{"id":9905,"date":"2026-08-10T22:17:26","date_gmt":"2026-08-10T15:17:26","guid":{"rendered":"https:\/\/useful.vn\/?p=9905"},"modified":"2026-08-10T22:17:26","modified_gmt":"2026-08-10T15:17:26","slug":"ai-giup-giai-bai-toan-kho-ton-tai-gan-90-nam","status":"publish","type":"post","link":"https:\/\/useful.vn\/?p=9905","title":{"rendered":"AI gi\u00fap gi\u1ea3i b\u00e0i to\u00e1n kh\u00f3 t\u1ed3n t\u1ea1i g\u1ea7n 90 n\u0103m"},"content":{"rendered":"
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\nAI gi\u00fap gi\u1ea3i b\u00e0i to\u00e1n kh\u00f3 t\u1ed3n t\u1ea1i g\u1ea7n 90 n\u0103m <\/h1>\n

Levent Alpoge, nh\u00e0 to\u00e1n h\u1ecdc 33 tu\u1ed5i t\u1ea1i \u0110\u1ea1i h\u1ecdc Harvard, thu h\u00fat ch\u00fa \u00fd khi c\u00f4ng b\u1ed1 l\u1eddi gi\u1ea3i v\u1edbi AI h\u1ed7 tr\u1ee3 cho gi\u1ea3 thuy\u1ebft Jacobian tr\u00ean X.<\/p>\n

Levent Alpoge cho bi\u1ebft, gi\u1ea3 thuy\u1ebft th\u1ef1c ch\u1ea5t l\u00e0 sai v\u00e0 ch\u1ee9ng minh b\u1eb1ng m\u1ed9t v\u00ed d\u1ee5 ng\u1eafn g\u1ecdn, \u0111\u01b0\u1ee3c ph\u00e1t hi\u1ec7n v\u1edbi s\u1ef1 tr\u1ee3 gi\u00fap c\u1ee7a m\u00f4 h\u00ecnh Claude Fable c\u1ee7a Anthropic. B\u00e0i \u0111\u0103ng tr\u00ean X c\u1ee7a \u00f4ng thu h\u00fat 30 tri\u1ec7u l\u01b0\u1ee3t xem, 41.000 l\u01b0\u1ee3t th\u00edch v\u00e0 h\u00e0ng lo\u1ea1t b\u00ecnh lu\u1eadn sau ch\u01b0a \u0111\u1ea7y ba ng\u00e0y. Nhi\u1ec1u chuy\u00ean gia \u0111\u00e1nh gi\u00e1 \u0111\u00e2y l\u00e0 b\u00e0i to\u00e1n kh\u00f3 nh\u1ea5t m\u00e0 AI t\u1eebng gi\u00fap gi\u1ea3i quy\u1ebft.<\/p>\n

Theo Fast Company<\/em>, gi\u1ea3 thuy\u1ebft Jacobian do nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi \u0110\u1ee9c Eduard Ott-Heinrich Keller \u0111\u01b0a ra n\u0103m 1939, cho r\u1eb1ng n\u1ebfu b\u1eaft \u0111\u1ea7u v\u1edbi m\u1ed9t \u0111i\u1ec3m tr\u00ean l\u01b0\u1edbi t\u1ecda \u0111\u1ed9 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng c\u00e1c bi\u1ebfn th\u00f4ng th\u01b0\u1eddng (ch\u1eb3ng h\u1ea1n x v\u00e0 y), sau \u0111\u00f3 d\u00f9ng \u0111a th\u1ee9c – ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a l\u0169y th\u1eeba nh\u01b0 x\u00b2 hay y\u00b3 – \u0111\u1ec3 t\u1ea1o ra t\u1ecda \u0111\u1ed9 m\u1edbi, th\u00ec ta c\u00f3 th\u1ec3 \u0111\u1ea3o ng\u01b0\u1ee3c qu\u00e1 tr\u00ecnh \u0111\u00f3 b\u1eb1ng c\u00e1ch d\u00f9ng \u0111a th\u1ee9c v\u00e0 kh\u00f4i ph\u1ee5c l\u1ea1i t\u1ecda \u0111\u1ed9 ban \u0111\u1ea7u. Gi\u1ea3 thuy\u1ebft Jacobian n\u1eb1m trong danh s\u00e1ch 18 b\u00e0i to\u00e1n si\u00eau kh\u00f3 c\u1ea7n gi\u1ea3i quy\u1ebft trong th\u1ebf k\u1ef7 21 do nh\u00e0 to\u00e1n h\u1ecdc Stephen Smale l\u1eadp ra n\u0103m 1998.<\/p>\n

