He replied, "How can I describe my astonishment and admiration on seeing my esteemed correspondent M leBlanc metamorphosed into this celebrated person. Although Gauss thought well of Germain, his replies to her letters were often delayed, and he generally did not review her work.
Eventually his interests turned away from number theory, and in the letters ceased. Despite the friendship of Germain and Gauss, they never met. When Germain's correspondence with Gauss ceased, she took interest in a contest sponsored by the Paris Academy of Sciences concerning Ernst Chladni's experiments with vibrating metal plates. The object of the competition, as stated by the Academy, was "to give the mathematical theory of the vibration of an elastic surface and to compare the theory to experimental evidence.
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 Germain began work. Legendre assisted by giving her equations, references, and current research. She submitted her paper early in the fall of , and did not win the prize.
The judging commission felt that "the true equations of the movement were not established," even though "the experiments presented ingenious results.
Seven years later this tradition was broken when she made friends with Joseph Fourier, a secretary of the Academy, who obtained tickets to the sessions for her. Germain published her prize-winning essay at her own expense in , 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.
Among her work done during this period is work on Fermat's Last Theorem and a theorem which has become known as Germain's Theorem. This was to remain the most important result related to Fermat 's Last Theorem from until the contributions of Kummer in She wrote to Gauss on 12 May [ 4 ] :- Although I have laboured for some time on the theory of vibrating surfaces to which I have much to add if I had the satisfaction of making some experiments on cylindrical surfaces I have in mind , I have never ceased to think of the theory of numbers.
A long time before our Academy proposed as the subject of a prize the proof of the impossibility of Fermat 's equation, this challenge Larry Riddle writes in [ 30 ] :- In this letter she laid out her grand plan to prove Fermat 's Last Theorem. Her letter and manuscripts found in various libraries showed her analysis for the primes p p p less than and for auxiliary primes with N N N from 1 to However, as Germain admitted to Gauss , she was unable to establish the existence of an infinite number of auxiliary primes even for a single prime exponent.
Indeed, Germain's grand plan was doomed to failure as it was later shown that for each odd prime p p p there are only a finite number of auxiliary primes that satisfy the non-consecutive p p p th power residue condition. Nevertheless, this was the first time anyone had devised a plan to prove Fermat 's Last Theorem for infinitely many prime exponents rather than on a case by case basis. Not only did she develop the theorem attributed to her independently from Legendre , in fact she did part of the additional work commonly credited to him, but she also proved or nearly proved results that were rediscovered many years later.
After almost years, her ideas were still central. Germain continued to work in mathematics and philosophy until her death. Her paper was highly praised by August Comte. She believed the intellectual universe is filled with analogies. The human spirit recognises these analogies, which then leads to the discovery of natural phenomena and the laws of the universe.
We should recognise the analogies between the life of Sophie Germain and our own, and they should lead us to strive for excellence in the face of prejudice. It is only recently that it has been discovered how distinctly he was anticipated in the main features of his system by Sophie Germain. Germain died in June at 13 rue de Savoie in Paris, which still stands today and has a commemorative plaque.
Her death certificate listed her not as mathematician or scientist, but 'rentier' property holder. In [ 35 ] the author quotes from H J Monans, Woman in Science :- And yet, strange as it may seem, when the state official came to make out the death certificate of this eminent associate and co-worker of the most illustrious members of the French Academy of Science , he designated her as a rentiere-annuitant - not as a mathematicienne.
Nor is this all. When the Eiffel Tower was erected in which the engineers were obliged to give special attention to the elasticity of the materials used, there were inscribed on this lofty structure the names of seventy-two savants. But one will not find in this list the name of that daughter of genius, whose researches contributed so much toward establishing the theory of the elasticity of metals, Sophie Germain.
Was she excluded from this list for the same reason that Agnesi was ineligible in the French Academy - because she was a woman? It would seem so. If such, indeed, was the case, more is the shame for those who were responsible for such ingratitude toward one who had deserved so well of science, and who by her achievements had won the enviable place in the hall of fame.
