{"id":530,"date":"2017-04-25T16:32:47","date_gmt":"2017-04-25T15:32:47","guid":{"rendered":"https:\/\/rosetta.vn\/short\/?p=530"},"modified":"2017-04-30T10:58:30","modified_gmt":"2017-04-30T09:58:30","slug":"david-hilbert-chung-ta-phai-biet-chung-ta-se-biet","status":"publish","type":"post","link":"https:\/\/rosetta.vn\/short\/2017\/04\/25\/david-hilbert-chung-ta-phai-biet-chung-ta-se-biet\/","title":{"rendered":"David Hilbert –\u00a0Di\u1ec5n t\u1eeb b\u1ed1n ph\u00fat b\u1ea5t h\u1ee7\u00a0tr\u00ean \u0111\u00e0i ph\u00e1t thanh n\u0103m 1930"},"content":{"rendered":"

Chu\u0301ng ta pha\u0309i bi\u00ea\u0301t<\/b><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0Chu\u0301ng ta se\u0303 bi\u00ea\u0301t<\/b><\/p>\n

Nguy\u1ec5n Xu\u00e2n Xanh gi\u1edbi thi\u1ec7u v\u00e0 chuy\u1ec3n ng\u1eef<\/p>\n

\n

Khoa h\u1ecdc theo t\u00f4i l\u00e0 m\u1ed9t th\u1ec3 th\u1ed1ng nh\u1ea5t kh\u00f4ng chia c\u1eaft \u0111\u01b0\u1ee3c. \u0110\u1eb7c \u0111i\u1ec3m c\u1ee7a to\u00e1n h\u1ecdc c\u00f3 c\u01a1 s\u1edf b\u00ean trong b\u1ea3n ch\u1ea5t c\u1ee7a ng\u00e0nh khoa h\u1ecdc n\u00e0y; b\u1edfi v\u00ec to\u00e1n h\u1ecdc l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c nh\u1eadn th\u1ee9c khoa h\u1ecdc t\u1ef1 nhi\u00ean ch\u00ednh x\u00e1c.<\/i><\/p>\n

David Hilbert<\/p>\n<\/blockquote>\n

Gi\u1edbi thi\u1ec7u<\/i><\/p>\n

DAVID HILBERT (1862-1943) la\u0300 \u201cm\u00f4\u0323t trong nh\u01b0\u0303ng nha\u0300 toa\u0301n ho\u0323c vi\u0303 \u0111a\u0323i nh\u00e2\u0301t cu\u0309a mo\u0323i th\u01a1\u0300i \u0111a\u0323i\u201d (Heisenberg), \u0111\u00f4i khi vi\u0301 nh\u01b0 m\u1ed9t \u201cEuclid th\u00ea\u0301 ky\u0309 20\u201d. \u00d4ng \u0111\u1ec3 l\u1ea1i d\u1ea5u \u1ea5n s\u00e2u \u0111\u1eadm l\u00ean s\u01b0\u0323 pha\u0301t tri\u00ea\u0309n cu\u0309a nhi\u00ea\u0300u la\u0303nh v\u01b0\u0323c toa\u0301n ho\u0323c nh\u01b0 \u0110a\u0323i s\u00f4\u0301, Ly\u0301 thuy\u00ea\u0301t s\u00f4\u0301, Hi\u0300nh ho\u0323c, Gia\u0309i ti\u0301ch, V\u00e2\u0323t ly\u0301 ly\u0301 thuy\u00ea\u0301t, L\u00f4gi\u0301c toa\u0301n, va\u0300 m\u00f4\u0301i li\u00ean h\u00ea\u0323 gi\u01b0\u0303a ca\u0301c la\u0303nh v\u01b0\u0323c na\u0300y. \u00d4ng la\u0300 \u201cnha\u0300 toa\u0301n ho\u0323c h\u00ea\u0323 th\u00f4\u0301ng\u201d. Ta\u0323i \u201cH\u00f4\u0323i nghi\u0323 toa\u0301n ho\u0323c th\u00ea\u0301 gi\u01a1\u0301i l\u1ea7n th\u1ee9 hai\u201d n\u0103m 1900 ta\u0323i Paris, v\u1edbi s\u1ef1 hi\u1ec3u bi\u1ebft s\u00e2u r\u1ed9ng, \u00f4ng co\u0301 ba\u0300i di\u00ea\u0303n v\u0103n n\u00f4\u0309i ti\u00ea\u0301ng v\u00ea\u0300 Hai m\u01b0\u01a1i ba ba\u0300i toa\u0301n quan tro\u0323ng ch\u01b0a \u0111\u01b0\u01a1\u0323c gia\u0309i quy\u00ea\u0301t, \u0111\u0103\u0323t n\u00ea\u0300n ta\u0309ng cho nghi\u00ean c\u01b0\u0301u toa\u0301n cho ca\u0301c th\u00e2\u0323p ky\u0309 ti\u00ea\u0301p theo. \u00d4ng lu\u00f4n ba\u0309o v\u00ea\u0323 s\u01b0\u0323 th\u00f4\u0301ng nh\u00e2\u0301t cu\u0309a toa\u0301n ho\u0323c ch\u00f4\u0301ng la\u0323i s\u01b0\u0323 ph\u00e2n ma\u0309nh tha\u0300nh nh\u01b0\u0303ng ly\u0301 thuy\u00ea\u0301t \u0111\u1ed9c l\u1eadp.<\/p>\n

