Sophie Germain
From Wikipedia, the free encyclopedia
- This article is about the mathematician Marie-Sophie Germain. See also Sophie Germain primes.
| Marie-Sophie Germain | |
 Marie-Sophie Germain
|
|
| Born | April 1, 1776 Paris, France |
|---|---|
| Died | June 27, 1831 (aged 55) |
| Nationality | French |
| Other names | Sophie, Auguste Antoine Le Blanc |
| 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, and to the study of Fermat's Last Theorem.
Contents |
[edit] 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 there upon 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]
Germain never formally attended any school or gained a degree. In order to read the works of Leonard Euler and Isaac Newton in their original professional languages, she taught herself Latin and Greek, and also taught herself geometry, algebra, and calculus.
[edit] 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.
[edit] 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.
[edit] 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.
[edit] 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:
[edit] Popular Culture
Germain is referenced and quoted in David Auburn's 2001 play Proof. The protagonist a young struggling female mathematician, who found great inspiration in the work of Germain.
[edit] 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.
- 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.
[edit] See also
[edit] Notes
- ^ Singh, Simon: "Fermat's Enigma", page 103. Walker and Company, 1997.
[edit] 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. doi:. JSTOR
- Amy Dahan Dalmédico (December 1991). "Sophie Germain". Scientific American 265: 116-122.
[edit] 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
- Voici ce que j'ai trouvé:": Sophie Germain's grand plan to prove Fermat's Last Theorem 2007
- Part 1: An Attack on Fermat , Part 2: A Mathematical Tragedy
- Dubreil-Jacotin on Sophie Germain from MacTutor
