{"id":207407,"date":"2026-09-08T18:41:31","date_gmt":"2026-09-08T18:41:31","guid":{"rendered":"https:\/\/www.europesays.com\/cz\/207407\/"},"modified":"2026-09-08T18:41:31","modified_gmt":"2026-09-08T18:41:31","slug":"claude-za-jedenact-dni-strojove-overil-dukaz-fermatovy-posledni-vety","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/cz\/207407\/","title":{"rendered":"Claude za jeden\u00e1ct dn\u00ed strojov\u011b ov\u011b\u0159il d\u016fkaz Fermatovy posledn\u00ed v\u011bty"},"content":{"rendered":"<p>Um\u011bl\u00e1 inteligence Claude od firmy Anthropic b\u011bhem jeden\u00e1cti dn\u00ed z velk\u00e9 \u010d\u00e1sti samostatn\u011b vytvo\u0159ila prvn\u00ed kompletn\u00ed, po\u010d\u00edta\u010dem ov\u011b\u0159en\u00fd d\u016fkaz Fermatovy posledn\u00ed v\u011bty. Nejde ale o to, \u017ee by AI vy\u0159e\u0161ila t\u0159istapades\u00e1t let star\u00fd matematick\u00fd probl\u00e9m sama od sebe, tu pr\u00e1ci u\u017e v roce 1995 odvedl britsk\u00fd matematik Andrew Wiles. \u00dasp\u011bch spo\u010d\u00edv\u00e1 v n\u011b\u010dem jin\u00e9m, a mo\u017en\u00e1 stejn\u011b d\u016fle\u017eit\u00e9m.<\/p>\n<p dir=\"ltr\">Firma Anthropic v\u00fdsledek zve\u0159ejnila 4. z\u00e1\u0159\u00ed 2026. Podle <a href=\"https:\/\/www.anthropic.com\/research\/formalizing-fermats-last-theorem\" rel=\"nofollow noopener\" target=\"_blank\">ofici\u00e1ln\u00edho ozn\u00e1men\u00ed na firemn\u00edm webu cel\u00fd projekt rozjel Tianyi Peng, v\u00fdzkumn\u00edk Anthropic, jeho\u017e skupina na Kolumbijsk\u00e9 univerzit\u011b vyv\u00edj\u00ed n\u00e1stroje pro takzvanou autoformalizaci matematiky, a cht\u011bl otestovat, jak daleko dok\u00e1\u017ee Claude s formalizac\u00ed Fermatovy posledn\u00ed v\u011bty doj\u00edt<\/a>. V\u00fdsledek p\u0159ed\u010dil jeho o\u010dek\u00e1v\u00e1n\u00ed. Claude b\u011bhem jeden\u00e1cti dn\u00ed z velk\u00e9 \u010d\u00e1sti samostatn\u00e9 pr\u00e1ce v srpnu 2026 vytvo\u0159il prvn\u00ed d\u016fkaz, kter\u00fd od za\u010d\u00e1tku do konce pro\u0161el po\u010d\u00edta\u010dov\u00fdm ov\u011b\u0159en\u00edm v programovac\u00edm jazyce Lean, a napsal p\u0159itom p\u0159es 13 milion\u016f \u0159\u00e1dk\u016f k\u00f3du, tedy v\u00edc ne\u017e p\u011btin\u00e1sobek velikosti Mathlibu, hlavn\u00ed komunitn\u00ed knihovny matematick\u00fdch d\u016fkaz\u016f, na kter\u00e9 cel\u00fd projekt stav\u011bl.<\/p>\n<p dir=\"ltr\">Na projektu podle stejn\u00e9ho zdroje pracovaly des\u00edtky agent\u016f Claude soub\u011b\u017en\u011b, koordinovan\u00fdch pomoc\u00ed n\u00e1stroje nazvan\u00e9ho Prove2Me a syst\u00e9mu postaven\u00e9ho na Claude Code, p\u0159i\u010dem\u017e dohromady dok\u00e1zaly ov\u011b\u0159it p\u0159es 30 300 d\u00edl\u010d\u00edch matematick\u00fdch v\u011bt, z nich\u017e 29 500 se nakonec vyu\u017eilo v samotn\u00e9m fin\u00e1ln\u00edm d\u016fkazu. Cel\u00fd proces spot\u0159eboval zhruba \u0161est miliard v\u00fdstupn\u00edch token\u016f. Podle <a href=\"https:\/\/aiwiki.ai\/wiki\/fermats_last_theorem_formalization\" rel=\"nofollow noopener\" target=\"_blank\">podrobn\u00e9ho p\u0159ehledu na wiki serveru AIWiki \u0161lo o intern\u00ed v\u00fdzkumn\u00fd model, kter\u00fd Anthropic ozna\u010duje jako p\u0159ibli\u017en\u011b srovnateln\u00fd s modelem Claude Fable 5.1<\/a>.