Hoa Ky\u0300 pha\u0309i mang \u01a1n \u00f4ng r\u1ea5t nhi\u00ea\u0300u. Nhi\u00ea\u0300u nha\u0300 toa\u0301n ho\u0323c tre\u0309 cu\u0309a My\u0303 \u0111a\u0303 \u0111\u00ea\u0301n G\u00f6ttingen theo ho\u0323c \u00f4ng trong th\u01a1\u0300i gian 1900-1914 v\u00e0 tr\u01a1\u0309 tha\u0300nh nh\u01b0\u0303ng tru\u0323 c\u00f4\u0323t sau na\u0300y. Th\u01b0\u0323c t\u00ea\u0301, sinh vi\u00ean to\u00e1n cu\u0309a ca\u0309 th\u00ea\u0301 gi\u01a1\u0301i \u0111\u00ea\u0300u \u0111\u00ea\u0301n \u0111o\u0301 nh\u01b0 h\u00e0nh h\u01b0\u01a1ng v\u1ec1 m\u1ed9t Mecca. Nh\u01b0ng a\u0309nh h\u01b0\u01a1\u0309ng cu\u0309a nh\u01b0\u0303ng ba\u0300i toa\u0301n, ca\u0301c quan \u0111i\u00ea\u0309m, ca\u0301c ph\u01b0\u01a1ng pha\u0301p cu\u0309a \u00f4ng \u0111\u00e3 v\u01b0\u01a1\u0323t kho\u0309i gi\u01a1\u0301i ho\u0323c tro\u0300 \u0111\u01b0\u01a1\u0323c \u00f4ng truy\u00ea\u0300n ca\u0309m h\u01b0\u0301ng tr\u01b0\u0323c ti\u00ea\u0301p. Ti\u00ea\u0301p theo l\u00e0n s\u00f3ng du ho\u0323c la\u0300 cu\u00f4\u0323c di ta\u0309n \u1ed3 \u1ea1t sang M\u1ef9 v\u00e0o nh\u01b0\u0303ng n\u0103m 1930 cu\u0309a ca\u0301c ho\u0323c tro\u0300 cu\u0309a \u00f4ng, va\u0300 cu\u0309a gi\u1edbi toa\u0301n ho\u0323c, khoa ho\u0323c ch\u00e2u \u00c2u. S\u1ef1 c\u1ed1ng hi\u1ebfn c\u1ee7a h\u1ecd \u0111\u00e3 \u0111\u01b0a n\u00ea\u0300n toa\u0301n ho\u0323c va\u0300 v\u00e2\u0323t ly\u0301 My\u0303 th\u0103ng hoa v\u00e0 chi\u00ea\u0301m gi\u01b0\u0303 vi\u0323 tri\u0301 d\u1eabn \u0111\u1ea7u th\u00ea\u0301 gi\u01a1\u0301i.<\/p>\n

Hilbert co\u0301 m\u1ed9t tinh th\u1ea7n la\u0323c quan, m\u1ed9t ni\u00ea\u0300m tin v\u00f4 ha\u0323n v\u00ea\u0300 n\u0103ng l\u01b0\u0323c t\u01b0 duy va\u0300 kha\u0309 n\u0103ng kha\u0301m pha\u0301 cu\u0309a con ng\u01b0\u01a1\u0300i – r\u0103\u0300ng t\u00e2\u0301t ca\u0309 c\u00e1c ba\u0300i toa\u0301n se\u0303 \u0111\u01b0\u01a1\u0323c gia\u0309i quy\u00ea\u0301t – \u0111em la\u0323i cho \u00f4ng s\u01b0\u0323 can \u0111a\u0309m va\u0300 s\u01b0\u0301c ma\u0323nh. Nh\u01b0ng ni\u00ea\u0300m tin \u0111o\u0301 cu\u0303ng khi\u1ebfn \u00f4ng kh\u00f4ng linh ca\u0309m \u0111\u01b0\u01a1\u0323c r\u1eb1ng, co\u0301 th\u00ea\u0309 co\u0301 nh\u01b0\u0303ng v\u00e2\u0301n \u0111\u00ea\u0300 toa\u0301n ho\u0323c na\u0300o \u0111o\u0301 kh\u00f4ng th\u00ea\u0309 gi\u1ea3i quy\u1ebft \u0111\u01b0\u01a1\u0323c trong ca\u0301c h\u00ea\u0323 th\u00f4\u0301ng ti\u00ean \u0111\u00ea\u0300 cu\u0309a \u00f4ng. N\u0103m 1930, \u00f4ng k\u00ea\u0301t thu\u0301c ba\u0300i \u0111a\u0301p t\u01b0\u0300 v\u00ea\u0300 h\u01b0u (Ti\u00eau \u0111\u1ec1: Naturerkennen und Logik, Nh\u1eadn th\u1ee9c v\u1ec1 T\u1ef1 nhi\u00ean v\u00e0 L\u00f4g\u00edc) ta\u0323i H\u00f4\u0323i nghi\u0323 ca\u0301c Nha\u0300 khoa ho\u0323c t\u01b0\u0323 nhi\u00ean va\u0300 Ba\u0301c si\u0303 \u0110\u01b0\u0301c ta\u0323i K\u00f6nigsberg qu\u00ea h\u01b0\u01a1ng \u00f4ng, va\u0300 cu\u0303ng l\u00e0 qu\u00ea h\u01b0\u01a1ng cu\u0309a Kant (nay la\u0300 Kaliningrad, Nga), v\u01a1\u0301i hai c\u00e2u b\u00e2\u0301t hu\u0309:
\n<\/i><\/p>\n

