{"id":16801,"date":"2024-06-02T18:22:17","date_gmt":"2024-06-02T18:22:17","guid":{"rendered":"https:\/\/www.lifescienceart.com\/?p=16801"},"modified":"2024-06-02T18:22:17","modified_gmt":"2024-06-02T18:22:17","slug":"what-is-mathematics-invented-or-discovered","status":"publish","type":"post","link":"https:\/\/www.lifescienceart.com\/vi\/science\/mathematics\/what-is-mathematics-invented-or-discovered\/","title":{"rendered":"To\u00e1n h\u1ecdc l\u00e0 g\u00ec? Kh\u00e1m ph\u00e1 b\u1ea3n ch\u1ea5t b\u00ed \u1ea9n c\u1ee7a n\u00f3"},"content":{"rendered":"

To\u00e1n h\u1ecdc l\u00e0 g\u00ec?<\/h2>\n\n

Trong l\u0129nh v\u1ef1c tri th\u1ee9c c\u1ee7a lo\u00e0i ng\u01b0\u1eddi, to\u00e1n h\u1ecdc hi\u1ec7n l\u00ean nh\u01b0 m\u1ed9t ch\u1ee7 \u0111\u1ec1 \u0111\u1ea7y b\u00ed \u1ea9n, th\u00f4i th\u00fac nh\u1eefng c\u00e2u h\u1ecfi s\u00e2u s\u1eafc v\u1ec1 b\u1ea3n ch\u1ea5t v\u00e0 ngu\u1ed3n g\u1ed1c c\u1ee7a n\u00f3. T\u1eeb th\u1eddi c\u00e1c nh\u00e0 tri\u1ebft h\u1ecdc Hy L\u1ea1p c\u1ed5 \u0111\u1ea1i cho \u0111\u1ebfn ng\u00e0y nay, c\u00e1c h\u1ecdc gi\u1ea3 v\u1eabn \u0111ang v\u1eadt l\u1ed9n v\u1edbi nh\u1eefng c\u00e2u h\u1ecfi c\u01a1 b\u1ea3n n\u00e0y.<\/p>\n\n

\u0110\u01b0\u1ee3c ph\u00e1t minh hay kh\u00e1m ph\u00e1?<\/h2>\n\n

M\u1ed9t trong nh\u1eefng cu\u1ed9c tranh lu\u1eadn tr\u1ecdng t\u00e2m xung quanh to\u00e1n h\u1ecdc l\u00e0 li\u1ec7u n\u00f3 c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t ph\u00e1t minh c\u1ee7a tr\u00ed \u00f3c con ng\u01b0\u1eddi hay l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c ch\u00e2n l\u00fd t\u1ed3n t\u1ea1i \u0111\u1ed9c l\u1eadp v\u1edbi ch\u00fang ta. Quan \u0111i\u1ec3m c\u1ee7a Platon cho r\u1eb1ng c\u00e1c ch\u00e2n l\u00fd to\u00e1n h\u1ecdc l\u00e0 v\u0129nh c\u1eedu v\u00e0 b\u1ea5t bi\u1ebfn, t\u1ed3n t\u1ea1i trong m\u1ed9t c\u00f5i phi v\u1eadt ch\u1ea5t b\u00ean ngo\u00e0i kh\u00f4ng gian v\u00e0 th\u1eddi gian. M\u1eb7t kh\u00e1c, nh\u1eefng ng\u01b0\u1eddi theo ch\u1ee7 ngh\u0129a kinh nghi\u1ec7m l\u1eadp lu\u1eadn r\u1eb1ng to\u00e1n h\u1ecdc l\u00e0 s\u1ea3n ph\u1ea9m c\u1ee7a ch\u00ednh nh\u1eefng quan s\u00e1t v\u00e0 kinh nghi\u1ec7m c\u1ee7a ch\u00fang ta, v\u00e0 c\u00e1c ch\u00e2n l\u00fd c\u1ee7a n\u00f3 b\u1eaft ngu\u1ed3n t\u1eeb th\u1ebf gi\u1edbi v\u1eadt ch\u1ea5t.<\/p>\n\n