V\u00ed d\u1ee5 ph\u1ea3n ch\u1ee9ng c\u1ee7a Alpoge ch\u1ec9 d\u00e0i 216 k\u00fd t\u1ef1 v\u00e0 ch\u01b0a tr\u1ea3i qua qu\u00e1 tr\u00ecnh b\u00ecnh duy\u1ec7t, nh\u01b0ng m\u1ed9t s\u1ed1 nh\u00e0 to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c cho l\u00e0 \u0111\u00e3 x\u00e1c nh\u1eadn ph\u00e9p t\u00ednh v\u00e0 ki\u1ec3m tra \u0111\u1ed9c l\u1eadp b\u1eb1ng SymPy (th\u01b0 vi\u1ec7n Python d\u00e0nh cho to\u00e1n h\u1ecdc k\u00fd hi\u1ec7u) v\u00e0 Lean (c\u00f4ng c\u1ee5 h\u1ed7 tr\u1ee3 ch\u1ee9ng minh \u0111\u1ecbnh l\u00fd). Nhi\u1ec1u ng\u01b0\u1eddi kh\u00e1c c\u0169ng d\u00f9ng AI h\u1ed7 tr\u1ee3, bao g\u1ed3m GPT c\u1ee7a OpenAI, \u0111\u1ec3 ki\u1ec3m ch\u1ee9ng ri\u00eang.<\/p>\n

Abhishek Saha, gi\u00e1o s\u01b0 to\u00e1n t\u1ea1i \u0110\u1ea1i h\u1ecdc Queen Mary London, cho bi\u1ebft nh\u1eefng ti\u1ebfn b\u1ed9 g\u1ea7n \u0111\u00e2y c\u1ee7a AI trong to\u00e1n h\u1ecdc v\u1ed1n \u0111\u00e3 g\u00e2y ng\u1ea1c nhi\u00ean, nh\u01b0ng th\u00e0nh t\u1ef1u m\u1edbi nh\u1ea5t c\u00f2n n\u00e2ng m\u1ecdi th\u1ee9 l\u00ean t\u1ea7m cao m\u1edbi. “\u0110\u1ebfn nay, c\u00f3 l\u1ebd \u0111\u00e2y l\u00e0 gi\u1ea3 thuy\u1ebft to\u00e1n h\u1ecdc l\u1edbn nh\u1ea5t m\u00e0 AI \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c ch\u1ee9ng minh ho\u1eb7c b\u00e1c b\u1ecf”, \u00f4ng n\u00f3i v\u1edbi New Scientist.<\/em><\/p>\n

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Logo m\u00f4 h\u00ecnh AI Claude Fable 5. \u1ea2nh: Anthropic<\/em><\/p>\n<\/figcaption><\/figure>\n

N\u1ebfu \u0111\u01b0\u1ee3c x\u00e1c th\u1ef1c, ph\u00e1t hi\u1ec7n c\u1ee7a Alpoge c\u00f3 th\u1ec3 cung c\u1ea5p m\u1ed9t trong nh\u1eefng b\u1eb1ng ch\u1ee9ng m\u1ea1nh nh\u1ea5t \u0111\u1ebfn nay v\u1ec1 \u0111i\u1ec1u m\u00e0 c\u00e1c nh\u00e0 ph\u00e1t tri\u1ec3n AI th\u01b0\u1eddng tuy\u00ean b\u1ed1: m\u00f4 h\u00ecnh ti\u00ean ti\u1ebfn s\u1ebd \u0111\u1ea9y nhanh \u0111\u00e1ng k\u1ec3 ph\u00e1t hi\u1ec7n to\u00e1n h\u1ecdc v\u00e0 khoa h\u1ecdc. Th\u00e0nh t\u1ef1u m\u1edbi c\u0169ng c\u00f3 th\u1ec3 th\u00e1ch th\u1ee9c nh\u1eefng ng\u01b0\u1eddi cho r\u1eb1ng AI kh\u00f4ng h\u1eefu \u00edch trong l\u0129nh v\u1ef1c \u0111\u00f2i h\u1ecfi \u0111\u1ed9 ch\u00ednh x\u00e1c cao.<\/p>\n