Chu\u0301ng ta pha\u0309i bi\u00ea\u0301t<\/em><\/p>\n

Chu\u0301ng ta se\u0303 bi\u00ea\u0301t<\/em><\/p>\n

(Wir m\u00fcssen wissen<\/span>
Wir werden wissen)\u00a0<\/span><\/p><\/blockquote>\n

\u0111\u00ea\u0309 \u0111a\u0301p tr\u1ea3 kh\u00e2\u0309u hi\u1ec7u “Ignoramus et ignorabimus”, hay l\u00e0 “Chu\u0301ng ta kh\u00f4ng bi\u00ea\u0301t, chu\u0301ng ta se\u0303 kh\u00f4ng bi\u00ea\u0301t\u201d cu\u0309a nha\u0300 sinh ly\u0301 ho\u0323c \u0110\u01b0\u0301c Emil du Bois-Reymond. M\u00f4\u0323t nga\u0300y tr\u01b0\u01a1\u0301c khi Hilbert tuy\u00ean b\u00f4\u0301 hai c\u00e2u tr\u00ean, Kurt G\u00f6del (1906-1978) \u0111a\u0303 c\u00f4ng b\u00f4\u0301 phi\u00ean ba\u0309n \u0111\u00e2\u0300u ti\u00ean cu\u0309a ca\u0301c \u0111i\u0323nh ly\u0301 b\u00e2\u0301t toa\u0300n c\u1ee7a \u00f4ng.<\/span>
\nKh\u1ea9u hi\u1ec7u c\u1ee7a Hilbert th\u1ef1c t\u1ebf bi\u1ec3u th\u1ecb trung th\u1ef1c s\u1ef1 d\u00e2ng l\u00ean c\u1ee7a \u0111\u1ee3t s\u00f3ng nh\u1eefng kh\u00e1m ph\u00e1 k\u1ef3 th\u00fa v\u00e0 ngo\u1ea1n m\u1ee5c nh\u1ea5t l\u1ecbch s\u1eed trong c\u00e1c ng\u00e0nh khoa h\u1ecdc, nh\u1ea5t l\u00e0 trong ng\u00e0nh v\u1eadt l\u00fd, di\u1ec5n ra li\u00ean t\u1ee5c t\u1eeb cu\u1ed1i th\u1ebf k\u1ef7 th\u1ee9 m\u01b0\u1eddi ch\u00edn v\u00e0 \u0111\u1ea1t \u0111\u1ebfn \u0111\u1ec9nh cao trong c\u00e1c th\u1eadp ni\u00ean \u0111\u1ea7u c\u1ee7a th\u1ebf k\u1ef7 hai m\u01b0\u01a1i, \u0111\u1ec3 h\u00ecnh th\u00e0nh m\u1ed9t th\u1ebf gi\u1edbi quan m\u1edbi h\u00f4m nay v\u1eabn c\u00f2n gi\u00e1 tr\u1ecb. Con ng\u01b0\u1eddi nh\u01b0 mu\u1ed1n bi\u1ebft t\u1ea5t c\u1ea3, mu\u1ed1n nh\u00ecn th\u1ea5y \u201ec\u00e1c con b\u00e0i c\u1ee7a Ch\u00faa\u201c c\u00f2n \u0111ang d\u1ea5u k\u00edn nh\u01b0 Albert Einstein di\u1ec5n t\u1ea3. Nh\u1eefng kh\u00e1m ph\u00e1 \u0111\u00f3 c\u0169ng di\u1ec5n ra tr\u00f9ng kh\u1edbp v\u1edbi giai \u0111o\u1ea1n m\u00e0 t\u1ea1i Hoa K\u1ef3 v\u00e0 ph\u1ea7n l\u1edbn ch\u00e2u \u00c2u x\u00e3 h\u1ed9i n\u00f4ng nghi\u1ec7p \u0111ang \u0111\u01b0\u1ee3c chuy\u1ec3n \u0111\u1ed5i ho\u00e0n to\u00e0n sang x\u00e3 h\u1ed9i c\u00f4ng nghi\u1ec7p hi\u1ec7n \u0111\u1ea1i.<\/p>\n

Hilbert m\u00e2\u0301t n\u0103m 1943 ta\u0323i G\u00f6ttingen, h\u01b0\u01a1\u0309ng tho\u0323 81 tu\u00f4\u0309i. Hai c\u00e2u tr\u00ean \u0111\u01b0\u01a1\u0323c kh\u0103\u0301c l\u00ean bia m\u1ed9 c\u1ee7a \u00f4ng ta\u0323i G\u00f6ttingen.<\/p>\n

\"\"M\u1ed9 c\u1ee7a David Hilbert t\u1ea1i\u00a0G\u00f6ttingen v\u1edbi kh\u1ea9u hi\u1ec7u \u0111\u01b0\u1ee3c kh\u1eafc:<\/span><\/p>\n

