{"id":1178,"date":"2018-03-16T21:40:25","date_gmt":"2018-03-16T14:40:25","guid":{"rendered":"https:\/\/rosetta.vn\/nguyenxuanxanh\/?p=1178"},"modified":"2023-01-31T20:14:04","modified_gmt":"2023-01-31T13:14:04","slug":"dinh-ly-cuoi-cung-cua-fermat","status":"publish","type":"post","link":"https:\/\/rosetta.vn\/nguyenxuanxanh\/dinh-ly-cuoi-cung-cua-fermat\/","title":{"rendered":"\u0110\u1ecbnh l\u00fd cu\u1ed1i c\u00f9ng c\u1ee7a Fermat"},"content":{"rendered":"

\u0110\u1ecaNH L\u00dd CU\u1ed0I C\u00d9NG C\u1ee6A FERMAT<\/span><\/h1>\n

Nguy\u1ec5n Xu\u00e2n Xanh gi\u1edbi thi\u1ec7u v\u00e0 d\u1eabn nh\u1eadp<\/em><\/strong>
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C\u1ee9u c\u00e1nh duy nh\u1ea5t c\u1ee7a n\u1ec1n khoa h\u1ecdc l\u00e0 ni\u1ec1m vinh d\u1ef1 c\u1ee7a tr\u00ed tu\u1ec7 con ng\u01b0\u1eddi.<\/span><\/p>\n

C. G. J. Jacobi 1830<\/span><\/strong><\/p>\n

T\u00f4i b\u1ecb \u00e1m \u1ea3nh b\u1edfi b\u00e0i to\u00e1n n\u00e0y \u0111\u1ebfn n\u1ed7i l\u00fac n\u00e0o t\u00f4i c\u0169ng ngh\u0129 \u0111\u1ebfn n\u00f3, khi t\u00f4i m\u1edbi th\u1ee9c d\u1eady bu\u1ed5i s\u00e1ng, c\u0169ng nh\u01b0 khi t\u00f4i \u0111i ng\u1ee7 bu\u1ed5i t\u1ed1i \u2013 v\u00e0 \u0111i\u1ec1u \u0111\u00f3 di\u1ec5n ra t\u00e1m n\u0103m li\u1ec1n.<\/span><\/p>\n

Andrew Wiles<\/strong><\/span><\/p>\n

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L\u1eddi n\u00f3i \u0111\u1ea7u<\/i>. \u0110\u00e2y l\u00e0 m\u1ed9t b\u00e0i to\u00e1n \u0111\u1ea7y huy\u1ec1n b\u00ed <\/i>v\u00e0 \u0111\u1ecbnh m\u1ec7nh<\/i>, l\u00f4i cu\u1ed1n kh\u00f4ng bi\u1ebft bao nhi\u00eau c\u00e1i \u0111\u1ea7u v\u0129 \u0111\u1ea1i, m\u00e0 c\u00f2n c\u00e1c nh\u00e0 vi\u1ebft s\u1eed t\u00ean tu\u1ed5i. \u0110\u01b0\u1ee3c \u0111\u1eb7t ra b\u1edfi Pierre de Fermat th\u1ebf k\u1ef7 th\u1ee9 17, b\u00e0i to\u00e1n v\u1eabn l\u00e0 m\u1ed9t th\u00e1ch \u0111\u1ed1 cho c\u1ea3 nh\u00e2n lo\u1ea1i h\u01a1n 300 n\u0103m qua, m\u00e3i cho \u0111\u1ebfn khi ng\u01b0\u1eddi ta r\u1ea5t t\u00ecnh c\u1edd t\u00ecm th\u1ea5y chi\u1ebfc ch\u00eca kh\u00f3a c\u1ee7a n\u00f3 n\u1eb1m t\u1ea1i Nh\u1eadt B\u1ea3n, n\u01a1i hai samurai tr\u1ebb th\u1eddi h\u1eadu chi\u1ebfn \u0111\u00e3 \u0111\u01b0a ra m\u1ed9t gi\u1ea3 thuy\u1ebft kh\u00f4ng li\u00ean can g\u00ec \u0111\u1ebfn b\u00e0i to\u00e1n, nh\u01b0ng l\u1ea1i l\u00e0 \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n h\u00f3c b\u00faa kia. V\u00e0 khi \u0111\u01b0a ra xong, m\u1ed9t trong hai t\u00e1c gi\u1ea3 \u0111\u00e3 t\u1ef1 s\u00e1t, m\u1ed9t\u00a0\u0111i\u1ec1u kh\u00f4ng ai hi\u1ec3u n\u1ed5i. TS L\u00ea Quang \u00c1nh t\u00e1i hi\u1ec7n l\u1ea1i c\u00e2u chuy\u1ec7n h\u1ebft s\u1ee9c ly k\u1ef3 n\u00e0y trong quy\u1ec3n s\u00e1ch d\u01b0\u1edbi \u0111\u00e2y b\u1eb1ng nh\u1eefng nghi\u00ean c\u1ee9u ri\u00eang c\u00f4ng phu v\u00e0 s\u00e2u s\u1eafc c\u1ee7a \u00f4ng. S\u00e1ch s\u1ebd ch\u00e0o \u0111\u00f3n H\u1ed9i s\u00e1ch Th\u00e0nh ph\u1ed1 trong nh\u1eefng ng\u00e0y t\u1edbi c\u1ee7a th\u00e1ng ba. T\u00e1c gi\u1ea3<\/p>\n

