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This article is about the mathematician Marie-Sophie Germain. See also Sophie Germain primes. In Number theory, a Prime number p is a Sophie Germain prime if 2 p  + 1 is also prime
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. Events 527 - Byzantine Emperor Justin I names his nephew Justinian I as co-ruler and successor to the throne Year 1776 ( MDCCLXXVI) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city This article is about the country For a topic outline on this subject see List of basic France topics. Events 1358 - Republic of Dubrovnik is founded 1709 - Peter the Great defeats Charles XII of Sweden Year 1831 ( MDCCCXXXI) was a Common year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry 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 Events 527 - Byzantine Emperor Justin I names his nephew Justinian I as co-ruler and successor to the throne Year 1776 ( MDCCLXXVI) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Events 1358 - Republic of Dubrovnik is founded 1709 - Peter the Great defeats Charles XII of Sweden Year 1831 ( MDCCCXXXI) was a Common year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry 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

Contents

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. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city This article is about the country For a topic outline on this subject see List of basic France topics. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer In it, she read that during the Roman invasion of Syracuse, Archimedes was so engrossed in his mathematics that he ignored a Roman soldier who thereupon killed him without comprehending the fame of his victim. This inspired the young Germain, as she thought that if someone could be so interested by mathematics as to not realize somebody was about to kill him, it must be an incredibly interesting subject.

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. A pseudonym is a fictitious alternative to a person's legal name (see Alias) 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.

Correspondence with Gauss

In 1804 she began corresponding with Carl Friedrich Gauss, again using her pseudonym, after reading his famous Disquisitiones Arithmeticae (1801). Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German The Disquisitiones Arithmeticae is a textbook of Number theory written by German Mathematician Carl Friedrich Gauss in 1798 He eventually learned her true identity in 1806, when Napoleon Bonaparte was invading Prussia and Gauss's birthplace, Brunswick. Napoleon Bonaparte (15 August 1769 – 5 May 1821 was a French military and political leader who had a significant impact on the History of Europe. Prussia ( Latin: Borussia, Prutenia; Prūsija Prūsija Prusy Old Prussian: Prūsa) was most recently a historic state Braunschweig, known as Brunswiek in Low German, is a city of 245810 people (as of 31 December 2007 located in Lower Saxony, Germany. 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. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer 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:

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. The University of Göttingen ( German: Georg-August-Universität Göttingen) is a University in the city of Göttingen, Germany. His interest shifted to applied mathematics, and he stopped replying to her letters. 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. The French Academy of Sciences ( French: Académie des sciences) is a Learned society, founded in 1666 by Louis XIV at the Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Ernst Florens Friedrich Chladni (ˈɛʀnst ˈfloːʀɛns ˈfʀiːdʀɪç ˈkladnɪ November 30, 1756 – April 3, 1827) was a German Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states A material is said to be elastic if it deforms under stress (e In Mathematics, the mean curvature H of a Surface S is an extrinsic measure of Curvature that comes from Differential After failing twice she finally won in 1816, thus bringing her into the ranks of great mathematicians. A mathematician is a person whose primary area of study and research is the field of Mathematics. She became the first female to attend sessions at the French Academy of Sciences—except the wives of other members.

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. 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 The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French In Mathematics, a divisor of an Integer n, also called a factor of n, is an integer which evenly divides n without 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. Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like One significant contribution is the concept of the Sophie Germain prime, which is a prime number p where 2p+1 is also prime. In Number theory, a Prime number p is a Sophie Germain prime if 2 p  + 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 One of her most famous identities; commonly known as Sophie Germain's Identity, states that for any two numbers x and y:

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. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Solid mechanics is the branch of Mechanics, Physics, and Mathematics that concerns the behavior of solid matter under external actions (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. The University of Göttingen ( German: Georg-August-Universität Göttingen) is a University in the city of Göttingen, Germany. An honorary degree or a degree honoris causa ( Latin: 'for the sake of the honour' is an Academic degree for which a university (or other degree-awarding Events 1358 - Republic of Dubrovnik is founded 1709 - Peter the Great defeats Charles XII of Sweden Year 1831 ( MDCCCXXXI) was a Common year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a

Recognition

References

External links

The MacTutor History of Mathematics archive is an award-winning website maintained by John J The Mathematics Genealogy Project is a web-based Database that gives an Academic genealogy based on Dissertation supervision relations
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