<\/p>\n<p dir=\"ltr\">Pr\u016fb\u011bh pr\u00e1ce lze podle stejn\u00e9ho zdroje sledovat t\u00e9m\u011b\u0159 den po dni. P\u00e1t\u00fd den, 11. srpna, agenti dok\u00e1zali kl\u00ed\u010dov\u00fd p\u0159\u00edpad Mazurovy v\u011bty, zat\u00edmco t\u00fdm je\u0161t\u011b r\u00e1no odhadoval, \u017ee mu zb\u00fdvaj\u00edc\u00ed \u010d\u00e1st argumentu zabere jeden a\u017e t\u0159i t\u00fddny. \u0160est\u00fd den bylo hotovo p\u0159es deset tis\u00edc v\u011bt, osm\u00fd den padl centr\u00e1ln\u00ed krok Ribetova argumentu a dev\u00e1t\u00fd den m\u011bli agenti na m\u00edst\u011b v\u0161ech \u0161estn\u00e1ct krok\u016f takzvan\u00e9 Eichler-\u0160imurovy v\u011bty, \u010dekaj\u00edc\u00edch u\u017e jen na jeden otev\u0159en\u00fd z\u00e1kladn\u00ed v\u00fdsledek. Jeden\u00e1ct\u00fd den, 17. srpna, byl dok\u00e1z\u00e1n pot\u0159ebn\u00fd p\u0159\u00edpad Langlandsovy-Tunnellovy v\u011bty a t\u00fd\u017e den ve\u010der byla Fermatova posledn\u00ed v\u011bta na intern\u00ed platform\u011b ozna\u010dena za dok\u00e1zanou. O dva dny pozd\u011bji t\u00fdm cel\u00fd strom 29 511 karet znovu zkompiloval ze zdrojov\u00e9ho k\u00f3du jako jedin\u00fd ucelen\u00fd projekt v jazyce Lean.<\/p>\n<p dir=\"ltr\">D\u016fle\u017eit\u00e9 je pochopit, co slovo formalizace v tomto kontextu znamen\u00e1. Wiles\u016fv p\u016fvodn\u00ed d\u016fkaz z roku 1995 stav\u011bl na my\u0161lenk\u00e1ch cel\u00e9 \u0159ady matematik\u016f, mezi nimi Freye, Serrea, Ribeta, Mazura, Langlandse, Tunnella, Tanijamy, \u0160imury a Weila, a byl napsan\u00fd b\u011b\u017en\u00fdm matematick\u00fdm jazykem, kter\u00fd ov\u011b\u0159uj\u00ed lid\u0161t\u00ed recenzenti. Formalizace znamen\u00e1 p\u0159ev\u00e9st tuto lidskou argumentaci do podoby, kterou dok\u00e1\u017ee \u0159\u00e1dek po \u0159\u00e1dku zkontrolovat po\u010d\u00edta\u010d, ani\u017e by musel d\u016fv\u011b\u0159ovat pouh\u00e9mu slovu matematika. Tento typ pr\u00e1ce b\u011b\u017en\u011b zabere m\u011bs\u00edce a\u017e roky ru\u010dn\u00edho \u00fasil\u00ed, a podle <a href=\"https:\/\/bitcoinethereumnews.com\/tech\/ai-just-solved-a-350-year-old-math-problem-by-writing-the-longest-proof-ever\/\" rel=\"nofollow noopener\" target=\"_blank\">technologick\u00e9ho serveru popisuj\u00edc\u00edho dosa\u017een\u00fd v\u00fdsledek na stejn\u00e9m \u00fakolu od roku 2024 pracuje i lidsk\u00fd t\u00fdm formaliz\u00e1tor\u016f na Imperial College London, kter\u00fd p\u0159itom svou pr\u00e1ci dosud nedokon\u010dil, zat\u00edmco Claude ho v tomto konkr\u00e9tn\u00edm z\u00e1vod\u011b p\u0159edb\u011bhl<\/a>.