provide structured learning although Jacques Antoine-Joseph Cousin did offer to meet with her.

It is worth noting that, since Germain was an unmarried woman, there were social difficulties in her meeting with men. Not everyone treated her with the respect she felt she deserved. This "astronomy for ladies" does not contain a single mathematical equation and Germain felt insulted by his suggestion. Lalande sent her a letter of apology on 4 November but she never forgave him.

Another who offended her was the Hellenist, Anase de Villoisson. He did this by praising her in a poem he had written and we know how displeased she was from Villoisson's letter of apology written to her on 14 July see [ 35 ] :- Mademoiselle: I dare to take the liberty to offer you, adjoined to this, a sample of the new edition of my unfortunate work with corrections and additions which I have told you about.

I repeat with my excuses and lively and eternal regret on my word of honour that I should never have permitted myself to speak of you, Mademoiselle, in writing, and that my admiration will always be silent and enchained by the desire to obtain pardon for an error, or for an involuntary fault, and by the deep respect which I have vowed to your mother and sister.

I have the honour to be, Mademoiselle, Your humble and obedient servant, Anase de Villoisson. However, Germain's most famous correspondence was with Gauss. Between and she wrote a dozen letters to him, initially adopting again the pseudonym "M LeBlanc" because she feared being ignored because she was a woman. After receiving her first letter, Gauss wrote to the astronomer Heinrich Wilhelm Matthias Olbers - see, for example, [ 7 ] :- I recently had the pleasure of receiving a letter from LeBlanc, a young mathematician in Paris, who made himself enthusiastically familiar with higher mathematics and showed how deeply he penetrated into my 'Disquisitiones Arithmeticae'.

During their correspondence, Gauss gave her number theory proofs high praise, an evaluation he repeated in letters to his colleagues. Germain's true identity was revealed to Gauss only after the French occupation of his hometown of Braunschweig. Recalling Archimedes ' fate and fearing for Gauss 's safety, she contacted a French general who was a friend of her family.

Gauss knew neither the general nor Sophie Germain and, after he made enquiries, she was forced to reveal her identity, writing to him [ 4 ] :- I am not as completely unknown to you as you might believe, but that fearing the ridicule attached to a female scientist, I have previously taken the name of M LeBlanc in communicating to you. I hope that the information that I have today confided to you will not deprive me of the honour you have accorded me under a borrowed name Around sources differ[ 21 ] during the Napoleonic wars, the French were occupying the German town of Braunschweigwhere Gauss lived.

Germain, concerned that he might suffer the fate of Archimedes, wrote to General Pernety Joseph Marie de Pernetya family friend, requesting that he ensure Gauss's safety. Three months after the incident, Germain disclosed her true identity to Gauss. How can I describe my astonishment and admiration on seeing my esteemed correspondent M.

Le Blanc metamorphosed into this celebrated person Gauss's letters to Olbers number theory sophie germain biography that his praise for Germain was sincere. Although Gauss thought well of Germain, his replies to her letters were often delayed, and he generally did not review her work. When Germain's correspondence with Gauss ceased, she took interest in a contest sponsored by the Paris Academy of Sciences concerning Ernst Chladni 's experiments with vibrating metal plates.

The object of the competition, as stated by the academy, was "to give the mathematical theory of the vibration of an elastic surface and to compare the theory to experimental evidence". Lagrange's comment that a solution to the problem would require the invention of a new branch of analysis deterred all but two contestants, Denis Poisson and Germain.

Then Poisson was elected to the academy, thus becoming a judge instead of a contestant, [ 26 ] and leaving Germain as the only entrant to the competition. In Germain began work. Legendre assisted by giving her equations, references, and current research. The judging commission felt that "the true equations of the movement were not established", even though "the experiments presented ingenious results".

The contest was extended by two years, and Germain decided to try again for the prize. At first Legendre continued to offer support, but then he refused all help. This time she consulted with Poisson. After winning the academy contest, she was still not able to attend its sessions because of the academy's tradition of excluding women other than the wives of members.

Seven years later this situation was transformed, when she made friends with Joseph Fouriera secretary of the academy, who obtained tickets to the sessions for her. Germain published her prize-winning essay at her own expense inmostly because she wanted to present her work in opposition to that of Poisson. In the essay she pointed out some of the errors in his method.

In she submitted a revised version of her essay to the academy. According to Andrea Del Centina, the revision included attempts to clarify her work by "introducing certain simplifying hypotheses". This put the academy in an awkward position, as they felt the paper to be "inadequate and trivial", but they did not want to "treat her as a professional colleague, as they would any man, by simply rejecting the work".

So Augustin-Louis Cauchywho had been appointed to review her work, recommended her to publish it, and she followed his advice. She used the mean curvature in her research see Honors in number theory. Germain's best work was in number theory, [ 4 ] and her most significant contribution to number theory dealt with Fermat's Last Theorem. 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 asked Gauss whether her approach to the theorem was worth pursuing. Gauss never answered. Fermat's Last Theorem can be divided into two cases. Case 1 involves all powers p that do not divide any of xyor z. Case 2 includes all p that divide at least one of xyor z. Germain proposed the number theory sophie germain biography, commonly called " Sophie Germain's theorem ": [ 38 ].

Fearful of the ridicule associated at that time with female scientists, yet resourceful and determined, Sophie used the male pseudonym Monsieur Le Blanc in order to have access to various lecture notes for academic courses held at the Ecole Polytechnique near Paris. When she submitted her written observations, which was a requirement of the Polytechnique, to mathematician Lagrange, the faculty member was so impressed that he requested to meet the brilliant student who turned out to be a young girl, a fact which did not bother him at all.

Her research was significantly based on mean curvature, a term coined by the famous French mathematician herself. The mean curvature is essential in the analysis of minimal surfaces as well as of the physical interfaces between fluids in fluid mechanics. However, she managed to get lecture notes and send her work to Joseph Louis Lagrange a faculty member.

Sophie first developed interest in elasticity when she heard of a contest sponsored by the Paris Academy of Sciences. She submitted her paper inbut she did not win the prize. She later tried the same contest again but failed.

Number theory sophie germain biography

On her third attempt, however, she won and became the first woman to win a prize from the Paris Academy of Sciences. Sophie was first interested in number theory in after studying the works of Adrien-Marie Legendre. She later opened correspondence with him on number theory, and later, elasticity. After a while, Sophie lost interest in number theory.