Marie-Sophie Germain
Marie-Sophie Germain
Born	April 1, 1776(1776-04-01) Paris, France
Died	June 27, 1831
Nationality	French
Other names	Sophie
Occupation	mathematician
Known for	differential geometry and number theory

Marie-Sophie Germain (April 1, 1776 – June 27, 1831) was a French mathematician who made important contributions to the fields of differential geometry and number theory. If you hold the copyright to an image (e. ... is the 91st day of the year (92nd in leap years) in the Gregorian calendar. ... For other uses, see 1776 (disambiguation). ... This article is about the capital of France. ... is the 178th day of the year (179th in leap years) in the Gregorian calendar. ... Leopold I 1831 (MDCCCXXXI) was a common year starting on Saturday (see link for calendar). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... is the 91st day of the year (92nd in leap years) in the Gregorian calendar. ... For other uses, see 1776 (disambiguation). ... is the 178th day of the year (179th in leap years) in the Gregorian calendar. ... Leopold I 1831 (MDCCCXXXI) was a common year starting on Saturday (see link for calendar). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...

Biography

Germain was born to a middle-class merchant family in Paris, France and at age 13, she read about Archimedes in a book in her father's extensive library. In this book, it said that he was so engrossed in his mathematics that he ignored a Roman soldier (one of the soldiers invading Syracuse) who would then killed him. This inspired the young Germain, as she thought that if someone could be so interested by mathematics as to not realise somebody was about to kill him, it must be an incredibly interesting subject.^{[citation needed]} This article is about the capital of France. ... For other uses, see Archimedes (disambiguation). ...

Mentorship with Lagrange

Germain was particularly interested in Joseph-Louis Lagrange's teachings and submitted papers and assignments under the pseudonym "Monsieur Le Blanc", a former student of Lagrange's. Lagrange was so impressed by the paper that he asked to meet with Le Blanc, and Germain was forced to reveal her identity to him. Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... For other uses, see Alias. ...

Correspondence with Gauss

In 1804 she began corresponding with Carl Friedrich Gauss, again using her pseudonym, after reading his famous Disquisitiones Arithmeticae (1801). He eventually learned her true identity in 1806, when Napoleon Bonaparte was invading Prussia and Gauss's birthplace, Brunswick. Fearful that Gauss would meet a fate like that of Archimedes, Germain requested that General Pernety, a friend of hers, personally ensure Gauss's safety. The general explained to Gauss that Germain had asked that he be protected, which confused Gauss since he had never heard of her. She then wrote to him admitting she was female, to which he responded: 1804 was a leap year starting on Sunday (see link for calendar). ... Johann Carl Friedrich Gauss (pronounced ,  ; in German usually Gauß, Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. ... The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ... The Union Jack, flag of the newly formed United Kingdom of Great Britain and Ireland. ... 1806 was a common year starting on Wednesday (see link for calendar). ... Bonaparte as general Napoleon Bonaparte ( 15 August 1769 – 5 May 1821) was a general of the French Revolution and was the ruler of France as First Consul (Premier Consul) of the French Republic from November 11, 1799 to May 18, 1804, then as Emperor of the French (Empereur des Français... For other uses, see Prussia (disambiguation). ... Map of Germany showing Braunschweig Braunschweig [ˈbraunʃvaik] (English & French: Brunswick) is a city of 245,500 people (as of December 31, 2004), located in Lower Saxony, Germany. ... For other uses, see Archimedes (disambiguation). ...

But how to describe to you my admiration and astonishment at seeing my esteemed correspondent Monsieur Le Blanc metamorphose himself into this illustrious personage who gives such a brilliant example of what I would find it difficult to believe. A taste for the abstract sciences in general and above all the mysteries of numbers is excessively rare: one is not astonished at it: the enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. Indeed nothing could prove to me in so flattering and less equivocal manner that the attractions of this science, which has enriched my life with so many joys, are not chimerical, [than] the predilection with which you have honored it.