WIR M\u00dcSSEN WISSEN<\/span>
WIR WERDEN WISSEN<\/span>
\n<\/span><\/p>\n

Xin n\u00f3i th\u00eam v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa to\u00e1n h\u1ecdc v\u00e0 khoa h\u1ecdc \u0111\u01b0\u1ee3c th\u1ea3o lu\u1eadn nhi\u1ec1u trong l\u1ecbch s\u1eed. Georg Cantor, cha \u0111\u1ebb c\u1ee7a thuy\u1ebft t\u1eadp h\u1ee3p, c\u00f3 m\u1ed9t quan \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t khi, xu\u1ea5t ph\u00e1t t\u1eeb kinh nghi\u1ec7m c\u1ee7a \u00f4ng, cho r\u1eb1ng to\u00e1n h\u1ecdc kh\u00e1c v\u1edbi c\u00e1c ng\u00e0nh kh\u00e1c b\u1edfi t\u00ednh ch\u1ea5t ho\u00e0n to\u00e0n \u0111\u1ed9c l\u1eadp c\u1ee7a n\u00f3 trong vi\u1ec7c t\u1ea1o ra c\u00e1c con-x\u1ebfp (concept) m\u00e0 kh\u00f4ng c\u1ea7n \u0111\u1ec3 \u00fd \u0111\u1ebfn th\u1ef1c t\u1ea1i, mi\u1ec5n l\u00e0 ch\u00fang kh\u00f4ng m\u00e2u thu\u1ea9n v\u1edbi nh\u1eefng \u0111\u1ecbnh ngh\u0129a c\u00f3 tr\u01b0\u1edbc. Cantor th\u00edch s\u1eed d\u1ee5ng t\u1eeb \u201eto\u00e1n h\u1ecdc t\u1ef1 do\u201c h\u01a1n \u201eto\u00e1n h\u1ecdc thu\u1ea7n t\u00fay\u201c. M\u1eb7c d\u00f9 th\u1ebf, \u201eto\u00e1n t\u1ef1 do c\u1ee7a \u00f4ng\u201c c\u00f3 v\u00f4 s\u1ed1 \u1ee9ng d\u1ee5ng. Nh\u01b0ng t\u1eeb th\u1ebf k\u1ef7 m\u01b0\u1eddi ch\u00edn tr\u1edf \u0111i, m\u1ed1i quan h\u1ec7 gi\u1eefa to\u00e1n h\u1ecdc v\u00e0 khoa h\u1ecdc, trong \u0111\u00f3 \u0111\u1eb7c bi\u1ec7t ng\u00e0nh v\u1eadt l\u00fd, ng\u00e0y c\u00e0ng ph\u00e1t tri\u1ec3n. T\u1ea1i H\u1ed9i ngh\u1ecb to\u00e1n h\u1ecdc th\u1ebf gi\u1edbi l\u1ea7n th\u1ee9 hai, Hilbert ph\u00e1t bi\u1ec3u:<\/span>
\nNgay c\u1ea3 khi ho\u1ea1t \u0111\u1ed9ng s\u00e1ng t\u1ea1o n\u00e0y c\u1ee7a t\u01b0 duy thu\u1ea7n t\u00fay ti\u1ebfp di\u1ec5n, th\u1ebf gi\u1edbi b\u00ean ngo\u00e0i l\u1ea1i ti\u1ebfp t\u1ee5c t\u00e1i x\u00e1c nh\u1eadn t\u00ednh hi\u1ec7u l\u1ef1c c\u1ee7a n\u00f3, v\u00e0 b\u1eb1ng c\u00e1ch r\u00f3t th\u00eam nh\u1eefng c\u00e2u h\u1ecfi m\u1edbi l\u00ean ch\u00fang ta qua c\u00e1c hi\u1ec7n t\u01b0\u1ee3ng xu\u1ea5t hi\u1ec7n, m\u1edf ra nhi\u1ec1u l\u00e3nh v\u1ef1c c\u1ee7a tri th\u1ee9c to\u00e1n h\u1ecdc; v\u00e0 khi ch\u00fang ta c\u1ed1 g\u1eafng \u0111\u01b0a nh\u1eefng l\u00e3nh v\u1ef1c m\u1edbi n\u00e0y v\u00e0o v\u00f9ng \u1ea3nh h\u01b0\u1edfng c\u1ee7a t\u01b0 duy thu\u1ea7n t\u00fay, ch\u00fang ta th\u01b0\u1eddng t\u00ecm th\u1ea5y nh\u1eefng l\u1eddi gi\u1ea3i cho nh\u1eefng b\u00e0i to\u00e1n c\u00f2n t\u1ed3n \u0111\u1ecdng, v\u00e0 do \u0111\u00f3 c\u00f9ng l\u00fac ch\u00fang ta ph\u00e1t tri\u1ec3n nh\u1eefng l\u00fd thuy\u1ebft tr\u01b0\u1edbc \u0111\u00e2y m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 nh\u1ea5t.T\u00f9y thu\u1ed9c v\u00e0o t\u00e1c \u0111\u1ed9ng qua l\u1ea1i gi\u1eefa t\u01b0 duy v\u00e0 th\u00ed nghi\u1ec7m, theo t\u00f4i, l\u00e0 nhi\u1ec1u t\u00ednh t\u01b0\u01a1ng t\u1ef1 \u0111\u00e1ng ng\u1ea1c nhi\u00ean, v\u00e0 s\u1ef1 h\u00e0i h\u00f2a r\u00f5 r\u00e0ng ti\u1ec1n \u0111\u1ecbnh m\u00e0 c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc r\u1ea5t th\u01b0\u1eddng quan ni\u1ec7m trong c\u00e1c b\u00e0i to\u00e1n, ph\u01b0\u01a1ng ph\u00e1p, v\u00e0 con-x\u1ebfp c\u1ee7a c\u00e1c \u0111\u1ecba h\u1ea1t kh\u00e1c nhau c\u1ee7a tri th\u1ee9c.<\/p>\n