C\u00e1c th\u1ef1c th\u1ec3 tr\u1eebu t\u01b0\u1ee3ng<\/h2>\n\n

Cho d\u00f9 \u0111\u01b0\u1ee3c ph\u00e1t minh hay kh\u00e1m ph\u00e1, to\u00e1n h\u1ecdc \u0111\u1ec1u li\u00ean quan \u0111\u1ebfn c\u00e1c th\u1ef1c th\u1ec3 tr\u1eebu t\u01b0\u1ee3ng nh\u01b0 s\u1ed1, ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u00ecnh h\u1ecdc. Nh\u1eefng kh\u00e1i ni\u1ec7m n\u00e0y kh\u00f4ng t\u1ed3n t\u1ea1i v\u1ec1 m\u1eb7t v\u1eadt l\u00fd, nh\u01b0ng ch\u00fang \u0111\u00f3ng m\u1ed9t vai tr\u00f2 then ch\u1ed1t trong vi\u1ec7c ch\u00fang ta hi\u1ec3u v\u1ec1 v\u0169 tr\u1ee5. Ch\u00fang cho ph\u00e9p ch\u00fang ta m\u00f4 h\u00ecnh h\u00f3a v\u00e0 d\u1ef1 \u0111o\u00e1n h\u00e0nh vi c\u1ee7a th\u1ebf gi\u1edbi xung quanh, t\u1eeb chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a c\u00e1c thi\u00ean th\u1ec3 cho \u0111\u1ebfn d\u00f2ng ch\u1ea3y c\u1ee7a ch\u1ea5t l\u1ecfng.<\/p>\n\n

T\u00ednh ph\u1ed5 qu\u00e1t c\u1ee7a to\u00e1n h\u1ecdc<\/h2>\n\n

C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc t\u1eeb l\u00e2u \u0111\u00e3 cho r\u1eb1ng ch\u00e2n l\u00fd c\u1ee7a to\u00e1n h\u1ecdc mang t\u00ednh ph\u1ed5 qu\u00e1t, ngh\u0129a l\u00e0 ch\u00fang s\u1ebd \u0111\u00fang \u0111\u1ed1i v\u1edbi m\u1ecdi th\u1ef1c th\u1ec3 th\u00f4ng minh, b\u1ea5t k\u1ec3 ngu\u1ed3n g\u1ed1c hay n\u1ec1n v\u0103n h\u00f3a c\u1ee7a h\u1ecd. Tuy nhi\u00ean, m\u1ed9t s\u1ed1 nh\u00e0 t\u01b0 t\u01b0\u1edfng hi\u1ec7n \u0111\u1ea1i l\u1ea1i th\u00e1ch th\u1ee9c quan \u0111i\u1ec3m n\u00e0y. H\u1ecd l\u1eadp lu\u1eadn r\u1eb1ng h\u00ecnh d\u1ea1ng c\u1ee7a Tr\u00e1i \u0111\u1ea5t v\u00e0 b\u1ea3n ch\u1ea5t c\u00e1c tr\u1ea3i nghi\u1ec7m v\u1eadt l\u00fd c\u1ee7a ch\u00fang ta \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn s\u1ef1 ph\u00e1t tri\u1ec3n c\u00e1c kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc, cho th\u1ea5y to\u00e1n h\u1ecdc c\u00f3 th\u1ec3 kh\u00f4ng ph\u1ed5 qu\u00e1t nh\u01b0 ng\u01b0\u1eddi ta t\u1eebng ngh\u0129.<\/p>\n\n

