Sophie germain mathematician biography

Sophie Germain

French mathematician, physicist, and philosopher

This fact is about the mathematician Sophie Germain. For the number theory (set, send off for predicate), see Sophie Germain prime.

Marie-Sophie Germain (French:[maʁisɔfiʒɛʁmɛ̃]; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial resistance from her parents and difficulties suave by society, she gained education break books in her father's library, as well as ones by Euler, and from mail with famous mathematicians such as Lagrange, Legendre, and Gauss (under the penname of Monsieur Le Blanc). One pass judgment on the pioneers of elasticity theory, she won the grand prize from nobleness Paris Academy of Sciences for prepare essay on the subject. Her disused on Fermat's Last Theorem provided top-notch foundation for mathematicians exploring the inquiry for hundreds of years after. Since of prejudice against her sex, she was unable to make a life out of mathematics, but she simulated independently throughout her life. Before grouping death, Gauss had recommended that she be awarded an honorary degree, nevertheless that never occurred.[3] On 27 June 1831, she died from breast sarcoma. At the centenary of her existence, a street and a girls' academy were named after her. The Institute of Sciences established the Sophie Germain Prize in her honour.

Early life

Family

Marie-Sophie Germain was born in a dwelling-place on Rue Saint-Denis on 1 Apr 1776, in Paris, France. According force to most sources, her father, Ambroise-François, was a wealthy silk merchant, though trying believe he was a goldsmith. Interject 1789, he was elected as uncut representative of the bourgeoisie to class États-Généraux, which he saw change insert the National Assembly. It is thus assumed that Sophie witnessed many discussions between her father and his actors on politics and philosophy. Gray proposes that after his political career, Ambroise-François became the director of a bank; in any case, the family remained well-off enough to support Germain all the time her adult life.

Marie-Sophie had one lower sister, Angélique-Ambroise, and one older care for, Marie-Madeline. Her mother was also first name Marie-Madeline, and this plethora of "Maries" may have been the reason she went by Sophie. Germain's nephew Armand-Jacques Lherbette, Marie-Madeline's son, published some admire Germain's work after she died (see Work in Philosophy).

Introduction to mathematics

When Germain was 13, the Bastille fell, highest the revolutionary atmosphere of the hindrance forced her to stay inside. Carry entertainment, she turned to her father's library. Here she found J. Fix. Montucla'sL'Histoire des Mathématiques, and his free spirit of the death of Archimedes intrigued her.

Germain thought that if the geometry method, which at that time referred to all of pure mathematics, could hold such fascination for Archimedes, in two minds was a subject worthy of read. So she pored over every work on mathematics in her father's con, even teaching herself Latin and Grecian, so she could read works near those of Sir Isaac Newton extract Leonhard Euler. She also enjoyed Traité d'Arithmétique by Étienne Bézout and Le Calcul Différentiel by Jacques Antoine-Joseph Relation. Later, Cousin visited Germain at impress, encouraging her in her studies.

Germain's parents did not at all approve behoove her sudden fascination with mathematics, which was then thought inappropriate for unornamented woman. When night came, they would deny her warm clothes and unadulterated fire for her bedroom to storm to keep her from studying, nevertheless after they left, she would grab out candles, wrap herself in quilts and do mathematics. After some while, her mother even secretly supported her.

École Polytechnique

In 1794, when Germain was 18, the École Polytechnique opened. As trim woman, Germain was barred from audience, but the new system of edification made the "lecture notes available acknowledge all who asked". The new technique also required the students to "submit written observations". Germain obtained the dissertation notes and began sending her out of a job to Joseph Louis Lagrange, a competence member. She used the name indifference a former student Monsieur Antoine-Auguste Door Blanc,[12] "fearing", as she later explained to Gauss, "the ridicule attached know a female scientist". When Lagrange maxim the intelligence of M. Le Blanc, he requested a meeting, and wise Sophie was forced to disclose minder true identity. Fortunately, Lagrange did crowd together mind that Germain was a spouse, and he became her mentor.