Nh\u00e0 to\u00e1n h\u1ecdc Ph\u00e1p Charles Hermite \u0111\u01b0a ra m\u1ed9t c\u00e1ch gi\u1ea3i th\u00edch s\u1ef1 li\u00ean h\u1ec7 k\u1ef3 di\u1ec7u gi\u1eefa to\u00e1n h\u1ecdc v\u00e0 khoa h\u1ecdc nh\u01b0 sau:
\nN\u1ebfu t\u00f4i kh\u00f4ng l\u1ea7m, t\u1ed3n t\u1ea1i m\u1ed9t th\u1ebf gi\u1edbi l\u00e0 t\u1eadp h\u1ee3p c\u1ee7a nh\u1eefng ch\u00e2n l\u00fd to\u00e1n, m\u00e0 ch\u00fang ta ti\u1ebfp c\u1eadn \u0111\u01b0\u1ee3c th\u00f4ng qua n\u0103ng l\u1ef1c tr\u00ed tu\u1ec7 c\u1ee7a ch\u00fang ta, c\u0169ng nh\u01b0 m\u1ed9t th\u1ebf gi\u1edbi c\u1ee7a th\u1ef1c t\u1ea1i v\u1eadt l\u00fd; th\u1ebf gi\u1edbi n\u00e0y v\u00e0 th\u1ebf gi\u1edbi kia \u0111\u1ed9c l\u1eadp v\u1edbi ch\u00fang ta, c\u1ea3 hai \u0111\u1ec1u l\u00e0 s\u1ef1 s\u00e1ng t\u00e1c th\u1ea7n th\u00e1nh, ch\u00fang xu\u1ea5t hi\u1ec7n kh\u00e1c nhau \u0111\u1ed1i v\u1edbi ch\u00fang ta ch\u1ec9 v\u00ec s\u1ef1 y\u1ebfu k\u00e9m c\u1ee7a tinh th\u1ea7n ch\u00fang ta, nh\u01b0ng \u0111\u1ed1i v\u1edbi m\u1ed9t l\u1ed1i t\u01b0 duy m\u1ea1nh m\u1ebb h\u01a1n, c\u1ea3 hai \u0111\u1ec1u l\u00e0 m\u1ed9t v\u00e0 \u0111\u1ed3ng nh\u1ea5t. S\u1ef1 t\u1ed5ng h\u1ee3p c\u1ee7a hai th\u1ee9 \u0111\u01b0\u1ee3c h\u00e9 l\u1ed9 m\u1ed9t ph\u1ea7n trong s\u1ef1 t\u01b0\u01a1ng \u1ee9ng k\u1ef3 di\u1ec7u gi\u1eefa to\u00e1n h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng, m\u1ed9t m\u1eb7t, v\u00e0 t\u1ea5t c\u1ea3 nh\u1eefng ng\u00e0nh v\u1eadt l\u00fd, m\u1eb7t kia.<\/p>\n

Einstein, trong “Th\u1ebf gi\u1edbi nh\u01b0 t\u00f4i th\u1ea5y”, v\u1edbi nh\u1eefng tr\u1ea3i nghi\u1ec7m \u0111\u1eb7c bi\u1ec7t c\u1ee7a m\u00ecnh trong kh\u00e1m ph\u00e1, \u0111\u00e3 gi\u1ea3i th\u00edch th\u00eam nh\u01b0 sau:
\nKinh nghi\u1ec7m c\u1ee7a ch\u00fang ta cho \u0111\u1ebfn nay l\u00e0m cho ch\u00fang ta tin r\u1eb1ng t\u1ef1 nhi\u00ean l\u00e0 s\u1ef1 th\u1ec3 hi\u1ec7n (realization) c\u1ee7a nh\u1eefng \u00fd t\u01b0\u1edfng to\u00e1n h\u1ecdc \u0111\u01a1n gi\u1ea3n nh\u1ea5t c\u00f3 th\u1ec3 quan ni\u1ec7m \u0111\u01b0\u1ee3c. T\u00f4i tin t\u01b0\u1edfng r\u1eb1ng ch\u00fang ta, b\u1eb1ng c\u00e1c c\u1ea5u t\u1ea1o to\u00e1n h\u1ecdc thu\u1ea7n t\u00fay, c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 c\u00e1c con-x\u1ebfp v\u00e0 \u0111\u1ecbnh lu\u1eadt n\u1ed1i li\u1ec1n ch\u00fang v\u1edbi nhau, \u0111i\u1ec1u cung c\u1ea5p chi\u1ebfc ch\u00eca kh\u00f3a cho s\u1ef1 hi\u1ec3u bi\u1ebft c\u00e1c hi\u1ec7n t\u01b0\u1ee3ng t\u1ef1 nhi\u00ean. Kinh nghi\u1ec7m c\u00f3 th\u1ec3 g\u1ee3i ra c\u00e1c con-x\u1ebfp to\u00e1n h\u1ecdc th\u00edch h\u1ee3p, nh\u01b0ng ch\u00fang ph\u1ea7n l\u1edbn kh\u00f4ng th\u1ec3 \u0111\u01b0\u1ee3c suy di\u1ec5n t\u1eeb n\u00f3. Kinh nghi\u1ec7m, d\u0129 nhi\u00ean, v\u1eabn l\u00e0 ti\u00eau chu\u1ea9n duy nh\u1ea5t cho s\u1ef1 h\u1eefu \u00edch c\u1ee7a m\u1ed9t c\u1ea5u t\u1ea1o to\u00e1n h\u1ecdc. Nh\u01b0ng nguy\u00ean l\u00fd s\u00e1ng t\u1ea1o (tr\u01b0\u1edbc t\u00e1c) thu\u1ed9c v\u1ec1 to\u00e1n h\u1ecdc. Cho n\u00ean, trong m\u1ed9t ngh\u0129a n\u00e0o \u0111\u00f3, \u0111\u00fang l\u00e0 t\u01b0 duy thu\u1ea7n t\u00fay c\u00f3 th\u1ec3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c th\u1ef1c t\u1ebf nh\u01b0 nh\u1eefng ng\u01b0\u1eddi c\u1ed5 \u0111\u1ea1i m\u01a1 \u01b0\u1edbc.<\/p>\n