T\u00ednh h\u1eefu \u00edch c\u1ee7a to\u00e1n h\u1ecdc<\/h2>\n\n

M\u1ed9t trong nh\u1eefng kh\u00eda c\u1ea1nh \u0111\u00e1ng ch\u00fa \u00fd nh\u1ea5t c\u1ee7a to\u00e1n h\u1ecdc l\u00e0 t\u00ednh h\u1eefu d\u1ee5ng phi th\u01b0\u1eddng c\u1ee7a n\u00f3 trong vi\u1ec7c m\u00f4 t\u1ea3 v\u00e0 d\u1ef1 \u0111o\u00e1n th\u1ebf gi\u1edbi v\u1eadt l\u00fd. C\u00e1c nh\u00e0 v\u1eadt l\u00fd v\u00e0 k\u1ef9 s\u01b0 ph\u1ee5 thu\u1ed9c r\u1ea5t nhi\u1ec1u v\u00e0o to\u00e1n h\u1ecdc \u0111\u1ec3 m\u00f4 h\u00ecnh h\u00f3a c\u00e1c h\u1ec7 th\u1ed1ng ph\u1ee9c t\u1ea1p, t\u1eeb ph\u1ea3n \u1ee9ng h\u1ea1t nh\u00e2n cho \u0111\u1ebfn h\u00e0nh vi c\u1ee7a c\u00e1c thi\u00ean h\u00e0. “Hi\u1ec7u qu\u1ea3 phi l\u00fd” n\u00e0y c\u1ee7a to\u00e1n h\u1ecdc \u0111\u00e3 khi\u1ebfn c\u00e1c nh\u00e0 khoa h\u1ecdc b\u1ed1i r\u1ed1i trong nhi\u1ec1u th\u1ebf k\u1ef7.<\/p>\n\n

Quan \u0111i\u1ec3m h\u01b0 c\u1ea5u<\/h2>\n\n

Trong nh\u1eefng n\u0103m g\u1ea7n \u0111\u00e2y, m\u1ed9t s\u1ed1 nh\u00e0 tri\u1ebft h\u1ecdc \u0111\u00e3 \u0111\u1ec1 xu\u1ea5t quan \u0111i\u1ec3m “h\u01b0 c\u1ea5u” v\u1ec1 to\u00e1n h\u1ecdc. H\u1ecd l\u1eadp lu\u1eadn r\u1eb1ng c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng to\u00e1n h\u1ecdc kh\u00f4ng c\u00f3 th\u1eadt theo c\u00f9ng m\u1ed9t c\u00e1ch nh\u01b0 c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng v\u1eadt l\u00fd, m\u00e0 \u0111\u00fang h\u01a1n l\u00e0 nh\u1eefng h\u01b0 c\u1ea5u h\u1eefu \u00edch m\u00e0 ch\u00fang ta t\u1ea1o ra \u0111\u1ec3 gi\u00fap ch\u00fang ta hi\u1ec3u th\u1ebf gi\u1edbi. C\u0169ng gi\u1ed1ng nh\u01b0 c\u00e1c nh\u00e2n v\u1eadt trong ti\u1ec3u thuy\u1ebft c\u00f3 th\u1ec3 h\u1eefu \u00edch \u0111\u1ec3 kh\u00e1m ph\u00e1 b\u1ea3n ch\u1ea5t con ng\u01b0\u1eddi, c\u00e1c kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc c\u00f3 th\u1ec3 h\u1eefu \u00edch \u0111\u1ec3 kh\u00e1m ph\u00e1 b\u1ea3n ch\u1ea5t c\u1ee7a th\u1ef1c t\u1ea1i.<\/p>\n\n