Chris Bowman-Scargill, ti\u1ebfn s\u0129 t\u1ea1i \u0110\u1ea1i h\u1ecdc York (Anh), cho r\u1eb1ng c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc ph\u1ea7n n\u00e0o \u0111\u00e3 th\u00edch nghi v\u1edbi n\u0103ng l\u1ef1c \u1ea5n t\u01b0\u1ee3ng c\u1ee7a AI. Tuy nhi\u00ean, \u00f4ng nh\u1ea5n m\u1ea1nh v\u1eabn c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa vi\u1ec7c t\u00ecm ra v\u00ed d\u1ee5 ph\u1ea3n ch\u1ee9ng \u0111\u1ec3 b\u00e1c b\u1ecf m\u1ed9t gi\u1ea3 thuy\u1ebft v\u1edbi vi\u1ec7c x\u00e2y d\u1ef1ng m\u1ed9t nh\u00e1nh to\u00e1n h\u1ecdc ho\u00e0n to\u00e0n m\u1edbi, v\u1ed1n \u0111\u00f2i h\u1ecfi s\u1ef1 s\u00e1ng t\u1ea1o c\u1ee7a con ng\u01b0\u1eddi. “\u0110i\u1ec1u th\u00fa v\u1ecb trong to\u00e1n h\u1ecdc th\u01b0\u1eddng kh\u00f4ng ph\u1ea3i l\u00e0 ‘\u1ed3, ch\u00fang ta \u0111\u00e3 gi\u1ea3i xong gi\u1ea3 thuy\u1ebft n\u00e0y r\u1ed3i’, m\u00e0 l\u00e0 nh\u1eefng th\u1ee9 b\u1ea1n ph\u1ea3i x\u00e2y d\u1ef1ng tr\u00ean \u0111\u01b0\u1eddng gi\u1ea3i quy\u1ebft gi\u1ea3 thuy\u1ebft \u0111\u00f3”, \u00f4ng n\u00f3i.<\/p>\n

Thu Th\u1ea3o<\/strong>t\u1ed5ng h\u1ee3p<\/em><\/p>\n<\/article>\n

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https:\/\/vnexpress.net\/ai-giup-giai-bai-toan-kho-ton-tai-gan-90-nam-5100336.html<\/p>\n","protected":false},"excerpt":{"rendered":"

AI gi\u00fap gi\u1ea3i b\u00e0i to\u00e1n kh\u00f3 t\u1ed3n t\u1ea1i g\u1ea7n 90 n\u0103m Levent Alpoge, nh\u00e0 to\u00e1n h\u1ecdc 33 tu\u1ed5i t\u1ea1i \u0110\u1ea1i h\u1ecdc Harvard, thu h\u00fat ch\u00fa \u00fd khi c\u00f4ng b\u1ed1 l\u1eddi gi\u1ea3i v\u1edbi AI h\u1ed7 tr\u1ee3 cho gi\u1ea3 thuy\u1ebft Jacobian tr\u00ean X. Levent Alpoge cho bi\u1ebft, gi\u1ea3 thuy\u1ebft th\u1ef1c ch\u1ea5t l\u00e0 sai v\u00e0 ch\u1ee9ng minh b\u1eb1ng<\/p>\n","protected":false},"author":1,"featured_media":9906,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-9905","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cong-nghe"],"_links":{"self":[{"href":"https:\/\/useful.vn\/index.php?rest_route=\/wp\/v2\/posts\/9905","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/useful.vn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/useful.vn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/useful.vn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/useful.vn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9905"}],"version-history":[{"count":0,"href":"https:\/\/useful.vn\/index.php?rest_route=\/wp\/v2\/posts\/9905\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/useful.vn\/index.php?rest_route=\/wp\/v2\/media\/9906"}],"wp:attachment":[{"href":"https:\/\/useful.vn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9905"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/useful.vn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9905"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/useful.vn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}