{"id":7564,"date":"2026-03-29T00:56:10","date_gmt":"2026-03-28T22:56:10","guid":{"rendered":"https:\/\/www.schooler.org.ua\/uk-uaii-teper-perevirjaye-matematichni-dokazi-nova-era-suvorosti-ta\/"},"modified":"2026-03-29T00:56:10","modified_gmt":"2026-03-28T22:56:10","slug":"uk-uaii-teper-perevirjaye-matematichni-dokazi-nova-era-suvorosti-ta","status":"publish","type":"post","link":"https:\/\/www.schooler.org.ua\/cs\/uk-uaii-teper-perevirjaye-matematichni-dokazi-nova-era-suvorosti-ta\/","title":{"rendered":"AI nyn\u00ed kontroluje matematick\u00e9 d\u016fkazy: Nov\u00e1 \u00e9ra p\u0159\u00edsnosti a rychlosti"},"content":{"rendered":"

Sv\u011bt matematiky proch\u00e1z\u00ed v\u00fdrazn\u00fdm posunem. Um\u011bl\u00e1 inteligence ji\u017e nepom\u00e1h\u00e1 pouze s v\u00fdpo\u010dty, ale je nyn\u00ed schopna kontrolovat<\/em> slo\u017eit\u00e9 matematick\u00e9 d\u016fkazy, co\u017e byl \u00fakol d\u0159\u00edve vyhrazen\u00fd v\u00fdhradn\u011b pro lidsk\u00e9 experty. Tento pr\u016flom slibuje urychlen\u00ed v\u00fdzkumu, odstran\u011bn\u00ed chyb a z\u00e1sadn\u00ed zm\u011bnu zp\u016fsobu vytv\u00e1\u0159en\u00ed a ov\u011b\u0159ov\u00e1n\u00ed matematick\u00fdch znalost\u00ed. <\/p>\n

V\u00fdzva k formalizaci<\/h3>\n

Po desetilet\u00ed snili matematici o automatick\u00e9 kontrole d\u016fkaz\u016f. Existuj\u00edc\u00ed n\u00e1stroje mohou ov\u011b\u0159it d\u016fkazy, ale pouze pokud jsou nejprve p\u0159elo\u017eeny do p\u0159\u00edsn\u00e9ho, \u200b\u200bpo\u010d\u00edta\u010dem \u010diteln\u00e9ho form\u00e1tu, co\u017e je proces zvan\u00fd formalizace<\/strong>. Je to notoricky \u00fanavn\u00e9 a \u010dasto vy\u017eaduje m\u011bs\u00edce nebo dokonce roky usilovn\u00e9 pr\u00e1ce. Probl\u00e9m nen\u00ed v matematice samotn\u00e9; ale v nepru\u017enosti programovac\u00edch jazyk\u016f, kter\u00e9 vy\u017eaduj\u00ed absolutn\u00ed p\u0159esnost tam, kde m\u016f\u017ee b\u00fdt lidsk\u00e1 notace plynulej\u0161\u00ed. <\/p>\n

Math, Inc. a Gauss AI<\/h3>\n

Startup s n\u00e1zvem Math, Inc. tvrd\u00ed, \u017ee tuto bari\u00e9ru p\u0159ekonal pomoc\u00ed sv\u00e9 AI, zvan\u00e9 Gauss. Spole\u010dnost \u00fasp\u011b\u0161n\u011b formalizovala dva pr\u016flomov\u00e9 d\u016fkazy Mariny Vjazovsk\u00e9, kter\u00e1 v roce 2022 obdr\u017eela presti\u017en\u00ed Fieldsovu medaili za pr\u00e1ci na balen\u00ed koul\u00ed ve vy\u0161\u0161\u00edch dimenz\u00edch. Tyto d\u016fkazy byly pova\u017eov\u00e1ny za extr\u00e9mn\u011b slo\u017eit\u00e9 a schopnost AI je automaticky p\u0159ekl\u00e1dat je d\u016fle\u017eit\u00fdm krokem vp\u0159ed. <\/p>\n

Puzzle balen\u00ed koul\u00ed: Pro\u010d je to d\u016fle\u017eit\u00e9<\/h3>\n

V\u00fdzkum Vjazovskaja vy\u0159e\u0161il klasick\u00fd probl\u00e9m: jak nej\u00fa\u010dinn\u011bji uspo\u0159\u00e1dat koule. Ve t\u0159ech rozm\u011brech je nejt\u011bsn\u011bj\u0161\u00ed balen\u00ed podobn\u00e9 skl\u00e1d\u00e1n\u00ed pomeran\u010d\u016f v obchod\u011b s potravinami. Ale jak se rozm\u011bry zv\u011bt\u0161uj\u00ed, \u00fakol se st\u00e1v\u00e1 exponenci\u00e1ln\u011b obt\u00ed\u017en\u011bj\u0161\u00edm. Vjazovskaja to vy\u0159e\u0161ila pro osm a 24 dimenz\u00ed, co\u017e dokazuje, \u017ee p\u0159enesen\u00ed efektivn\u00edch uspo\u0159\u00e1d\u00e1n\u00ed z ni\u017e\u0161\u00edch dimenz\u00ed m\u016f\u017ee pojmout dal\u0161\u00ed kouli v ka\u017ed\u00e9m vy\u0161\u0161\u00edm prostoru. <\/p>\n