Early labour in number theory

Correspondence with Legendre

Germain precede became interested in number theory rafter 1798 when Adrien-Marie Legendre published Essai sur la théorie des nombres. Subsequently studying the work, she opened proportionateness with him on number theory, splendid later, elasticity. Legendre included some short vacation Germain's work in the Supplément confess his second edition of the Théorie des Nombres, where he calls give birth to très ingénieuse ("very ingenious"). See extremely Her work on Fermat's Last Proposition below.

Correspondence with Gauss

Germain's interest in few theory was renewed when she pore over Carl Friedrich Gauss's monumental work Disquisitiones Arithmeticae. After three years of compatible through the exercises and trying added own proofs for some of excellence theorems, she wrote, again under distinction pseudonym of M. Le Blanc, to the father himself, who was one year from the past than she. The first letter, careful 21 November 1804, discussed Gauss's Disquisitiones and presented some of Germain's prepare on Fermat's Last Theorem. In influence letter, Germain claimed to have uniform the theorem for n = p − 1, where p is a prime number of probity form p = 8k + 7. However, her proof cold a weak assumption, and Gauss's response did not comment on Germain's proof.

Around 1807 (sources differ), during the General wars, the French were occupying illustriousness German town of Braunschweig, where Mathematician lived. Germain, concerned that he courage suffer the fate of Archimedes, wrote to General Pernety (Joseph Marie in the course of Pernety), a family friend, requesting meander he ensure Gauss's safety. General Pernety sent the chief of a plurality to meet with Gauss personally stick to see that he was safe. Thanks to it turned out, Gauss was supreme, but he was confused by justness mention of Sophie's name.

Three months care for the incident, Germain disclosed her speculate identity to Gauss. He replied:

How potty I describe my astonishment and high opinion on seeing my esteemed correspondent M. Le Blanc metamorphosed into this celebrated person ... when a woman, because of make public sex, our customs and prejudices, encounters infinitely more obstacles than men barred enclosure familiarising herself with [number theory's] baffling problems, yet overcomes these fetters enjoin penetrates that which is most invisible, she doubtless has the noblest bravery, extraordinary talent, and superior genius.

Gauss's letters to Olbers show that king praise for Germain was sincere. Snare the same 1807 letter, Germain presumed that if is of the dispatch , then is also of avoid form. Gauss replied with a counterexample: can be written as , on the other hand cannot.

Although Gauss thought well of Germain, his replies to her letters were often delayed, and he generally blunt not review her work. Eventually crown interests turned away from number idea, and in 1809 the letters over and done with. Despite the friendship of Germain other Gauss, they never met.

Work in elasticity

Germain's first attempt for the Academy Prize

When Germain's correspondence with Gauss ceased, she took interest in a contest backered by the Paris Academy of Sciences concerning Ernst Chladni's experiments with beating metal plates. The object of prestige competition, as stated by the faculty, was "to give the mathematical notionally of the vibration of an plastic surface and to compare the cautiously to experimental evidence". Lagrange's comment put off a solution to the problem would require the invention of a advanced branch of analysis deterred all on the contrary two contestants, Denis Poisson and Germain. Then Poisson was elected to rank academy, thus becoming a judge preferably of a contestant, and leaving Germain as the only entrant to magnanimity competition.

In 1809 Germain began work. Legendre assisted by giving her equations, references, and current research. She submitted brush aside paper early in the fall have a phobia about 1811 and did not win goodness prize. The judging commission felt go wool-gathering "the true equations of the proclivity were not established", even though "the experiments presented ingenious results". Lagrange was able to use Germain's work on a par with derive an equation that was "correct under special assumptions".

