ࡱ> 7 MbjbjUU _7|7|1l       d',6666L&&&&&&&$) + '" '%6L'%%%b 86L&%&%H%&&L*   g%&&4'0d'&,g%4,&%  Mihai Florin et Cl. a-X-a D. Radwan Rawad date: Augustin-Louis Cauchy Augustin-Louis Cauchy (21 aot 1789 [Paris] - 23 mai 1857 [Sceaux]) Augustin-Louis Cauchy est le mathmaticien franais le plus prolifique (avec presque 800 articles publis). Ses ides politiques et religieuses ont pourtant plusieurs reprises contrari sa carrire. Il est n le 21 aot 1789, au lendemain des vnements de juillet. Son pre, premier commis du lieutenant de police de Paris, voyait sa vie menace par la colre du peuple. Il s'tait, pour quelques temps, rfugi avec sa famille Arcueil. Ds le plus jeune ge, il prend en main l'ducation de son fils, et Augustin est admis l'Ecole Polytechnique. Celle-ci a peine 10 ans d'ge, mais dj les savants les plus prestigieux y enseignent. A la sortie de l'cole, Cauchy est admis dans le corps le plus prestigieux (celui des Ponts et Chausses), et en 1810, nomm aspirant ingnieur, il participe la construction du port de Cherbourg. C'est Cherbourg que Cauchy commence ses recherches mathmatiques sur les polydres, et ses premiers rsultats sont prometteurs. Mais, fatigu par le cumul de la charge d'ingnieur et des longues veilles de recherche, Cauchy connait un tat dpressif qui s'ternise et le pousse retourner vivre chez ses parents. A Paris, il cherche une situation en adquation avec sa volont de faire de la recherche mathmatique pure. Malgr l'appui de son pre, il se voit devanc par d'autres pour plusieurs postes, avant d'tre lu, en 1814, la socit philomatique, antichambre de l'Acadmie (alors nomm Institut). A la chute de l'empire, Cauchy, royaliste et dvt, voit de nombreux protecteurs accder au pouvoir. Leur influence permet sa nomination comme professeur d'analyse l'Ecole Polytechnique en 1815. Entre-temps, il vient d'achever un brillant mmoire o il dmontre un clbre thorme de Fermat sur les nombres polygonaux. Ceci fera beaucoup pour sa notorit, et en 1816, il accde L'Acadmie des Sciences, en remplacement de Carnot et Monge touchs par l'puration. Il est alors temps pour Cauchy de se marier, et sous l'influence de ses amis , il pouse Alose de Bure, ne d'une famille de clbres libraires parisiens. Ils auront deux filles. Le cours d'analyse que Cauchy professe l'Ecole Polytechnique est dcri tant par ses lves que par ses collgues des autres matires. Pourtant c'est ce cours, publi en 1821 et 1823, qui devait devenir la rfrence de l'analyse au XIXs. en mettant en avant la rigueur, et plus seulement l'intuition. C'est la premire fois que de vraies dfinitions de limites, de continuit, de convergence de suites, de sries, sont nonces. Cette rigueur reste toutefois encore relative, puisque que Cauchy "prouve" que la limite d'une srie de fonctions continues est continue, ce qui est faux. Il est vrai que Cauchy ne dispose pas encore d'une dfinition claire et prcise des nombres rels. C'est l'poque aussi o Cauchy ralise des travaux profonds sur les fonctions d'une variable complexe (tablissant par exemple la formule des rsidus), ainsi que des avances dans la thorie des groupes finis. Cauchy ne fut jamais le chef d'une cole de mathmaticiens, et il se comporta parfois maladroitement avec de jeunes chercheurs comme Abel ou Galois, dont il sous-estime, ou mme perd, des mmoires de premire importance. Ses relations avec ses collgues ne sont en gnral pas trs faciles. On lui a beaucoup reprocher les conditions de son accession l'Acadmie, et sa bigoterie intransigeante ne permet pas toujours un contact ais. En 1830 clate la rvolution de Juillet, qui va brutalement changer le cours de sa vie. En effet, Cauchy, antilibral trs marqu, s'exile en Suisse, et Italie, en laissant femme et enfants Paris. Paralllement, son activit mathmatique dcroit. Il enseigne Turin, avant de devenir le prcepteur de l'hritier au trone, le petit fils de Charles X, en exil Pragues! En 1834, sa famille peut enfin le rejoindre.En 1838, il retourne en France sous les injonctions de sa mre mourante. Il lui faut retrouver une situation, et il est lu au Bureau des longitudes. Elu, mais pas nomm, car il refuse de prter serment d'allgeance au roi des franais (Louis-Philippe), et ne peroit donc pas son salaire. Son soutien aux Jsuites lui barre galement la route du Collge de France. En 1848 a lieu une novelle rvolution, et le problme du serment n'est plus un obstacle pour Cauchy qui peut reprendre ses cours la Sorbonne. Cauchy apparat comme un des mathmaticiens, qui, outre son travail de recherches et de dcouvertes de nouveaux rsultats, a commenc mettre un peu d'ordre dans les bases de l'Analyse. Cette branche des mathmatiques, qui s'tait dveloppe de faon foisonnante depuis le XVIIme sicle, reposait en effet, l'poque de Cauchy, sur des bases assez instables et obscures. Au fil de ses traits et de ses manuels d'enseignement, il tente de dfinir les notions de limite, de continuit, de convergences d'une suite ou d'une srie, et de dmontrer des rsultats qui taient admis jusque l comme des vidences, et dont la preuve manquait. . . quand ils n'taient pas faux. Son nom reste attach un certain type de suites, les suites de Cauchy. Cauchy n'atteint pas la prcision et la rigueur parfaite, beaucoup de ses noncs sont encore imprcis, et l'on peut en trouver certains qui sont faux, mais il amorce l'effort vers plus de rigueur, que poursuivront jusqu' la perfection Riemann, Weierstrass, Dedekind, Cantor et d'autres. Mais Cauchy fait progresser aussi remarquablement les connaissances mathmatiques de son poque, et son uvre est d'un volume impressionnant. Il domine son poque, aux cts de Gauss. Il s'intresse particulirement aux fonctions drivables de C dans C, qui gnralisent les fonctions relles de la variable relle, mais galement aux quations diffrentielles, l'intgration, aux quations et aux substitutions (il apparat ainsi comme un des prcurseurs, avec Galois, de la Thorie des Groupes). Il travaille aussi sur les dterminants ; il s'intresse diffrents problmes de Physique mathmatique et d'astronomie... Cauchy tait fervent catholique, royaliste et lgitimiste. Ses opinions politiques valurent sa carrire quelques succs, et beaucoup de difficults. Cauchy dcde dans la nuit du 22 au 23 mai 1857, des suites d'un tat de fatigue gnralis. 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