<\/p>\n<p dir=\"ltr\">V\u00fdsledek si p\u0159ed zve\u0159ejn\u011bn\u00edm ov\u011b\u0159il i uzn\u00e1van\u00fd britsk\u00fd matematik Kevin Buzzard z Imperial College London, jeden z kl\u00ed\u010dov\u00fdch odborn\u00edk\u016f na formalizaci matematiky v jazyce Lean. Podle jeho hodnocen\u00ed citovan\u00e9ho v <a href=\"https:\/\/www.anthropic.com\/research\/formalizing-fermats-last-theorem\" rel=\"nofollow noopener\" target=\"_blank\">ozn\u00e1men\u00ed Anthropic jde o mimo\u0159\u00e1dn\u00fd v\u00fdsledek autoformalizace, kter\u00fd dokazuje Fermatovu posledn\u00ed v\u011btu bez jak\u00fdchkoli dal\u0161\u00edch p\u0159edpoklad\u016f krom\u011b z\u00e1kladn\u00edch axiom\u016f matematiky, a cestou k n\u011bmu vznikla i formalizace algebry, harmonick\u00e9 anal\u00fdzy, geometrie a teorie \u010d\u00edsel, co\u017e ukazuje, \u017ee n\u00e1stroje pro automatizovanou formalizaci jsou u\u017e dost robustn\u00ed na to, aby se na nich dalo d\u00e1l stav\u011bt<\/a>.<\/p>\n<p dir=\"ltr\">Titulky typu um\u011bl\u00e1 inteligence vy\u0159e\u0161ila t\u0159istapades\u00e1t let star\u00fd matematick\u00fd probl\u00e9m jsou tedy zav\u00e1d\u011bj\u00edc\u00ed. Jak p\u0159esn\u011b upozor\u0148uje i kritick\u00fd koment\u00e1\u0159 na blogu Exploring ChatGPT, probl\u00e9m vy\u0159e\u0161il Andrew Wiles, Claude jeho existuj\u00edc\u00ed \u0159e\u0161en\u00ed p\u0159evedl do strojov\u011b ov\u011b\u0159iteln\u00e9 podoby, co\u017e je jin\u00fd, by\u0165 s\u00e1m o sob\u011b n\u00e1ro\u010dn\u00fd a \u010dasov\u011b zdlouhav\u00fd \u00fakol. Skute\u010dn\u00e1 novinka spo\u010d\u00edv\u00e1 v tempu: proces, kter\u00fd lidsk\u00fdm matematik\u016fm typicky zabere m\u011bs\u00edce nebo roky pe\u010dliv\u00e9 ru\u010dn\u00ed pr\u00e1ce, dok\u00e1zal syst\u00e9m agent\u016f zvl\u00e1dnout za necel\u00e9 dva t\u00fddny, a to u jednoho z nejslo\u017eit\u011bj\u0161\u00edch matematick\u00fdch d\u016fkaz\u016f dvac\u00e1t\u00e9ho stolet\u00ed.<\/p>\n","protected":false},"excerpt":{"rendered":"Um\u011bl\u00e1 inteligence Claude od firmy Anthropic b\u011bhem jeden\u00e1cti dn\u00ed z velk\u00e9 \u010d\u00e1sti samostatn\u011b vytvo\u0159ila prvn\u00ed kompletn\u00ed, po\u010d\u00edta\u010dem ov\u011b\u0159en\u00fd&hellip;\n","protected":false},"author":2,"featured_media":207408,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0"},"categories":[11],"tags":[2038,2233,4432,25416,2037,54,53,52],"class_list":["post-207407","post","type-post","status-publish","format-standard","has-post-thumbnail","category-svet","tag-clanek","tag-claude","tag-dukazy","tag-matematika","tag-nedd","tag-svet","tag-world","tag-world-news"],"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@cz\/117236890717982888","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/posts\/207407","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/comments?post=207407"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/posts\/207407\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/media\/207408"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/media?parent=207407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/categories?post=207407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/cz\/wp-json\/wp\/v2\/tags?post=207407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}