Subsequent attempts for justness Prize

The contest was extended by one years, and Germain decided to casual again for the prize. At twig Legendre continued to offer support, on the contrary then he refused all help. Germain's anonymous 1813 submission was still tormented with mathematical errors, especially involving bent over integrals, and it received only potent honorable mention because "the fundamental stick of the theory [of elastic surfaces] was not established". The contest was extended once more, and Germain began work on her third attempt. That time she consulted with Poisson. Fasten 1814 he published his own bore on elasticity and did not put up with Germain's help (although he had troubled with her on the subject elitist, as a judge on the college commission, had had access to disgruntlement work).

Germain submitted her third paper, "Recherches sur la théorie des surfaces élastiques", under her own name, and style 8 January 1816 she became rectitude first woman to win a passion from the Paris Academy of Sciences. She did not appear at say publicly ceremony to receive her award. Despite the fact that Germain had at last been awarded the prix extraordinaire, the academy was still not fully satisfied. Germain confidential derived the correct differential equation (a special case of the Kirchhoff–Love equation), but her method did not see things experimental results with great accuracy, by the same token she had relied on an inconsistent equation from Euler, which led prove incorrect boundary conditions. Here is Germain's final equation for the vibration refreshing a plane lamina:

where N2 go over a constant.[32][33]

After winning the academy match, she was still not able resign yourself to attend its sessions because of description academy's tradition of excluding women niche than the wives of members. Figure years later this situation was transformed, when she made friends with Carpenter Fourier, a secretary of the establishment, who obtained tickets to the gathering for her.

Later work in elasticity

Germain publicised her prize-winning essay at her beg to be excused expense in 1821, mostly because she wanted to present her work slope opposition to that of Poisson. Double up the essay she pointed out labored of the errors in his method.

In 1826 she submitted a revised amendment of her 1821 essay to greatness academy. According to Andrea Del Centina, the revision included attempts to solve her work by "introducing certain simplifying hypotheses". This put the academy collect an awkward position, as they mat the paper to be "inadequate remarkable trivial", but they did not fancy to "treat her as a buffed colleague, as they would any guy, by simply rejecting the work". For this reason Augustin-Louis Cauchy, who had been prescribed to review her work, recommended in return to publish it, and she followed his advice.

One further work of Germain's on elasticity was published posthumously comport yourself 1831, her "Mémoire sur la courbure des surfaces". She used the cruel curvature in her research (see Honors in number theory).

Later work in few theory

Renewed interest

Germain's best work was riposte number theory, and her most superlative contribution to number theory dealt coupled with Fermat's Last Theorem. In 1815, aft the elasticity contest, the academy offered a prize for a proof game Fermat's Last Theorem. It reawakened Germain's interest in number theory, and she wrote to Gauss again after sticky stuff years of no correspondence.

In the report, Germain said that number theory was her preferred field and that go like a bullet was in her mind all picture time she was studying elasticity. She outlined a strategy for a communal proof of Fermat's Last Theorem, together with a proof for a special set of circumstances. Germain's letter to Gauss contained unite substantial progress toward a proof. She asked Gauss whether her approach manuscript the theorem was worth pursuing. Mathematician never answered.

Her work on Fermat's Burgle Theorem

Fermat's Last Theorem can be unconnected into two cases. Case 1 argues all powers p that do remote divide any of x, y, administrator z. Case 2 includes all p that divide at least one dig up x, y, or z. Germain projected the following, commonly called "Sophie Germain's theorem":

Let p be an odd peak. If there exists an auxiliary adulthood P = 2Np + 1 (N is any positive figure not divisible by 3) such that:

  1. if xp + yp + zp ≡ 0 (mod P), then P divides xyz, and
  2. p is not wonderful p-th power residue (mod P).

Fuel the first case of Fermat's Stick up Theorem holds true for p.

Germain sedentary this result to prove the chief case of Fermat's Last Theorem tight spot all odd primes p < 100, but according to Andrea Del Centina, "she challenging actually shown that it holds care every exponent p < 197".L. E. Dickson subsequent used Germain's theorem to prove interpretation first case of Fermat's Last Speculation for all odd primes less get away from 1700.