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D\u00e0nh t\u1eb7ng GS \u0110\u1eb7ng \u0110\u00ecnh \u00c1ng (1926-), ng\u01b0\u1eddi \u0111\u00e3 mi\u1ec7t m\u00e0i \u0111\u00e0o t\u1ea1o, h\u01b0\u1edbng d\u1eabn v\u00e0 h\u1ed7 tr\u1ee3 sinh vi\u00ean ng\u00e0nh to\u00e1n h\u1ecdc hi\u1ec7n \u0111\u1ea1i t\u1ea1i \u0110\u1ea1i h\u1ecdc S\u00e0i G\u00f2n n\u1eeda th\u1ebf k\u1ef7 li\u1ec1n, lu\u00f4n lu\u00f4n truy\u1ec1n c\u1ea3m h\u1ee9ng v\u00e0 t\u00ecnh th\u01b0\u01a1ng. Ph\u1ea3i c\u00f3 t\u00ecnh th\u01b0\u01a1ng th\u00ec m\u1edbi l\u00e0m \u0111\u01b0\u1ee3c vi\u1ec7c l\u1edbn<\/i>, m\u1ed9t trong nh\u1eefng c\u00e2u n\u00f3i c\u1ee7a ng\u01b0\u1eddi Th\u1ea7y \u0111\u00e1ng k\u00ednh y\u00eau ng\u00e0y nay l\u1ea1i c\u00e0ng c\u00f3 gi\u00e1 tr\u1ecb.<\/p>\n<\/blockquote>\n

Xin gi\u1edbi thi\u1ec7u n\u1ed3ng nhi\u1ec7t v\u1edbi b\u1ea1n \u0111\u1ecdc. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u00e0i ti\u1ec3u lu\u1eadn c\u1ee7a t\u00f4i vi\u1ebft cho quy\u1ec3n s\u00e1ch, ch\u1eb3ng \u0111\u1eb7ng \u0111\u1eebng tr\u01b0\u1edbc c\u00e2u chuy\u1ec7n ly k\u1ef3 v\u00e0 s\u1ef1 k\u1ec3 chuy\u1ec7n hay c\u1ee7a t\u00e1c gi\u1ea3. NXX<\/p>\n