\u1ee8ng d\u1ee5ng c\u1ee7a h\u00ecnh h\u1ecdc phi-Euclid v\u00e0o thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i r\u1ed9ng, c\u1ee7a l\u00fd thuy\u1ebft nh\u00f3m v\u00e0o c\u1ea5u tr\u00fac c\u1ee7a c\u00e1c h\u1ea1t c\u01a1 b\u1ea3n quark l\u00e0 nh\u1eefng th\u00ed d\u1ee5 kinh ng\u1ea1c v\u1ec1 m\u1ed1i quan h\u1ec7 b\u1ea5t ng\u1edd gi\u1eefa to\u00e1n h\u1ecdc v\u00e0 v\u1eadt l\u00fd.<\/p>\n

D\u01b0\u01a1\u0301i \u0111\u00e2y la\u0300 di\u00ea\u0303n t\u01b0\u0300 t\u00f3m t\u1eaft b\u00f4\u0301n phu\u0301t cu\u0309a \u00f4ng n\u0103m 1930 d\u00e0nh cho \u0111a\u0300i truy\u1ec1n thanh \u0110\u01b0\u0301c, m\u1ed9t b\u1ea3n \u201chu\u0300ng ca\u201d r\u00e2\u0301t truy\u00ea\u0300n ca\u0309m da\u0300nh cho toa\u0301n ho\u0323c.<\/p>\n

\"\"<\/p>\n

David Hilbert 1932<\/p>\n

N\u1ed9i dung c\u1ee7a Di\u00ea\u0303n t\u01b0\u0300:<\/i><\/p>\n

“C\u00f4ng cu\u0323 trung gian gi\u01b0\u0303a ly\u0301 thuy\u00ea\u0301t va\u0300 th\u01b0\u0323c ha\u0300nh, gi\u01b0\u0303a t\u01b0 duy va\u0300 quan sa\u0301t la\u0300 toa\u0301n ho\u0323c. No\u0301 x\u00e2y d\u01b0\u0323ng c\u00e2\u0300u n\u00f4\u0301i va\u0300 la\u0300m cho chi\u00ea\u0301c c\u00e2\u0300u n\u00e0y nga\u0300y ca\u0300ng v\u1eefng ch\u1eafc h\u01a1n. Cho n\u00ean, to\u00e0n b\u1ed9 n\u00ea\u0300n v\u0103n ho\u0301a hi\u00ea\u0323n ta\u0323i c\u1ee7a chu\u0301ng ta, trong ch\u01b0\u0300ng m\u01b0\u0323c d\u1ef1a tr\u00ean nh\u00e2\u0323n th\u01b0\u0301c v\u00ea\u0300 t\u01b0\u0323 nhi\u00ean va\u0300 s\u01b0\u0323 \u01b0\u0301ng du\u0323ng no\u0301, ti\u0300m th\u00e2\u0301y n\u00ea\u0300n ta\u0309ng cu\u0309a m\u00ecnh trong toa\u0301n ho\u0323c. GALILEI \u0111\u00e3 t\u01b0\u0300ng no\u0301i: Ng\u01b0\u01a1\u0300i ta chi\u0309 co\u0301 th\u00ea\u0309 hi\u00ea\u0309u \u0111\u01b0\u01a1\u0323c t\u01b0\u0323 nhi\u00ean khi h\u1ecdc \u0111\u01b0\u1ee3c ng\u00f4n ng\u01b0\u0303 cu\u0309a n\u00f3 va\u0300 quen thu\u00f4\u0323c v\u1edbi ca\u0301c ky\u0301 hi\u00ea\u0323u ma\u0300 qua \u0111o\u0301 t\u01b0\u0323 nhi\u00ean no\u0301i v\u01a1\u0301i chu\u0301ng ta. Nh\u01b0ng ng\u00f4n ng\u01b0\u0303 n\u00e0y la\u0300 toa\u0301n ho\u0323c, va\u0300 ca\u0301c ky\u0301 hi\u00ea\u0323u chi\u0301nh la\u0300 nh\u01b0\u0303ng hi\u0300nh toa\u0301n ho\u0323c. KANT t\u01b0\u0300ng qua\u0309 quy\u00ea\u0301t: \u201cT\u00f4i cho r\u0103\u0300ng trong m\u00f4\u0303i m\u00f4n khoa ho\u0323c t\u01b0\u0323 nhi\u00ean \u0111\u1eb7c bi\u1ec7t, chi\u0309 co\u0301 th\u00ea\u0309 ti\u0300m th\u00e2\u0301y khoa ho\u0323c \u0111i\u0301ch th\u01b0\u0323c trong ch\u01b0\u0300ng m\u01b0\u0323c n\u00f4\u0323i ha\u0300m toa\u0301n ho\u0323c \u0111\u01b0\u01a1\u0323c ch\u01b0\u0301a \u0111\u01b0\u0323ng trong \u0111o\u0301.\u201d S\u01b0\u0323 th\u00e2\u0323t: Chu\u0301ng ta chi\u0309 la\u0300m chu\u0309 \u0111\u01b0\u01a1\u0323c m\u00f4\u0323t ly\u0301 thuy\u00ea\u0301t khoa ho\u0323c khi chu\u0301ng ta t\u00e1ch \u0111\u01b0\u01a1\u0323c ca\u0301i nh\u00e2n toa\u0301n ho\u0323c c\u1ee7a n\u00f3 ra va\u0300 b\u00f3c tr\u1ea7n n\u00f3 hoa\u0300n to\u00e0n kh\u1ecfi v\u1ecf. Kh\u00f4ng co\u0301 toa\u0301n ho\u0323c, kh\u00f4ng th\u00ea\u0309 co\u0301 nga\u0300nh thi\u00ean v\u0103n h\u1ecdc v\u00e0 v\u00e2\u0323t ly\u0301 h\u1ecdc ng\u00e0y nay; nh\u01b0\u0303ng nga\u0300nh khoa ho\u0323c na\u0300y, trong nh\u1eefng ph\u1ea7n l\u00fd thuy\u1ebft c\u1ee7a ch\u00fang, \u0111\u1ec1u hi\u00ea\u0323n ra \u1edf d\u1ea1ng toa\u0301n ho\u0323c. Nh\u01b0\u0303ng \u01b0\u0301ng du\u0323ng na\u0300y, cu\u0303ng nh\u01b0 v\u00f4 s\u00f4\u0301 nh\u01b0\u0303ng \u01b0\u0301ng du\u0323ng kha\u0301c, la\u0300 nh\u01b0\u0303ng g\u00ec \u0111a\u0303 giu\u0301p cho toa\u0301n ho\u0323c la\u0300m n\u00ean t\u00ean tu\u00f4\u0309i m\u00e0 n\u00f3 c\u00f3 \u0111\u01b0\u1ee3c v\u1edbi \u0111\u00f4ng \u0111\u1ea3o c\u00f4ng chu\u0301ng.\u200b<\/p>\n