\u00dd ngh\u0129a \u0111\u1ed1i v\u1edbi gi\u00e1o d\u1ee5c<\/h2>\n\n

Cu\u1ed9c tranh lu\u1eadn v\u1ec1 b\u1ea3n ch\u1ea5t c\u1ee7a to\u00e1n h\u1ecdc c\u00f3 \u00fd ngh\u0129a \u0111\u1ed1i v\u1edbi c\u00e1ch ch\u00fang ta d\u1ea1y m\u00f4n h\u1ecdc n\u00e0y. N\u1ebfu to\u00e1n h\u1ecdc l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c ch\u00e2n l\u00fd ph\u1ed5 qu\u00e1t, th\u00ec vi\u1ec7c ghi nh\u1edb c\u00e1c c\u00f4ng th\u1ee9c v\u00e0 \u0111\u1ecbnh l\u00fd l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft. Tuy nhi\u00ean, n\u1ebfu to\u00e1n h\u1ecdc l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 m\u00e0 ch\u00fang ta t\u1ea1o ra \u0111\u1ec3 gi\u00fap ch\u00fang ta hi\u1ec3u th\u1ebf gi\u1edbi, th\u00ec vi\u1ec7c ph\u00e1t tri\u1ec3n c\u00e1c k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 c\u1ee7a h\u1ecdc sinh v\u00e0 kh\u1ea3 n\u0103ng \u00e1p d\u1ee5ng c\u00e1c kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc v\u00e0o c\u00e1c t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf quan tr\u1ecdng h\u01a1n nhi\u1ec1u.<\/p>\n\n

K\u1ebft lu\u1eadn<\/h2>\n\n

B\u1ea3n ch\u1ea5t c\u1ee7a to\u00e1n h\u1ecdc v\u1eabn l\u00e0 m\u1ed9t c\u00e2u h\u1ecfi m\u1edf, m\u1ed9t c\u00e2u h\u1ecfi \u0111\u00e3 khi\u1ebfn c\u00e1c h\u1ecdc gi\u1ea3 say m\u00ea trong h\u00e0ng thi\u00ean ni\u00ean k\u1ef7. Khi ch\u00fang ta ti\u1ebfp t\u1ee5c kh\u00e1m ph\u00e1 ranh gi\u1edbi tri th\u1ee9c c\u1ee7a lo\u00e0i ng\u01b0\u1eddi, ch\u00fang ta c\u00f3 th\u1ec3 \u0111i \u0111\u1ebfn s\u1ef1 hi\u1ec3u bi\u1ebft s\u00e2u s\u1eafc h\u01a1n v\u1ec1 ch\u1ee7 \u0111\u1ec1 \u0111\u1ea7y b\u00ed \u1ea9n n\u00e0y. Tuy nhi\u00ean, ngay c\u1ea3 khi ch\u00fang ta kh\u00f4ng bao gi\u1edd ho\u00e0n to\u00e0n gi\u1ea3i m\u00e3 \u0111\u01b0\u1ee3c nh\u1eefng b\u00ed \u1ea9n c\u1ee7a n\u00f3, to\u00e1n h\u1ecdc s\u1ebd v\u1eabn ti\u1ebfp t\u1ee5c l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 m\u1ea1nh m\u1ebd \u0111\u1ec3 m\u1edf kh\u00f3a nh\u1eefng b\u00ed m\u1eadt c\u1ee7a v\u0169 tr\u1ee5.<\/p>","protected":false},"excerpt":{"rendered":"

To\u00e1n h\u1ecdc l\u00e0 g\u00ec? Trong l\u0129nh v\u1ef1c tri th\u1ee9c c\u1ee7a lo\u00e0i ng\u01b0\u1eddi, to\u00e1n h\u1ecdc hi\u1ec7n l\u00ean nh\u01b0 m\u1ed9t ch\u1ee7 \u0111\u1ec1 \u0111\u1ea7y b\u00ed \u1ea9n, th\u00f4i th\u00fac nh\u1eefng c\u00e2u h\u1ecfi s\u00e2u s\u1eafc…<\/p>\n","protected":false},"author":1,"featured_media":23583,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[220],"tags":[22223,22220,22219,22218,22222,22221,214,22217],"class_list":["post-16801","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-fictionalist-view","tag-abstract-entities","tag-empiricism","tag-platonism","tag-usefulness-of-mathematics","tag-universality-of-mathematics","tag-mathematics","tag-philosophy-of-mathematics"],"_links":{"self":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts\/16801","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/comments?post=16801"}],"version-history":[{"count":1,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts\/16801\/revisions"}],"predecessor-version":[{"id":16802,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts\/16801\/revisions\/16802"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/media\/23583"}],"wp:attachment":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/media?parent=16801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/categories?post=16801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/tags?post=16801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}