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\u0110\u1ecbnh l\u00fd cu\u1ed1i c\u00f9ng c\u1ee7a Femat<\/i> l\u00e0 m\u1ed9t trong nh\u1eefng c\u00e2u chuy\u1ec7n b\u00ed \u1ea9n, v\u00e2ng, huy\u1ec1n b\u00ed v\u00e0 c\u00f3 l\u1ebd th\u00fa v\u1ecb nh\u1ea5t trong l\u1ecbch s\u1eed to\u00e1n h\u1ecdc th\u1ebf gi\u1edbi \u0111\u01b0\u1ee3c nh\u00e0 to\u00e1n h\u1ecdc Ph\u00e1p th\u1eddi Ph\u1ee5c H\u01b0ng Pierre de Fermat (1607 – 1665) \u0111\u1eb7t ra n\u0103m 1637. N\u0103m 1995, t\u1ee9c sau 358 n\u0103m, sau khi \u0111\u00e1nh b\u1ea1i bao nhi\u00eau b\u1ed9 \u00f3c v\u0129 \u0111\u1ea1i c\u1ee7a n\u1ec1n to\u00e1n h\u1ecdc th\u1ebf gi\u1edbi, n\u00f3 \u0111\u01b0\u1ee3c nh\u00e0 to\u00e1n h\u1ecdc Anh Andrew Wiles gi\u1ea3i, m\u1ed9t c\u00f4ng tr\u00ecnh nh\u01b0 c\u1ee7a Hercule th\u1ea7n tho\u1ea1i. \u0110\u1ecbnh l\u00fd Fermat c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c v\u00ed nh\u01b0 l\u00e0 ng\u1ecdn n\u00fai Everest cao nh\u1ea5t c\u1ee7a d\u00e3y Hy M\u00e3 L\u1ea1p S\u01a1n c\u1ee7a ng\u00e0nh l\u00fd thuy\u1ebft s\u1ed1, m\u00e0 Wiles l\u00e0 ng\u01b0\u1eddi leo n\u00fai \u0111\u1ea7u ti\u00ean \u0111\u00e3 \u0111\u1eb7t ch\u00e2n t\u1edbi. B\u00e0i to\u00e1n \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u v\u00f4 c\u00f9ng \u0111\u01a1n gi\u1ea3n, m\u1ed7i h\u1ecdc sinh trung h\u1ecdc \u0111\u1ec1u c\u00f3 th\u1ec3 hi\u1ec3u, nh\u01b0ng l\u1eddi gi\u1ea3i c\u1ee7a n\u00f3 l\u1ea1i v\u00f4 c\u00f9ng ph\u1ee9c t\u1ea1p, v\u00e0 cu\u1ed1i c\u00f9ng ng\u01b0\u1eddi ta ph\u1ea3i s\u1eed d\u1ee5ng nh\u1eefng c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng m\u00e0 ng\u01b0\u1eddi th\u01b0\u1eddng kh\u00f3 c\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c. B\u00e0i to\u00e1n Fermat l\u00e0 c\u1ee7a l\u00fd thuy\u1ebft s\u1ed1, m\u1ed9t l\u00fd thuy\u1ebft c\u00f3 ngu\u1ed3n g\u1ed1c c\u1ed5 \u0111\u1ea1i v\u00e0 thu h\u00fat m\u1ea1nh m\u1ebd c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc t\u1eeb th\u1ebf k\u1ef7 17 tr\u1edf \u0111i. Gauss, m\u1ed9t th\u1ea7n \u0111\u1ed3ng v\u00e0 m\u1ed9t \u00f4ng ho\u00e0ng to\u00e1n h\u1ecdc c\u1ee7a th\u1ebf k\u1ef7 19 t\u1eebng cho r\u1eb1ng l\u00fd thuy\u1ebft s\u1ed1 c\u00f3 s\u1ee9c m\u00ea ho\u1eb7c to l\u1edbn, nh\u01b0 Hilbert di\u1ec5n t\u1ea3, v\u00e0 tr\u1edf th\u00e0nh \u201ckhoa 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.\u201d Gauss \u0111\u01b0\u1ee3c k\u1ec3 l\u1ea1i (M. Kline) c\u0169ng \u0111\u00e3 c\u00f3 \u201cth\u1eed s\u1ee9c\u201d cho m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t (n = 7) c\u1ee7a \u0110\u1ecbnh l\u00fd cu\u1ed1i c\u00f9ng c\u1ee7a Fermat nh\u01b0ng kh\u00f4ng th\u00e0nh c\u00f4ng, t\u1eeb \u0111\u00f3 \u00f4ng b\u1ecf n\u00f3. Th\u1eadt ra, cho \u0111\u1ebfn gi\u1eefa th\u1ebf k\u1ef7 20 c\u00f3 l\u1ebd s\u1ebd kh\u00f4ng c\u00f3 ai c\u00f3 n\u0103ng l\u1ef1c m\u1ed9t m\u00ecnh gi\u1ea3i b\u00e0i to\u00e1n n\u00e0y. B\u00e0i to\u00e1n Fermat, li\u00ean quan \u0111\u1ebfn \u0111\u1ecbnh l\u00fd Pythagoras, tuy c\u00f3 xu\u1ea5t x\u1ee9 t\u1eeb n\u1ec1n v\u0103n minh L\u01b0\u1ee1ng H\u00e0, tr\u00f4ng r\u1ea5t \u201cm\u1ed9c m\u1ea1c\u201d, nh\u01b0ng l\u1ea1i c\u00f3 ngu\u1ed3n g\u1ed1c r\u1ea5t ph\u1ee9c t\u1ea1p n\u1eb1m tr\u00ean nh\u1eefng \u201c\u0111\u00e1m m\u00e2y\u201d c\u1ee7a to\u00e1n h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng m\u00e0 cho \u0111\u1ebfn nh\u1eefng n\u0103m sau Th\u1ebf chi\u1ebfn II m\u1edbi c\u00f3 nh\u1eefng c\u00f4ng c\u1ee5 k\u1ef9 thu\u1eadt manh nha \u0111\u1ec3 x\u1eed l\u00fd n\u00f3 \u2013 m\u1ed9t c\u00e1ch r\u1ea5t t\u00ecnh c\u1edd. Ch\u1eb3ng ph\u1ea3i v\u00ec c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc mu\u1ed1n gi\u1ea3i b\u00e0i to\u00e1n Fermat m\u00e0 ngh\u0129 ra nh\u1eefng c\u00f4ng c\u1ee5 \u0111\u00f3. Sau nh\u1eefng th\u1ea5t b\u1ea1i v\u00e0o \u0111\u1ea7u th\u1ebf k\u1ef7 20, trong \u0111\u00f3 c\u00f3 c\u1ea3 v\u1ecb th\u1ea7y Minkowski c\u1ee7a Einstein, ng\u01b0\u1eddi ta \u0111\u00e3 d\u00e8 d\u1eb7t. Hilbert c\u0169ng \u0111\u00e3 \u201ckh\u00f4ng d\u00e1m\u201d. V\u00ec ng\u01b0\u1eddi ta kh\u00f4ng th\u1ea5y m\u1ed9t manh m\u1ed1i n\u00e0o \u0111\u1ec3 ti\u1ebfp c\u1eadn. B\u00e0i to\u00e1n \u0111\u1ee9ng h\u1ea7u nh\u01b0 ri\u00eang l\u1ebb v\u00e0 bi\u1ec7t l\u1eadp ngo\u00e0i d\u00f2ng ch\u1ea3y ch\u00ednh th\u1ed1ng c\u1ee7a to\u00e1n h\u1ecdc hi\u1ec7n \u0111\u1ea1i. Th\u1eadm ch\u00ed c\u00f3 l\u00fac ng\u01b0\u1eddi ta nghi ng\u1edd kh\u00f4ng bi\u1ebft b\u00e0i to\u00e1n Fermat c\u00f3 ph\u1ea3i r\u01a1i v\u00e0o ph\u1ea1m tr\u00f9 \u201ckh\u00f4ng quy\u1ebft \u0111\u1ecbnh \u0111\u01b0\u1ee3c\u201d c\u1ee7a Kurt G\u00f6del hay kh\u00f4ng.<\/p>\n