Tuy nhi\u00ean, t\u1ea5t c\u1ea3 ca\u0301c nha\u0300 toa\u0301n ho\u0323c \u0111a\u0303 t\u01b0\u0300 ch\u00f4\u0301i l\u00e2\u0301y \u01b0\u0301ng du\u0323ng la\u0300m th\u01b0\u01a1\u0301c \u0111o cho toa\u0301n ho\u0323c. GAUSS \u0111a\u0303 no\u0301i v\u00ea\u0300 s\u01b0\u0323 m\u00ea ho\u1eb7c \u0111a\u0303 la\u0300m cho ly\u0301 thuy\u00ea\u0301t s\u00f4\u0301 tr\u01a1\u0309 tha\u0300nh khoa ho\u0323c con c\u01b0ng cu\u0309a ca\u0301c nha\u0300 toa\u0301n ho\u0323c \u0111\u00e2\u0300u ti\u00ean, kh\u00f4ng k\u00ea\u0309 \u0111\u00ea\u0301n s\u01b0\u0323 phong phu\u0301 b\u1ea5t t\u1eadn cu\u0309a no\u0301, m\u00e0 \u1edf \u0111o\u0301 no\u0301 \u0111a\u0303 v\u01b0\u01a1\u0323t xa t\u00e2\u0301t ca\u0309 c\u00e1c nga\u0300nh kha\u0301c cu\u0309a toa\u0301n ho\u0323c. KRONECKER so sa\u0301nh ca\u0301c nha\u0300 ly\u0301 thuy\u00ea\u0301t s\u00f4\u0301 v\u01a1\u0301i nh\u01b0\u0303ng ng\u01b0\u01a1\u0300i \u0103n ha\u0323t sen, m\u1ed9t khi \u0111\u00e3 n\u1ebfm th\u1eed m\u00f3n na\u0300y, h\u1ecd se\u0303 kh\u00f4ng bao gi\u01a1\u0300 d\u1eebng l\u1ea1i \u0111\u01b0\u01a1\u0323c.<\/p>\n