However, in 1808 Gauss was appointed professor of astronomy at the University of Göttingen. His interest shifted to applied mathematics, and he stopped replying to her letters. Year 1808 (MDCCCVIII) was a leap year starting on Friday (link will display the full calendar) of the Gregorian calendar (or a leap year starting on Wednesday of the 12-day slower Julian calendar). ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. ...

Work on elastic surfaces

In 1811 Germain entered the French Academy of Sciences' contest to explain the underlying mathematical law of a German mathematician, attempting to explain Ernst Chladni's study on vibrations of elastic surfaces, in which she originated the concept of mean curvature. After failing twice she finally won in 1816, thus bringing her into the ranks of great mathematicians. She became the first female to attend sessions at the French Academy of Sciences—except the wives of other members. For the US Federal Agent designation, see Special agent. ... Louis XIV visiting the Académie in 1671 The French Academy of Sciences (Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... Ernst Chladni Ernest Florenz Friedrich Chladni (November 30, 1756–April 3, 1827) was a German physicist. ... Oscillation is the variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. ... Elasticity is a branch of physics which studies the properties of elastic materials. ... In mathematics, mean curvature of a surface is a notion from differential geometry. ... Year 1816 (MDCCCXVI) was a leap year starting on Monday (link will display the full calendar) of the Gregorian calendar (or a leap year starting on Saturday of the 12-day slower Julian calendar). ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

Contributions to number theory

One of Germain's major contributions to number theory was the following theorem: if x, y, and z are integers, and x⁵ + y⁵ = z⁵ then either x, y, or z has to be divisible by five. This proof, which she first described in a letter to Gauss, became quite significant as it restricted the possible solutions of Fermat's last theorem. One significant contribution is the concept of the Sophie Germain prime, which is a prime number p where 2p+1 is also prime. One of her most famous identities; commonly known as Sophie Germain's Identity, states that for any two numbers x and y: Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... The integers are commonly denoted by the above symbol. ... In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ... Pierre de Fermats conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised. ... A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. ... In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ...

x⁴ + 4y⁴ = (x² + 2y² + 2xy)(x² + 2y² − 2xy).

Later work

Later in life, her central contribution to mathematics was in the field of elasticity theory. For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Solid mechanics (also known as the theory of elasticity) is a branch of physics, which governs the response of solid material to applied stress (e. ...

With prompting from Gauss, in 1830 the University of Göttingen agreed to award Germain an honorary degree, but before she received it she died on June 27, 1831. Liberty Leading the People by Eugène Delacroix commemorates the July Revolution 1830 (MDCCCXXX) was a common year starting on Friday (see link for calendar). ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... An honorary degree (Latin: honoris causa ad gradum, not to be confused with an honors degree) is an academic degree awarded to an individual as a decoration, rather than as the result of matriculating and studying for several years. ... is the 178th day of the year (179th in leap years) in the Gregorian calendar. ... Leopold I 1831 (MDCCCXXXI) was a common year starting on Saturday (see link for calendar). ...

Recognition

• Rue Sophie Germain in the 14^th arrondissement of Paris is named after her.
• Crater Germain on Venus is named after her.
• Lycée Sophie Germain is a high school in 4th arrondissement of Paris.

The 14th arrondissement, located on the Left Bank is one of the 20 arrondissements of Paris. ... This article is about the capital of France. ... For other uses, see Venus (disambiguation). ...

References

• M. W. Gray, Sophie Germain in Louise S. Grinstein (Editor), Paul J. Campbell (Editor) (1987). Women of Mathematics: A Bio-Bibliographic Sourcebook. Greenwood Press, New York. ISBN 978-0313248498. 
• M. Thomas a Kempis (1939). "An Appreciation of Sophie Germain". National Mathematics Magazine 14 (2): 81-90.  JSTOR

External links

• O'Connor, John J; Edmund F. Robertson "Sophie Germain". MacTutor History of Mathematics archive.  
• Sophie Germain at the Mathematics Genealogy Project
• A recent reappraisal of her work on Fermat Last Theorem
• Images of Sophie Germain
• A Mathematical Tragedy
• An Attack on Fermat