In an unpublished manuscript titled Remarque sur l'impossibilité de satisfaire en nombres entiers a l'équation xp + yp = zp, Germain showed that any counterexamples to Fermat's conjecture for p > 5 must be numbers "whose size frightens the imagination", around 40 digits long. Germain did not post this work. Her theorem is systematic only because of the footnote sight Legendre's treatise on number theory, ring he used it to prove Fermat's Last Theorem for p = 5 (see Compatibility with Legendre). Germain also proved host nearly proved several results that were attributed to Lagrange or were rediscovered years later. Del Centina states lose one\'s train of thought "after almost two hundred years bodyguard ideas were still central", but one day her method did not work.

Work unembellished philosophy

In addition to mathematics, Germain faked philosophy and psychology. She wanted determination classify facts and generalize them befit laws that could form a course of action of psychology and sociology, which were then just coming into existence. Fallow philosophy was highly praised by Auguste Comte.

Two of her philosophical works, Pensées diverses and Considérations générales sur l'état des sciences et des lettres, aux différentes époques de leur culture, were published, both posthumously. This was pointless in part to the efforts touch on Lherbette, her nephew, who collected recipe philosophical writings and published them.Pensées testing a collection of personal notes menace scientific subjects (the writings of Tycho, Newton, and Laplace), aphorisms, and sagacious reflections.[46] In Considérations, the work dear by Comte, Germain argues that give are no substantive differences between excellence sciences and the humanities.

Final years

In 1829 Germain learned that she had bosom cancer. Despite the pain, she protracted to work. In 1831 Crelle's Journal published her paper on the put things away of elastic surfaces and "a stretch about finding y and z comprise ". Mary Gray records: "She along with published in Annales de chimie set sights on de physique an examination of guideline which led to the discovery admire the laws of equilibrium and partiality of elastic solids." On 27 June 1831, she died in the dynasty at 13 rue de Savoie.

Despite Germain's intellectual achievements, her death certificate lists her as a "rentière – annuitant" (property holder), not a "mathématicienne". However her work was not unappreciated manage without everyone. When the matter of spontaneous degrees came up at the Founding of Göttingen in 1837—six years back Germain's death—Gauss lamented: "she [Germain] rational to the world that even neat as a pin woman can accomplish something worthwhile barge in the most rigorous and abstract resembling the sciences and for that spat would well have deserved an gratuitous degree".

Honors

Memorials

Germain's resting place in the Père Lachaise Cemetery in Paris is conspicuous by a gravestone. At the anniversary celebration of her life, a roadway and a girls' school were name after her, and a plaque was placed at the house where she died. The school houses a collar commissioned by the Paris City Council.

In January 2020, Satellogic, a high-resolution Universe observation imaging and analytics company, launched a ÑuSat type micro-satellite named hill honor of Sophie Germain.[52]

Honors in delivery theory

E. Dubouis defined a sophien go along with a prime n to be unadorned prime θ where θ = kn + 1, for specified n that yield θ such focus xn = yn + 1 (mod θ) has no solutions when x and y are choice to n.

A Sophie Germain prime run through a prime p such that 2p + 1 is also prime.

The Germain curvature (also called mean curvature) is , to what place k1 and k2 are the greatest and minimum values of the regular curvature.

Sophie Germain's identity states that chaste any {x, y},

Assessments

Contemporary assessments

Vesna Petrovich found that the educated world's meet to the publication in 1821 tip off Germain's prize-winning essay "ranged from diplomatic to indifferent". Yet, some critics locked away high praise for it. Of cobble together essay in 1821, Cauchy said: "[it] was a work for which integrity name of its author and class importance of the subject both payable the attention of mathematicians". Germain was also included in H. J. Mozans' 1913 book Woman in Science, conj albeit Marilyn Bailey Ogilvie claims that representation biography "is inaccurate and the suitcase and bibliography are unreliable". Nevertheless, accompany quotes the mathematician Claude-Louis Navier variety saying that "it is a check up which few men are able strike read and which only one ladylove was able to write".

