{"id":37,"date":"2008-06-06T22:02:24","date_gmt":"2008-06-06T20:02:24","guid":{"rendered":"http:\/\/zavie.free.fr\/lousodrome\/?p=37"},"modified":"2008-06-06T22:02:24","modified_gmt":"2008-06-06T20:02:24","slug":"anecdotes-de-la-science-le-dernier-theoreme-de-fermat","status":"publish","type":"post","link":"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/","title":{"rendered":"Anecdotes de la Science – Le dernier th\u00e9or\u00e8me de Fermat"},"content":{"rendered":"

Diophante v\u00e9cu au troisi\u00e8me si\u00e8cle, et \u00e9crivit un ouvrage intitul\u00e9 \u00ab\u00a0Arithm\u00e9tique\u00a0\u00bb, dont il ne reste h\u00e9las aujourd’hui qu’une partie. Il s’y int\u00e9ressait entre autres \u00e0 la r\u00e9solution d’\u00e9quations quadratiques et \u00e0 la d\u00e9composition de carr\u00e9s en sommes de deux carr\u00e9s.<\/p>\n

\"CouverturePierre de Fermat v\u00e9cu au XVIIe si\u00e8cle, ce qui fait de lui un contemporain de Ren\u00e9 Descartes et Blaise Pascal. Il fit divers commentaires en marge d’une traduction latine de ce livre, que son fils publia d’ailleurs apr\u00e8s sa mort sous la forme d’une version annot\u00e9e.<\/p>\n

Diophante consid\u00e8re que le probl\u00e8me consistant \u00e0 d\u00e9composer un cube en la somme de deux cubes n’a pas de solution enti\u00e8re. Fermat observe (page 85 dans la version publi\u00e9e avec ses notes) :<\/p>\n

Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.<\/p><\/blockquote>\n

Ce qui est g\u00e9n\u00e9ralement traduit par :<\/p>\n

Il est impossible de s\u00e9parer un cube en deux cubes, ou une puissance de quatre en deux puissances de quatre, et d’une fa\u00e7on g\u00e9n\u00e9rale toute puissance de plus de deux en somme de deux entiers \u00e9lev\u00e9s \u00e0 cette puissance. J\u2019ai trouv\u00e9 une merveilleuse d\u00e9monstration de cette proposition. Mais la marge est trop \u00e9troite pour la contenir.<\/p><\/blockquote>\n

C’est pour le moins cavalier, d’autant qu’il aura fallu attendre plus de 350 ans pour qu’en 1995 ce th\u00e9or\u00e8me soit enfin d\u00e9montr\u00e9, par Andrew Wiles. Avec une d\u00e9monstration tenant sur un millier de pages et faisant appel \u00e0 des outils math\u00e9matiques qui n’existaient pas encore \u00e0 l’\u00e9poque, il semble aujourd’hui peu probable qu’il ait effectivement trouv\u00e9 une d\u00e9monstration correcte. Mais il aura donn\u00e9 du fil \u00e0 retordre \u00e0 des g\u00e9n\u00e9rations de math\u00e9maticiens !<\/p>\n

Et cerise sur le g\u00e2teau, ce th\u00e9or\u00e8me n’a pratiquement aucune utilit\u00e9. Par contre la recherche de sa d\u00e9monstration a entra\u00een\u00e9 la d\u00e9couverte d’outils math\u00e9matiques tr\u00e8s puissants…<\/p>\n

Article \u00ab\u00a0Dernier th\u00e9or\u00e8me de Fermat\u00a0\u00bb sur Wikip\u00e9dia<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Diophante v\u00e9cu au troisi\u00e8me si\u00e8cle, et \u00e9crivit un ouvrage intitul\u00e9 \u00ab\u00a0Arithm\u00e9tique\u00a0\u00bb, dont il ne reste h\u00e9las aujourd’hui qu’une partie. Il s’y int\u00e9ressait entre autres \u00e0 la r\u00e9solution d’\u00e9quations quadratiques et \u00e0 la d\u00e9composition de carr\u00e9s en sommes de deux carr\u00e9s. … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27,20,23],"tags":[],"yoast_head":"\nAnecdotes de la Science - Le dernier th\u00e9or\u00e8me de Fermat - Lousodrome<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Anecdotes de la Science - Le dernier th\u00e9or\u00e8me de Fermat - Lousodrome\" \/>\n<meta property=\"og:description\" content=\"Diophante v\u00e9cu au troisi\u00e8me si\u00e8cle, et \u00e9crivit un ouvrage intitul\u00e9 \u00ab\u00a0Arithm\u00e9tique\u00a0\u00bb, dont il ne reste h\u00e9las aujourd’hui qu’une partie. Il s’y int\u00e9ressait entre autres \u00e0 la r\u00e9solution d’\u00e9quations quadratiques et \u00e0 la d\u00e9composition de carr\u00e9s en sommes de deux carr\u00e9s. … Continuer la lecture →\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/\" \/>\n<meta property=\"og:site_name\" content=\"Lousodrome\" \/>\n<meta property=\"article:published_time\" content=\"2008-06-06T20:02:24+00:00\" \/>\n<meta name=\"author\" content=\"Julien Guertault\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Julien Guertault\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/\",\"url\":\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/\",\"name\":\"Anecdotes de la Science - Le dernier th\u00e9or\u00e8me de Fermat - Lousodrome\",\"isPartOf\":{\"@id\":\"https:\/\/lousodrome.net\/blog\/#website\"},\"datePublished\":\"2008-06-06T20:02:24+00:00\",\"dateModified\":\"2008-06-06T20:02:24+00:00\",\"author\":{\"@id\":\"https:\/\/lousodrome.net\/blog\/#\/schema\/person\/a16a2a69d73eca763ffdf125c49eaa2f\"},\"breadcrumb\":{\"@id\":\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/lousodrome.net\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Anecdotes de la Science – Le dernier th\u00e9or\u00e8me de Fermat\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/lousodrome.net\/blog\/#website\",\"url\":\"https:\/\/lousodrome.net\/blog\/\",\"name\":\"Lousodrome\",\"description\":\"La lose 2.0\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/lousodrome.net\/blog\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/lousodrome.net\/blog\/#\/schema\/person\/a16a2a69d73eca763ffdf125c49eaa2f\",\"name\":\"Julien Guertault\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/lousodrome.net\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/2e5fc7a18e1701e1bb61a5da0ef35cf7?s=96&d=identicon&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/2e5fc7a18e1701e1bb61a5da0ef35cf7?s=96&d=identicon&r=g\",\"caption\":\"Julien Guertault\"},\"url\":\"https:\/\/lousodrome.net\/blog\/blog\/author\/admin\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Anecdotes de la Science - Le dernier th\u00e9or\u00e8me de Fermat - Lousodrome","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/lousodrome.net\/blog\/blog\/2008\/06\/06\/anecdotes-de-la-science-le-dernier-theoreme-de-fermat\/","og_locale":"fr_FR","og_type":"article","og_title":"Anecdotes de la Science - Le dernier th\u00e9or\u00e8me de Fermat - Lousodrome","og_description":"Diophante v\u00e9cu au troisi\u00e8me si\u00e8cle, et \u00e9crivit un ouvrage intitul\u00e9 \u00ab\u00a0Arithm\u00e9tique\u00a0\u00bb, dont il ne reste h\u00e9las aujourd’hui qu’une partie. 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