Nh\u01b0ng r\u1ed3i tri th\u1ee9c nh\u01b0 m\u1ed9t c\u00e1i c\u00e2y c\u1ee9 ph\u00e1t tri\u1ec3n, l\u00fd t\u00ednh c\u1ee7a con ng\u01b0\u1eddi li\u00ean k\u1ebft ch\u00fang l\u1ea1i v\u1edbi nhau. N\u1ebfu xem L\u01b0\u1ee1ng H\u00e0, n\u01a1i g\u1ed1c r\u1ec5 c\u1ee7a to\u00e1n h\u1ecdc, l\u00e0 v\u00f9ng ph\u01b0\u01a1ng \u0110\u00f4ng (Orient), nh\u01b0 l\u1ecbch s\u1eed th\u01b0\u1eddng xem, th\u00ec sau Th\u1ebf chi\u1ebfn II, xa h\u01a1n, \u1edf ph\u01b0\u01a1ng \u0110\u00f4ng, l\u1ea1i cung c\u1ea5p m\u1ed9t manh m\u1ed1i \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n Fermat b\u00ed \u1ea9n. \u0110\u00f3 l\u00e0 Nh\u1eadt B\u1ea3n, \u0111\u1ea5t n\u01b0\u1edbc \u0111ang h\u1ed3i sinh sau c\u1ea3nh \u0111i\u00eau t\u00e0n, v\u1edbi hai nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb Goro Shimura v\u00e0 Yutaka Taniyama \u0111ang ph\u1ea5n \u0111\u1ea5u g\u00f3p ph\u1ea7n x\u00e2y d\u1ef1ng l\u1ea1i n\u1ec1n to\u00e1n h\u1ecdc \u0111\u1ea5t n\u01b0\u1edbc. Nh\u01b0 \u0111\u00e3 n\u00f3i, hai \u00f4ng kh\u00f4ng h\u1ec1 c\u00f3 \u00fd gi\u1ea3i b\u00e0i to\u00e1n Fermat. Nh\u01b0ng, \u0111\u1ecbnh m\u1ec7nh run r\u1ee7i, nh\u1eefng g\u00ec hai \u00f4ng ph\u00e1t tri\u1ec3n, c\u0169ng c\u00f2n \u1edf d\u1ea1ng ti\u00ean \u0111o\u00e1n nh\u01b0 \u0111\u1ecbnh l\u00fd Fermat, g\u1ecdi l\u00e0 Ti\u00ean \u0111o\u00e1n Shimura – Taniyama<\/i>, \u0111\u00e3 kh\u00e9p l\u1ea1i v\u00f2ng tr\u00f2n nh\u1eadn th\u1ee9c trong to\u00e1n h\u1ecdc. Ti\u00ean \u0111o\u00e1n n\u00e0y l\u1ea1i r\u1ea5t \u0111\u1eb9p, r\u1ea5t quy\u1ebfn r\u0169, khi\u1ebfn cho nh\u00e0 to\u00e1n h\u1ecdc Canada Robert Langlands b\u1eaft \u0111\u1ea7u thi\u1ebft l\u1eadp Ch\u01b0\u01a1ng tr\u00ecnh mang t\u00ean \u00f4ng li\u1ec7t k\u00ea nh\u1eefng m\u1ed1i li\u00ean h\u1ec7 ch\u01b0a ch\u1ee9ng minh \u0111\u01b0\u1ee3c nh\u01b0ng c\u00f3 s\u1ee9c thuy\u1ebft ph\u1ee5c nh\u01b0 nh\u1eefng chi\u1ebfc c\u1ea7u n\u1ed1i gi\u1eefa c\u00e1c mi\u1ec1n to\u00e1n h\u1ecdc kh\u00e1c nhau, trong \u0111\u00f3 c\u00f3 \u201cB\u1ed5 \u0111\u1ec1 c\u0103n b\u1ea3n\u201d m\u00e0 15 n\u0103m sau Wiles, Ng\u00f4 B\u1ea3o Ch\u00e2u \u0111\u00e3 gi\u1ea3i \u0111\u01b0\u1ee3c. V\u00e0 ch\u00ednh ti\u00ean \u0111o\u00e1n c\u1ee7a hai nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb Nh\u1eadt B\u1ea3n \u0111\u00f3 l\u00e0 ch\u00eca kh\u00f3a \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n Fermat.<\/p>\n