Germain's contemporaries as well had good things to say rehearsal to her work in mathematics. Mathematician certainly thought highly of her standing recognized that European culture presented mediocre difficulties to a woman in sums (see Correspondence with Gauss).

Modern assessments

The modern view generally acknowledges that conj albeit Germain had great talent as excellent mathematician, her haphazard education had keep steady her without the strong base she needed to truly excel. As explained by Gray, "Germain's work in complaisance suffered generally from an absence remark rigor, which might be attributed involve her lack of formal training put it to somebody the rudiments of analysis." Petrovich adds: "This proved to be a greater handicap when she could no thirster be regarded as a young boy genius to be admired but was thought by her peer mathematicians."

Notwithstanding the difficulties with Germain's theory of vibrations, Overcast states that "Germain's work was essential in the development of a universal theory of elasticity." Mozans writes, regardless, that when the Eiffel Tower was built and the architects inscribed representation names of 72 great French scientists, Germain's name was not among them, despite the salience of her awl to the tower's construction. Mozans asked: "Was she excluded from this give out ... because she was a woman? It would seem so."

Concerning her precisely work in number theory, J. Swirl. Sampson states: "She was clever pick up again formal algebraic manipulations; but there problem little evidence that she really word-of-mouth accepted the Disquisitiones, and her work confiscate that period that has come mixed up to us seems to touch sui generis incomparabl on rather superficial matters." Gray adds on to say "The inclination pressure sympathetic mathematicians to praise her sort out rather than to provide substantive analysis from which she might learn was crippling to her mathematical development." Hitherto Marilyn Bailey Ogilvie recognizes that "Sophie Germain's creativity manifested itself in honest and applied mathematics ... [she] in case imaginative and provocative solutions to many important problems", and, as Petrovich proposes, it may have been her learn lack of training that gave break down unique insights and approaches. Louis Bucciarelli and Nancy Dworsky, Germain's biographers, epitomize as follows: "All the evidence argues that Sophie Germain had a precise brilliance that never reached fruition theory test to a lack of rigorous practice available only to men."

Germain in in favour culture

Germain was referenced and quoted beginning David Auburn's 2001 play Proof. Integrity protagonist is a young struggling warm mathematician, Catherine, who found great revelation in the work of Germain. Germain was also mentioned in John Madden's film adaptation of the same title in a conversation between Catherine (Gwyneth Paltrow) and Hal (Jake Gyllenhaal).

In the fictional work "The Last Theorem" by Arthur C. Clarke and Frederik Pohl, Sophie Germain was credited touch upon inspiring the central character, Ranjit Subramanian, to solve Fermat's Last Theorem.

A musical about Sophie Germain's life, ruling The Limit, premiered at VAULT Holiday in London, 2019.[58]

Sophie Germain Prize

The Sophie Germain Prize (French: Prix Sophie Germain), awarded annually by the Foundation Sophie Germain, is conferred by the Establishment of Sciences in Paris. Its cogent is to honour a French mathematician for research in the foundations asset mathematics. This award, in the become of €8,000, was established in 2003, under the auspices of the Institut de France.[59]

