Marie-Sophie Germain (; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher.

The Academy of Sciences established the Sophie Germain Prize in her honor. ==Early life== ===Family=== Marie-Sophie Germain was born on April 1, 1776, in Paris, France, in a house on Rue Saint-Denis.

In 1789, he was elected as a representative of the bourgeoisie to the États-Généraux, which he saw change into the Constitutional Assembly.

After some time, her mother even secretly supported her. ===École Polytechnique=== In 1794, when Germain was 18, the École Polytechnique opened.

Fortunately, Lagrange did not mind that Germain was a woman, and he became her mentor. ==Early work in number theory== ===Correspondence with Legendre=== Germain first became interested in number theory in 1798 when Adrien-Marie Legendre published Essai sur la théorie des nombres.

The first letter, dated 21 November 1804, discussed Gauss' Disquisitiones and presented some of Germain's work on Fermat's Last Theorem.

However, her proof contained a weak assumption, and Gauss' reply did not comment on Germain's proof. Around 1807 (sources differ), during the Napoleonic wars, the French were occupying the German town of Braunschweig, where Gauss lived.

In the same 1807 letter, Germain claimed that if x^n + y^n is of the form h^2 + nf^2, then x + y is also of that form.

Eventually his interests turned away from number theory, and in 1809 the letters ceased.

Then Poisson was elected to the Academy, thus becoming a judge instead of a contestant, and leaving Germain as the only entrant to the competition. In 1809 Germain began work.

She submitted her paper early in the fall of 1811 and did not win the prize.

Germain's anonymous 1813 submission was still littered with mathematical errors, especially involving double integrals, and it received only an honorable mention because "the fundamental base of the theory [of elastic surfaces] was not established".

In 1814 he published his own work on elasticity and did not acknowledge Germain's help (although he had worked with her on the subject and, as a judge on the Academy commission, had had access to her work). Germain submitted her third paper, "Recherches sur la théorie des surfaces élastiques", under her own name, and on 8 January 1816 she became the first woman to win a prize from the Paris Academy of Sciences.

In 1815, after the elasticity contest, the Academy offered a prize for a proof of Fermat's Last Theorem.

In 1814 he published his own work on elasticity and did not acknowledge Germain's help (although he had worked with her on the subject and, as a judge on the Academy commission, had had access to her work). Germain submitted her third paper, "Recherches sur la théorie des surfaces élastiques", under her own name, and on 8 January 1816 she became the first woman to win a prize from the Paris Academy of Sciences.

Seven years later this situation was transformed, when she made friends with Joseph Fourier, a secretary of the Academy, who obtained tickets to the sessions for her. ===Later work in elasticity=== Germain published her prize-winning essay at her own expense in 1821, mostly because she wanted to present her work in opposition to that of Poisson.

In the essay she pointed out some of the errors in her method. In 1826 she submitted a revised version of her 1821 essay to the Academy.

Of her essay in 1821, Cauchy said: "[it] was a work for which the name of its author and the importance of the subject both deserved the attention of mathematicians".

In the essay she pointed out some of the errors in her method. In 1826 she submitted a revised version of her 1821 essay to the Academy.

In Considérations, the work admired by Comte, Germain argues that there are no differences between the sciences and the humanities. ==Final years== In 1829 Germain learned that she had breast cancer.

Marie-Sophie Germain (; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher.

On 27 June 1831, she died from breast cancer.

So Augustin-Louis Cauchy, who had been appointed to review her work, recommended her to publish it, and she followed his advice. One further work of Germain's on elasticity was published posthumously in 1831, her "Mémoire sur la courbure des surfaces".

In 1831 Crelle's Journal published her paper on the curvature of elastic surfaces and "a note about finding and in \tfrac{4(x^p - 1)}{x - 1} = y^2 \pm pz^2".

Mary Gray records: "She also published in Annales de chimie et de physique an examination of principles which led to the discovery of the laws of equilibrium and movement of elastic solids." On 27 June 1831, she died in the house at 13 rue de Savoie. Despite Germain's intellectual achievements, her death certificate lists her as a "rentière – annuitant" (property holder), not a "mathématicienne".

When the matter of honorary degrees came up at the University of Göttingen in 1837—six years after Germain's death—Gauss lamented: "she [Germain] proved to the world that even a woman can accomplish something worthwhile in the most rigorous and abstract of the sciences and for that reason would well have deserved an honorary degree". ==Honors== ===Memorials=== Germain's resting place in the Père Lachaise Cemetery in Paris is marked by a gravestone.

Louis Bucciarelli and Nancy Dworsky, Germain's biographers, summarize as follows: "All the evidence argues that Sophie Germain had a mathematical brilliance that never reached fruition due to a lack of rigorous training available only to men." ==Germain in popular culture== Germain was referenced and quoted in David Auburn's 2001 play Proof.

This award, in the amount of €8,000, was established in 2003, under the auspices of the Institut de France. ==See also== Proof of Fermat's Last Theorem for specific exponents Sophie Germain Counter Mode Sophie Germain prime Sophie Germain Prize Sophie Germain's theorem Timeline of women in science ==Citations== ==References== reprinted as Bucciarelli, Louis L; Dworsky, Nancy (1980).

Clarke and Frederik Pohl, Sophie Germain was credited with inspiring the central character, Ranjit Subramanian, to solve Fermat's Last Theorem. A new musical about Sophie Germain's life, entitled The Limit, premiered at VAULT Festival in London, 2019. ==Sophie Germain Prize== The Sophie Germain Prize (Prix Sophie Germain), awarded annually by the Foundation Sophie Germain, is conferred by the Academy of Sciences in Paris.

The school houses a bust commissioned by the Paris City Council. In January 2020, Satellogic, a high-resolution Earth observation imaging and analytics company, launched a ÑuSat type micro-satellite named in honor of Sophie Germain. ===Honors in number theory=== E.

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