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\u0110\u1ec3 c\u00f3 m\u1ed9t ch\u00fat m\u01b0\u1eddng t\u01b0\u1ee3ng v\u1ea5n \u0111\u1ec1 th\u00fa v\u1ecb n\u1eb1m \u1edf \u0111\u00e2u, v\u00e0 hi\u1ec3u m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa b\u00e0i to\u00e1n Fermat v\u00e0 ti\u00ean \u0111o\u00e1n Shimura – Taniyama, ch\u00fang ta h\u00e3y xem l\u1ea1i n\u1ed9i dung \u0110\u1ecbnh l\u00fd cu\u1ed1i c\u00f9ng c\u1ee7a Fermat m\u1ed9t ch\u00fat. B\u00e0i to\u00e1n \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: Kh\u00f4ng c\u00f3<\/i> c\u00e1c s\u1ed1 nguy\u00ean d\u01b0\u01a1ng a, b, c (= 1, 2, 3, 4\u2026) n\u00e0o th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n

an<\/sup> + bn<\/sup> = cn<\/sup> (1)<\/p>\n

khi n l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean l\u1edbn h\u01a1n<\/i> 2 (n > 2). Ngh\u0129a l\u00e0 \u0111\u01a1n gi\u1ea3n ph\u01b0\u01a1ng tr\u00ecnh (1) kh\u00f4ng c\u00f3 nghi\u1ec7m.<\/p>\n

\u0110\u1ed1i v\u1edbi n = 1, ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh a + b = c, qu\u00e1 hi\u1ec3n nhi\u00ean l\u00e0 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m. V\u1edbi n = 2, bi\u1ec3u th\u1ee9c tr\u00ean tr\u1edf th\u00e0nh<\/p>\n