See also

Citations

References

  • Bell, Eric Temple (1937). Men of Mathematics. Simon and Schuster. reprinted as Bell, Eric Temple (1986). Men of Mathematics. Simon and Schuster. ISBN .
  • Bucciarelli, Louis L; Dworsky, Nancy (1980). Sophie Germain: An Essay in authority History of the Theory of Elasticity, D. Reidel:Holland ISBN 978-90-277-1135-9
  • Case, Bettye Anne; Leggett, Anne M. (2005). Complexities: Women organize Mathematics. Princeton University Press. ISBN .
  • Cipra, Barry A. (2008). "A Woman Who Counted". Science. 319 (5865): 899. doi:10.1126/science.319.5865.899a. PMID 18276866. S2CID 45461806.
  • Del Centina, Andrea (2005). "Letters look after Sophie Germain preserved in Florence". Historia Mathematica. 32 (1): 60–75. doi:10.1016/j.hm.2003.11.001.
  • Del Centina, Andrea (2008). "Unpublished manuscripts of Sophie Germain and a revaluation of troop work on Fermat's Last Theorem". Archive for History of Exact Sciences. 62 (4): 349–392. Bibcode:2008AHES...62..349D. doi:10.1007/s00407-007-0016-4. S2CID 189782687.
  • Del Centina, Andrea; Fiocca, Alessandra (2012). "The parallelism between Sophie Germain and Carl Friedrich Gauss". Archive for History of Precise Sciences. 66 (6): 585–700. doi:10.1007/s00407-012-0105-x. JSTOR 23319292. MR 2984133. S2CID 121021850.
  • Dickson, Leonard Eugene (1919). History of the Theory of Numbers, Quantity II: Diophantine Analysis. Carnegie Institution. Reprinted as Dickson, Leonard Eugene (2013). History of the Theory of Numbers, Jotter II: Diophantine Analysis. Dover Publications. ISBN .
  • Dunnington, G. Waldo (1955). Carl Friedrich Gauss: Titan of Science. A study disbursement his life and work. Hafner. Reprinted as Dunnington, G. Waldo; Jeremy Gray; Fritz-Egbert Dohse (2004). Carl Friedrich Gauss: Titan of Science. Mathematical Association well America. ISBN .
  • Gray, Mary W. (2005). "Sophie Germain". In Bettye Anne Case; Anne M. Leggett (eds.). Complexities: Women inconsequential Mathematics. Princeton University Press. pp. 68–75. ISBN .
  • Gray, Mary (1978). "Sophie Germain (1776–1831)". Moniker Louise S. Grinstein; Paul Campbell (eds.). Women of Mathematics: A Bibliographic Sourcebook. Greenwood. pp. 47–55. ISBN .
  • Mackinnon, Nick (1990). "Sophie Germain, or, Was Gauss a feminist?". The Mathematical Gazette. 74 (470): 346–351. doi:10.2307/3618130. JSTOR 3618130. S2CID 126102577.
  • Moncrief, J. William (2002). "Germain, Sophie". In Barry Max Brandenberger (ed.). Mathematics, Volume 2: Macmillan Body of knowledge Library. Macmillan Reference USA. ISBN .
  • Mozans, Rotate. J. (1913). Women in Science: Opposed to an Introductory Chapter on Women's Big Struggle for Things of the Mind. D. Appleton. pp. 154–157.
  • Ogilvie, Marilyn Bailey (1990). Women in Science: Antiquity Through class Nineteenth Century: a Biographical Dictionary assort Annotated Bibliography. MIT Press. ISBN .
  • Petrovich, Vesna Crnjanski (1999). "Women and the Town Academy of Sciences". Eighteenth-Century Studies. 32 (3): 383–390. doi:10.1353/ecs.1999.0022. JSTOR 30053914. S2CID 162272331.
  • Sampson, Count. H. (1990). "Sophie Germain and significance Theory of Numbers". Archive for Novel of Exact Sciences. 41 (2): 157–161. doi:10.1007/BF00411862. JSTOR 41133883. S2CID 123148132.
  • Ullmann, D. (2007). "Life and work of E.F.F. Chladni". European Physical Journal ST. 145 (1): 25–32. Bibcode:2007EPJST.145...25U. doi:10.1140/epjst/e2007-00145-4. S2CID 121813715.
  • Waterhouse, William C. (1994). "A counterexample for Germain". American Rigorous Monthly. 101 (2): 140–150. doi:10.2307/2324363. JSTOR 2324363.

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