He refused the monetary component of this award, accepting instead an astronomical clock Germain and the institute's secretary bought for him with part of the prize. Gauss' biographer, G. Waldo Dunnington, reported that this pendulum clock was used by the great man for the rest of his life. Gauss survived her, expressing at an celebration that he regretted Germain was not alive to receive an honorary doctorate with the others being feted that day.
He alone had lobbied to make her the first such honored female in history. A hint of why Gauss valued her above the men who joined him in the Academie is expressed in a letter he sent to her in , to thank her for intervening on his behalf with the invading French military.
A taste for such subjects as mathematics and science is rare enough, he announced, but true intellectual rewards can only be reaped by those who delve into obscurities with a courage that matches their talents. Germain was such a rarity. She outshone even Joseph-Louis Lagrange by not only showing an interest in prime numbers and considering a few theorems, about which Lagrange had corresponded with Gauss, but already attempting a few proofs.
It was this almost reckless attack of the most novel unsolved problems, so typical of her it is considered Germain's weak point by twentieth century historians, that endeared her to Gauss. Germain's one formal prize, the Institut de France's Gold Medal Prix Extraordinaire of , was awarded to her on her third attempt, despite persistent weaknesses in her arguments.
For this unremedied incompleteness, and the fact that she did not attend their public awards ceremony for fear of a scandal, this honor is still not considered fully legitimate.
However, the labor and innovation Germain had brought to the subjects she tackled proved of invaluable aid and inspiration to colleagues and other mathematical professionals as late as In that year, L. Dickson, an algebraist, generalized Germain's Theorem to all prime numbers below 1,, just another small step towards a complete proof of Fermat's Last Theorem.
Germain died childless and unmarried, of untreatable breast cancer on June 27, in Paris. The responsibility of preparing her writings for posterity was left to a nephew, Armand-Jacques Lherbette, the son of Germain's older sister. Her prescient ideas on the unity of all intellectual disciplines and equal importance of the arts and sciences, as well as her stature as a pioneer in women's history, are amply memorialized in the Ecole Sophie Germain and the rue Germain in Paris.
The house on the rue de Savoie in which she spent her last days was also designated a historical landmark. Thirteen years later the French Revolution began in her own country. In many ways Sophie embodied the spirit of revolution into which she was born. She was a middle class female who went against the wishes of her family and the social prejudices of the time to become a highly recognized mathematician.
Like the member of a revolution, her life was full of perseverance and hard work. It took a long time for her to be recognized and appreciated for her contributions to the field of mathematics, but she did not give up. Even today, it is felt that she was never given as much credit as she was due for the contributions she made in number theory and mathematical physics because she was a woman.
Her family was quite wealthy. Her father was a merchant and later became a director of the Bank of France. Sophie's interest in mathematics began during the French Revolution when she was 13 years old and confined to her home due to the danger caused by revolts in Paris.
She spent a great deal of time in her father's library, and one day she ran across a book in which the legend of Archimedes' death was recounted.
Legend has it that "during the invasion of his city by the Romans Archimedes was so engrossed in the study of a geometric figure in the sand that he failed to respond to the questioning of a Roman soldier. As a result he was speared to death" Perl This sparked Sophie's interest.
If someone could be so engrossed in a problem as to ignore a soldier and then die for it, the subject must be interesting! Thus she began her study of mathematics. Sophie began teaching herself mathematics using the books in her father's library.
Her parents felt that her interest was inappropriate for a female the common belief of the middle-class in the 19th century and did all that they could to discourage her. She began studying at night to escape them, but they went to such measures as taking away her clothes once she was in bed and depriving her of heat and light to make her stay in her bed at night instead of studying. Sophie's parents' efforts failed.
She would wrap herself in quilts and use candles she had hidden in order to study at night. Finally her parents realized that Sophie's passion for mathematics was "incurable," and they let her learn.
Thus Sophie "spent the years of the Reign of Terror studying differential calculus" Osen 85 without the aid of a tutor!
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