a2<\/sup> + b2<\/sup> = c2<\/sup> (2)<\/p>\n

\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh Pythagoras quen thu\u1ed9c t\u1eeb h\u00ecnh h\u1ecdc Euclid. Ph\u01b0\u01a1ng tr\u00ecnh c\u0169ng v\u1eabn c\u00f2n c\u00f3 v\u00f4 s\u1ed1 b\u1ed9 nghi\u1ec7m a-b-c. Nghi\u1ec7m \u0111\u1ea7u l\u00e0 3-4-5 m\u1ecdi ng\u01b0\u1eddi h\u1ecdc \u0111\u1ecbnh l\u00fd Pythago \u0111\u00e3 bi\u1ebft. Nghi\u1ec7m k\u1ebf ti\u1ebfp: 5-12-13. V\u00e2n v\u00e2n. Ph\u01b0\u01a1ng tr\u00ecnh Pythagoras, \u0111\u01b0\u1ee3c m\u1ed9t h\u1ecdc gi\u1ea3 x\u1ebfp v\u00e0o lo\u1ea1i h\u1eefu \u00edch h\u00e0ng th\u1ee9 hai sau ph\u01b0\u01a1ng tr\u00ecnh Einstein E = mc2<\/sup><\/strong>, \u0111\u00e3 g\u00e2y ng\u1ea1c nhi\u00ean v\u00e0 th\u00edch th\u00fa cho bao b\u1ed9 \u00f3c v\u0129 \u0111\u1ea1i trong l\u1ecbch s\u1eed. N\u0103m 1628, Thomas Hobbes, m\u1ed9t ng\u00e0y t\u00ecm \u0111\u01b0\u1ee3c quy\u1ec3n H\u00ecnh h\u1ecdc<\/i> c\u1ee7a Euclid, \u0111\u1ecdc \u0111\u1ebfn M\u1ec7nh \u0111\u1ec1 th\u1ee9 47 l\u00e0 \u0111\u1ecbnh l\u00fd Pythagoras, \u00f4ng th\u1ed1t l\u00ean \u201cCh\u00faa \u01a1i, c\u00f3 th\u1ec3 n\u00e0o nh\u01b0 th\u1ebf?\u201d tr\u01b0\u1edbc s\u1ef1 ng\u1ea1c nhi\u00ean v\u00f4 h\u1ea1n. \u201cNi\u1ec1m vui c\u1ef1c \u0111\u1ed9 t\u00f4i c\u00f3 trong nghi\u00ean c\u1ee9u \u0111\u00e3 v\u01b0\u1ee3t qua m\u1ecdi s\u1ef1 ham mu\u1ed1n kh\u00e1c trong t\u00f4i.\u201d \u00d4ng y\u00eau h\u00ecnh h\u1ecdc Euclid \u0111\u1ebfn \u0111\u1ed9 ki\u00ean quy\u1ebft b\u1ea3o v\u1ec7 n\u00f3 v\u1ec1 m\u1eb7t tri\u1ebft h\u1ecdc tr\u01b0\u1edbc calculus, to\u00e1n vi t\u00edch ph\u00e2n \u0111ang l\u00ean tr\u01b0\u1edbc khi \u0111\u01b0\u1ee3c Newton v\u00e0 Leibniz ho\u00e0n t\u1ea5t. M\u1ed9t cu\u1ed9c \u0111\u1ea5u tranh k\u1ecbch li\u1ec7t gi\u1eefa \u00f4ng v\u00e0 John Wallis, m\u1ed9t \u0111\u1ea1i bi\u1ec3u s\u00e1ng ch\u00f3i c\u1ee7a calculus di\u1ec5n ra, v\u00e0 d\u0129 nhi\u00ean Hobbes cu\u1ed1i c\u00f9ng ph\u1ea3i ch\u1ecbu thua.<\/p>\n

(1) l\u00e0 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a Diophantus, nh\u00e0 to\u00e1n h\u1ecdc th\u1eddi Hy L\u1ea1p h\u00f3a \u1edf Alexandria, t\u00e1c gi\u1ea3 c\u1ee7a nhi\u1ec1u t\u1eadp s\u00e1ch c\u00f3 t\u00ean Arithmetica<\/i> (S\u1ed1 h\u1ecdc). S\u1ed1 h\u1ecdc l\u00e0 m\u00f4n h\u1ecdc d\u1ef1a tr\u00ean c\u00e1c s\u1ed1 nguy\u00ean. Ph\u01b0\u01a1ng tr\u00ecnh Phythagoras \u0111\u01b0\u1ee3c bi\u1ebft t\u1eeb th\u1eddi Babylon v\u00e0 Ai C\u1eadp nh\u01b0ng kh\u00f4ng c\u00f3 ch\u1ee9ng minh. N\u1ebfu \u0111\u1eb7t a = b = 1 trong (2), th\u00ec c s\u1ebd b\u1eb1ng \u221a2 . Con s\u1ed1 n\u00e0y r\u1ea5t l\u1ea1 \u0111\u1ed1i v\u1edbi ng\u01b0\u1eddi Hy L\u1ea1p, v\u00ec n\u00f3 kh\u00f4ng l\u00e0 s\u1ed1 nguy\u00ean, c\u0169ng kh\u00f4ng ph\u1ea3i l\u00e0 t\u1ef7 s\u1ed1 c\u1ee7a hai s\u1ed1 nguy\u00ean, g\u1ecdi chung l\u00e0 s\u1ed1 h\u1eefu t\u1ef7 (rational number). H\u1ecd g\u1ecdi\u00a0\u221a2 l\u00e0 s\u1ed1 v\u00f4 t\u1ef7 (irrational number), nh\u1eefng kh\u00e1i ni\u1ec7m ch\u00fang ta v\u1eabn c\u00f2n s\u1eed d\u1ee5ng \u0111\u1ebfn ng\u00e0y nay.<\/p>\n