Toto nen\u00ed jen abstraktn\u00ed teorie.<\/strong> Sphere packing m\u00e1 aplikace v oblastech, jako je teorie k\u00f3dov\u00e1n\u00ed, v\u011bda o materi\u00e1lech a dokonce i v\u00fdvoj l\u00e9k\u016f. K pokroku v t\u00e9to pr\u00e1ci jsou zapot\u0159eb\u00ed p\u0159esn\u00e9 d\u016fkazy. <\/p>\n

P\u0159eru\u0161en\u00e1 spolupr\u00e1ce<\/h3>\n

Gauss\u016fv \u00fasp\u011b\u0161n\u00fd p\u0159\u00edb\u011bh je tak\u00e9 varovn\u00fdm p\u0159\u00edb\u011bhem. V\u00fdzkumn\u00edci roky spolupracovali na ru\u010dn\u00ed formalizaci Vjazovskajan\u00fdch d\u016fkaz\u016f, \u010d\u00edm\u017e pr\u00e1ci rozd\u011blili na zvl\u00e1dnuteln\u00e9 kousky pro komunitu Lean formalizace. Spole\u010dnost Math, Inc. v tichosti vyu\u017eila sv\u016fj pokrok a pot\u00e9 vyvinula svou AI, aby dokon\u010dila \u00fakol b\u011bhem n\u011bkolika t\u00fddn\u016f, ani\u017e by pln\u011b odhalila sv\u016fj pokrok. <\/p>\n

Jak \u0159\u00edk\u00e1 Hariharan, jeden ze spoluautor\u016f, \u201eAI je ru\u0161iv\u00e1\u201c. T\u00fdm pl\u00e1noval pou\u017e\u00edt jejich formalizaci jako z\u00e1klad pro studentskou pr\u00e1ci, ale AI to vy\u0159e\u0161ila jako prvn\u00ed. <\/p>\n

Budoucnost: AI jako matematick\u00fd pozorovatel<\/h3>\n

Math, Inc. od t\u00e9 doby formalizovala druh\u00fd d\u016fkaz Vyazovskaja, vygenerovala 120 000 \u0159\u00e1dk\u016f Lean k\u00f3du. N\u00e1sledky jsou dalekos\u00e1hl\u00e9. AI dok\u00e1\u017ee nejen p\u0159ekl\u00e1dat d\u016fkazy, ale tak\u00e9 odhalit a opravit<\/em> chyby v p\u016fvodn\u00edch \u010dl\u00e1nc\u00edch. <\/p>\n

Poiroux, zakladatel Math, Inc., si p\u0159edstavuje budoucnost, ve kter\u00e9 um\u011bl\u00e1 inteligence \u201eovl\u00e1d\u00e1 ve\u0161kerou matematiku… a ve v\u00fdzkumu m\u016f\u017ee dokonce p\u0159ekonat lidi\u201c. Jakmile um\u011bl\u00e1 inteligence pln\u011b pochop\u00ed matematick\u00e9 koncepty, bude k nim schopna p\u0159istupovat zcela nov\u00fdmi zp\u016fsoby a vytv\u00e1\u0159et nov\u00e9 v\u00fdsledky. <\/p>\n

To vyvol\u00e1v\u00e1 kritick\u00e9 ot\u00e1zky o roli lidsk\u00fdch matematik\u016f. Stane se AI kone\u010dn\u00fdm arbitrem matematick\u00e9 pravdy? Gauss\u016fv v\u00fdvoj nazna\u010duje, \u017ee odpov\u011b\u010f m\u016f\u017ee b\u00fdt bl\u00ed\u017ee, ne\u017e si mysl\u00edme.<\/p>\n","protected":false},"excerpt":{"rendered":"

Sv\u011bt matematiky proch\u00e1z\u00ed v\u00fdrazn\u00fdm posunem. Um\u011bl\u00e1 inteligence ji\u017e nepom\u00e1h\u00e1 pouze s v\u00fdpo\u010dty, ale je nyn\u00ed schopna kontrolovat slo\u017eit\u00e9 matematick\u00e9 d\u016fkazy, co\u017e byl \u00fakol d\u0159\u00edve vyhrazen\u00fd v\u00fdhradn\u011b pro lidsk\u00e9 experty. Tento pr\u016flom slibuje urychlen\u00ed v\u00fdzkumu, odstran\u011bn\u00ed chyb a z\u00e1sadn\u00ed zm\u011bnu zp\u016fsobu vytv\u00e1\u0159en\u00ed a ov\u011b\u0159ov\u00e1n\u00ed matematick\u00fdch znalost\u00ed. V\u00fdzva k formalizaci Po desetilet\u00ed snili matematici o automatick\u00e9 kontrole […]<\/p>\n","protected":false},"author":1,"featured_media":7563,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":""},"categories":[1],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/7564"}],"collection":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/comments?post=7564"}],"version-history":[{"count":0,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/7564\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media\/7563"}],"wp:attachment":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media?parent=7564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/categories?post=7564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/tags?post=7564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}