Sophie Germain.html



This article is about the mathematician Marie-Sophie Germain. See also Sophie Germain primes.

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.

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 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.¹

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. He later became her mentor.

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:

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.

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.

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:

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.

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.

Recognition

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

References

1. ^ Singh, Simon: "Fermat's Enigma", page 103. Walker and Company, 1997.

• 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. doi:10.2307/3028203.  JSTOR

External links

• "Sophie Germain", Biographies of Women Mathematicians, Agnes Scott College
• O'Connor, John J.; Robertson, Edmund F., "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
• Dubreil-Jacotin on Sophie Germain
• Women in Science

Trivia

In the fictional work "The Last Theorem" by Arthur C. Clarke and Frederick Pohl, Sophie Germain is credited with inspiring Ranjit Subramanian to solve Fermat's Last Theorem.