May m\u1eafn l\u00e0m sao khi t\u00e1c ph\u1ea9m Arithmetica<\/i> s\u1ed1ng s\u00f3t qua th\u1eddi g\u1ecdi l\u00e0 Th\u1eddi \u0111en t\u1ed1i, \u0111\u01b0\u1ee3c truy\u1ec1n nhi\u1ec1u \u0111\u1eddi qua th\u1ebf gi\u1edbi \u1ea2 R\u1eadp Trung C\u1ed5, r\u1ed3i \u0111\u1ebfn ch\u00e2u \u00c2u Trung C\u1ed5 v\u00e0o th\u1ebf k\u1ef7 12, 13. B\u1ea3n d\u1ecbch Latinh t\u1ed1t nh\u1ea5t l\u00e0 do cha d\u00f2ng Claude Gaspard Bachet (de M\u00e9ziriac) th\u1ef1c hi\u1ec7n v\u00e0 \u0111\u01b0\u1ee3c xu\u1ea5t b\u1ea3n \u0111\u1ea7u ti\u00ean n\u0103m 1621. B\u1ea3n d\u1ecbch Fermat s\u1eed d\u1ee5ng l\u00e0 do con trai \u00f4ng xu\u1ea5t b\u1ea3n n\u0103m 1670.<\/p>\n

Khi \u0111\u1ecdc Arithmetica<\/i>, <\/i>Fermat, nh\u00e0 to\u00e1n h\u1ecdc \u201cnghi\u1ec7p d\u01b0\u201d nh\u01b0ng r\u1ea5t t\u00e0i t\u00ecnh, \u201cc\u1eafc c\u1edb\u201d mu\u1ed1n n\u1edbi r\u1ed9ng ra ph\u01b0\u01a1ng tr\u00ecnh (2) cho nh\u1eefng s\u1ed1 n > 2, v\u00e0 qu\u1ea3 quy\u1ebft r\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh (1) kh\u00f4ng c\u00f2n nghi\u1ec7m s\u1ed1 n\u00e0o n\u1eefa. \u00d4ng c\u00f2n ghi ti\u1ebfp, r\u1eb1ng \u201ct\u00f4i \u0111\u00e3 kh\u00e1m ph\u00e1 m\u1ed9t ch\u1ee9ng minh th\u1eadt s\u1ef1 k\u1ef3 di\u1ec7u c\u1ee7a \u0111\u1ecbnh l\u00fd (t\u1ed5ng qu\u00e1t n\u00e0y), \u0111i\u1ec1u m\u00e0 l\u1ec1 gi\u1ea5y qu\u00e1 nh\u1ecf \u0111\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c.\u201d \u0110\u1ea5y l\u00e0 s\u1ef1 kh\u1edfi \u0111\u1ea7u c\u1ee7a m\u1ed9t th\u00e1ch th\u1ee9c xuy\u00ean th\u1ebf k\u1ef7.<\/p>\n

***<\/span><\/p>\n

Nh\u01b0 \u0111\u00e3 n\u00f3i, ph\u1ea3i ch\u1edd th\u00eam \u0111\u1ebfn s\u1ef1 ph\u1ecfng \u0111o\u00e1n (conjecture) c\u00f3 t\u00ean Taniyama\u2013Shimura<\/i> gi\u1eefa th\u1ebf k\u1ef7 20, b\u00ed m\u1eadt s\u00e2u th\u1eb3m c\u1ee7a \u0111\u1ecbnh l\u00fd Fermat m\u1edbi b\u1eaft \u0111\u1ea7u l\u1ed9 di\u1ec7n. N\u0103m 1955, t\u1ee9c 10 n\u0103m sau Th\u1ebf chi\u1ebfn th\u1ee9 hai, hai nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb c\u1ee7a Nh\u1eadt B\u1ea3n Goro Shimura v\u00e0 Yutaka Taniyama quan s\u00e1t r\u1eb1ng c\u00f3 th\u1ec3 c\u00f3 m\u1ed9t m\u1ed1i li\u00ean l\u1ea1c gi\u1eefa hai l\u00e3nh v\u1ef1c ho\u00e0n to\u00e0n kh\u00e1c nhau sau \u0111\u00e2y c\u1ee7a to\u00e1n h\u1ecdc:<\/p>\n

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Gi\u1ea3 thuy\u1ebft<\/i> Taniyama\u2013Shimura<\/i>: M\u1ed7i ph\u01b0\u01a1ng tr\u00ecnh elliptic \u0111\u1ec1u g\u1eafn li\u1ec1n v\u1edbi m\u1ed9t d\u1ea1ng modular. (Xem \u0111\u1ecbnh ngh\u0129a trong s\u00e1ch)<\/p>\n<\/blockquote>\n