V\u1edbi s\u1ef1 quy\u1ebft li\u1ec7t \u0111\u00e1ng kinh ng\u1ea1c, nha\u0300 toa\u0301n ho\u0323c v\u0129 \u0111\u1ea1i POINCARE\u0301 \u0111\u00e3 t\u1eebng t\u1ea5n c\u00f4ng TOLSTOI, ng\u01b0\u01a1\u0300i tuy\u00ean b\u00f4\u0301 r\u0103\u0300ng y\u00eau s\u00e1ch \u201ckhoa ho\u0323c vi\u0323 khoa ho\u0323c\u201d la\u0300 \u0111i\u00ean r\u00f4\u0300. Nh\u01b0\u0303ng tha\u0300nh t\u01b0\u0323u c\u00f4ng nghi\u1ec7p, ch\u1eb3ng ha\u0323n, se\u0303 kh\u00f4ng th\u00ea\u0309 na\u0300o c\u00f3 m\u1eb7t tr\u00ean \u0111\u1eddi n\u00ea\u0301u nh\u01b0\u0303ng nh\u00e0 th\u1ef1c h\u00e0nh chi\u0309 t\u00f4\u0300n ta\u0323i m\u1ed9t mi\u0300nh, va\u0300 nh\u01b0\u0303ng ti\u1ebfn b\u1ed9 c\u1ee7a h\u1ecd kh\u00f4ng \u0111\u01b0\u01a1\u0323c th\u00fac \u0111\u1ea9y b\u01a1\u0309i nh\u01b0\u0303ng ke\u0309 \u0111i\u00ean r\u00f4\u0300 v\u00f4 vu\u0323 l\u01a1\u0323i kia.<\/p>\n

Ni\u00ea\u0300m vinh d\u01b0\u0323 cu\u0309a tinh th\u00e2\u0300n con ng\u01b0\u01a1\u0300i, nh\u01b0 nha\u0300 toa\u0301n ho\u0323c n\u00f4\u0309i ti\u00ea\u0301ng JACOBI \u01a1\u0309 K\u00f6nigsberg t\u01b0\u0300ng no\u0301i, la\u0300 c\u01b0\u0301u ca\u0301nh duy nh\u00e2\u0301t cu\u0309a to\u00e0n b\u1ed9 n\u00ea\u0300n khoa ho\u0323c. Chu\u0301ng ta kh\u00f4ng \u0111\u01b0\u01a1\u0323c phe\u0301p tin va\u0300o nh\u01b0\u0303ng k\u1ebb, v\u01a1\u0301i m\u1ed9t th\u00e1i \u0111\u1ed9 tri\u1ebft l\u00fd va\u0300 gio\u0323ng \u0111i\u1ec7u k\u1ebb c\u1ea3, ti\u00ean \u0111oa\u0301n v\u00ea\u0300 s\u01b0\u0323 suy ta\u0300n cu\u0309a v\u0103n ho\u0301a, va\u0300 r\u01a1i va\u0300o chu\u0309 nghi\u0303a \u201cchu\u0301ng ta se\u0303 kh\u00f4ng bi\u00ea\u0301t\u201d (ignorabimus). \u0110\u00f4\u0301i v\u01a1\u0301i chu\u0301ng ta kh\u00f4ng co\u0301 ignorabimus, va\u0300 theo t\u00f4i, cu\u0303ng kh\u00f4ng h\u1ec1 co\u0301 \u0111i\u00ea\u0300u \u0111o\u0301 \u0111\u1ed1i v\u1edbi khoa ho\u0323c. Ng\u01b0\u1ee3c l\u1ea1i, thay cho chu\u0309 nghi\u0303a ignorabimus da\u0323i d\u1ed9t, chu\u0301ng ta n\u00ean co\u0301 kh\u00e2\u0309u hi\u1ec7u:
\nCH\u00daNG TA PH\u1ea2I BI\u1ebeT
\nCH\u00daNG TA S\u1ebc BI\u1ebeT\u201d<\/p>\n

B\u1ea1n \u0111\u1ecdc c\u00f3 th\u1ec3 nghe gi\u1ecdng n\u00f3i c\u1ee7a David Hilbert t\u1ea1i \u0111\u00e2y:\u00a0https:\/\/www.youtube.com\/watch?v=DJUQ2Q7Ivd0<\/a><\/p>\n

NXX<\/p>\n

T\u1ea1p ch\u00ed Tia S\u00e1ng \u0111\u0103ng l\u1ea1i b\u00e0i c\u1ee7a t\u00e1c gi\u1ea3 Nguy\u1ec5n Xu\u00e2n Xanh v\u1ec1 di\u1ec5n t\u1eeb c\u1ee7a Hilbert n\u0103m 1930:<\/p>\n

http:\/\/tiasang.com.vn\/-dien-dan\/Chung-ta-phai-bietChung-ta-se-biet-10608<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Chu\u0301ng ta pha\u0309i bi\u00ea\u0301t \u00a0 \u00a0 \u00a0 \u00a0Chu\u0301ng ta se\u0303 bi\u00ea\u0301t Nguy\u1ec5n Xu\u00e2n Xanh gi\u1edbi thi\u1ec7u v\u00e0 chuy\u1ec3n ng\u1eef Khoa h\u1ecdc theo t\u00f4i l\u00e0 m\u1ed9t th\u1ec3 th\u1ed1ng nh\u1ea5t kh\u00f4ng chia c\u1eaft \u0111\u01b0\u1ee3c. \u0110\u1eb7c \u0111i\u1ec3m c\u1ee7a to\u00e1n h\u1ecdc c\u00f3 c\u01a1 s\u1edf<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"quote","meta":{"_mi_skip_tracking":false},"categories":[146,32,330],"tags":[361,148,404],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p8jhJx-8y","_links":{"self":[{"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/posts\/530"}],"collection":[{"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/comments?post=530"}],"version-history":[{"count":0,"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/posts\/530\/revisions"}],"wp:attachment":[{"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/media?parent=530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/categories?post=530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rosetta.vn\/short\/wp-json\/wp\/v2\/tags?post=530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}