Manual Oeuvres Philosophiques de Sophie Germain (French Edition)

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Despite this, notes Margaret. Alic , "she was viewed by her contemporaries as a phenomenon, not as a serious student in need of teaching and guidance. All abstract knowledge, all knowledge which is dry, it is cautioned, must be abandoned to the laborious and solid mind of man. For this reason, women will never learn geometry.

Germain was so taken with his theories of cyclotomy and arithmetical forms that in she sent him a copy of her own calculations, again employing the pen name M. The pair began a lively correspondence. When Napoleon's forces invaded Prussia and besieged Breslau, near Gauss' home, Germain apparently feared that Gauss might suffer a fate similar to that of Archimedes. She interceded on his behalf with General Pernety, a family friend. But Gauss denied knowledge of anyone named Sophie Germain when the general sent a messenger to enquire after Gauss' safety. The misunderstanding was cleared up when Germain admitted that she was not M.

Replied Gauss:. The tastes for the abstract sciences in general and above all, for the mysteries of numbers, is very rare: this is not surprising, since the charms of this sublime science in all their beauty reveal themselves only to those who have the courage to fathom them. But when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarizing herself with their knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius.

Gauss' admiration was not reserved for Sophie's ears alone. He also sang her praises to his colleagues, as a letter written to H. Oblers on July 21, , demonstrates:. Lagrange is warmly interested in astronomy and the higher arithmetic; the two test-theorems for which the prime 2 is a cubic or a biquadratic residue , which I also communicated to him some time ago, he considers "among the most difficult to prove. Germain's early research focused exclusively on number theory.

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However, by the turn of the century, the interests of French mathematicians were turning increasingly to the work of Ernst Chladni, a German physicist living and working in Paris. Chladni's research involved the vibration of elastic surfaces. By sprinkling sand on a metal sheet and striking the edge with a violin bow, he conducted experiments on elastic surfaces. The pattern formed by the sand's nodal lines was then recorded on a piece of paper. Interest in the vibrations of elastic materials dated back to the Pythagoreans, but no mathematical theory existed to explain the phenomenon.

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Napoleon was greatly impressed by Chladni's research and ordered the French Academy of Sciences to hold an essay competition on the subject. The question to be answered was: formulate a mathematical theory of elastic surfaces and indicate just how it agrees with empirical evidence. French mathematicians refused to enter the contest, following assurances from Lagrange that contemporary mathematical methods were unequal to the task. Sophie Germain, however, was intrigued by the challenge.

Œuvres philosophiques de Sophie Germain

She completed her entry in eight months and submitted the results anonymously on September 21, She was the sole entrant. Lagrange, who was a member of the selection committee, thought that her method of passing from a line to the surface was neither accurate nor complete. Thus, her entry was rejected. The Academy informed her that her mathematical equation was incorrect, although her hypothesis was plausible. The deadline for entries was extended until October For the next year and a half Germain worked on her second essay. Adrien Legendre, who also sat on the selection committee, wrote to her on December 4, , having just read the results:.

I do not understand the analysis you send me at all; there is certainly an error in the writing or the reasoning, and I am led to believe that you do not have a very clear idea of the operations on double integrals in the calculus of variations. Your explanation of the four points does not satisfy me any more.

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I will not try to point out to you all the difficulties in a matter that I have not especially studied and that does not attract me; therefore it is useless to offer to meet with you and discuss them. In , Germain's essay received an honorable mention from the French Academy of Sciences. Again the deadline for entries was extended. Germain, however, was concerned about the impartiality of some of the judges sitting on the selection committee.

In a letter to an unknown correspondent she wrote:. I enjoin your probation of memoir No. If I had found the occasion, I would have consulted you before adopting this quotation, since it has an air of pretentiousness, which hardly suits me, having so many reasons to mistrust my own skills and, indeed, not seeing any strong objection to my theory other than the improbability of having it meet with justice. I fear, however, the influence of opinion that M. Lagrange expressed. Without doubt, the problem has been abandoned only because this grand geometer judged it difficult.

Possibly this same prejudgment will mean a condemnation of my work without a reflective examination. Three years later, in , Sophie Germain's third essay was awarded the grand prize. She exposed the laws of vibrating elastic surfaces by describing a fourth-order partial differential equation which explained what was happening in Chladni's research. For her efforts, she was awarded a one kilogram gold medal, worth 3, francs. To the disappointment of the public, however, Germain refused to participate in the awards ceremony, which was held on January 8, One can only speculate as to the reason.

It should be noted, however, that Germain was not allowed to attend public sessions of the French Academy of Sciences until , when Joseph Fourier was elected permanent secretary. Winning the grand prize was the highlight of Sophie Germain's career. As a result, she was welcomed into mathematical circles and met Augustin L. A published version of Germain's work appeared in It was celebrated by Navier, who was so impressed with Sophie Germain's powers of analysis that he wrote of her research, "It is a work which few men are able to read and which only a woman was able to write.

Germain continued to pursue research on elasticity and published several other works on the topic. The most significant of these included an essay on the qualities and binding abilities of elastic surfaces and another work which explored the mysteries of the curvature of elastic surfaces. Her best work, however, was in the field of number theory. She proved Pierre de Fermat 's Last Theorem.

In , the American algebraist Leonard E. Dickson generalized her theorem to primes less than 1,, and, more recently, Barkley Roser extended the upper range to 41,, The interests of Sophie Germain were varied—from chemistry to physics, from geography to history. Enrico Guglielmo Mattia Olbers.

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Catalogo dei manoscritti ora posseduti da D. Baldassarre Boncompagni, by E. Roma: Tipografia delle Scienze Matematiche e Fisiche. Catalogo della insigne biblioteca appartenuta alla chiara memoria del Principe Baldassarre Boncompagni, Parte I. Roma: Cecchini. Bucciarelli, L. Dordrect: Reidel. Candido, G. Roma: Edizioni Cremonese. Comte, A. Cours de philosophie positive. Paris: Bachelier. Historia Mathematica — MathSciNet CrossRef. Del Centina, A.

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Letters of Sophie Germain Preserved in Florence. Historia Mathematica 60— Archive for History of Exact Sciences — Firenze: Olschki. Guglielmo Libri matematico e storico della matematica. Dickson, L. History of the Theory of Numbers , 3 vols. New York: Chelsea. Dunnington, G. New-York: Hafner. Edwards, H. New York: Springer.

Germain and proof of flt musielak

Gauss, C. Disquisitiones Arithmeticae , Lipsia apud Gerh.

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Genocchi, A. Atti della Accademia delle scienze di Torino — Alcune asserzioni di C. Teoremi di Sofia Germain intorno ai residui biquadratici. Germain, S. Annales de Chimie — Grattan-Guinness, I. Die Briefwechsel zwischen Gauss and Sophie Germain. Henry, C.