Gi\u1ea3 thuy\u1ebft n\u00e0y n\u1ed1i li\u1ec1n hai ng\u00e0nh quan tr\u1ecdng l\u00e0 t\u00f4p\u00f4 v\u00e0 l\u00fd thuy\u1ebft s\u1ed1. C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc d\u1ef1 \u0111o\u00e1n, gi\u1ea3 thuy\u1ebft n\u00e0y ph\u1ea3i \u0111\u00fang. \u0110i\u1ec1u n\u00e0y tho\u1ea1t \u0111\u1ea7u ch\u01b0a li\u00ean quan g\u00ec \u0111\u1ebfn b\u00e0i to\u00e1n Fermat. Nh\u01b0ng r\u1ed3i b\u1ea5t ng\u1edd n\u0103m 1985, Gerhard Frey, nh\u00e0 to\u00e1n h\u1ecdc \u0110\u1ee9c \u1edf Saarbr\u00fccken, v\u1ebd ra m\u1ed1i li\u00ean h\u1ec7 b\u00ed m\u1eadt \u0111\u00f3. T\u1ea1i m\u1ed9t h\u1ed9i ngh\u1ecb t\u1ea1i Oberwolfach trong R\u1eebng \u0110en c\u1ee7a bang Baden W\u00fcrttemberg, \u00f4ng bi\u1ebfn h\u00f3a t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh Pythagor aN<\/sup> + bN<\/sup> = cN<\/sup> cho m\u1ed9t tr\u1ecb s\u1ed1 N > 2 nh\u1ea5t \u0111\u1ecbnh, t\u1ee9c gi\u1ea3 thi\u1ebft r\u1eb1ng c\u00f3 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh nh\u01b0 th\u1ebf, th\u00e0nh m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh elliptic, v\u00e0 l\u00fd lu\u1eadn b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p ph\u1ea3n ch\u1ee9ng<\/i> (hay c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u00e1n ti\u1ebfp), m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p c\u0169ng \u0111\u01b0\u1ee3c ph\u00e1t minh t\u1eeb th\u1eddi c\u1ed5 \u0111\u1ea1i, r\u1eb1ng:<\/p>\n

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N\u1ebfu gi\u1ea3 thi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh Pythagoras c\u00f3 m\u1ed9t nghi\u1ec7m N > 2, ngh\u0129a l\u00e0 \u0110\u1ecbnh l\u00fd Fermat l\u00e0 sai, th\u00ec s\u1ebd t\u1ed3n t\u1ea1i m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh v\u1ed1n d\u1ea1ng elliptic, nh\u01b0ng kh\u00e1 l\u1ea1 th\u01b0\u1eddng, (ph\u01b0\u01a1ng tr\u00ecnh elliptic t\u1ed5ng qu\u00e1t c\u00f3 d\u1ea1ng t\u1ed5ng qu\u00e1t y2<\/sup> = Ax3<\/sup> + Bx2<\/sup> + Cx + D), v\u00e0 Frey ti\u00ean \u0111o\u00e1n ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y l\u1ea1i kh\u00f4ng<\/i> c\u00f3 t\u00ednh modular.<\/p>\n<\/blockquote>\n

T\u1eeb \u0111\u00f3, ta c\u00f3 th\u1ec3 suy ra: gi\u1ea3 thuy\u1ebft Taniyama\u2013Shimura l\u00e0 sai. Cho n\u00ean, \u0111i ng\u01b0\u1ee3c l\u1ea1i: N\u1ebfu gi\u1ea3 thuy\u1ebft Taniyama\u2013Shimura \u0111\u01b0\u1ee3c ch\u1ee9ng minh l\u00e0 \u0111\u00fang, th\u00ec ph\u01b0\u01a1ng tr\u00ecnh aN<\/sup> + bN<\/sup> = cN<\/sup> kh\u00f4ng th\u1ec3 c\u00f3 nghi\u1ec7m s\u1ed1 cho m\u1ed9t N > 2, ngh\u0129a l\u00e0 \u0110\u1ecbnh l\u00fd Fermat l\u00e0 \u0110\u00daNG! V\u1eady then ch\u1ed1t n\u1eb1m \u1edf hai ph\u1ea7n c\u00f2n l\u1ea1i n\u00e0y:<\/p>\n

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  1. Ch\u1ee9ng minh r\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng elliptic c\u1ee7a Frey r\u00fat ra t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh Fermat l\u00e0 KH\u00d4NG ph\u1ea3i d\u1ea1ng modular.<\/li>\n
  2. Ch\u1ee9ng minh r\u1eb1ng Gi\u1ea3 thuy\u1ebft Taniyama\u2013Shimura l\u00e0 \u0110\u00daNG.<\/li>\n<\/ol>\n

    Kh\u00f4ng ph\u1ea3i ch\u1ec9 R\u1eebng \u0110en, m\u00e0 c\u1ea3 th\u1ebf gi\u1edbi to\u00e1n h\u1ecdc b\u1ecb ch\u1ea5n \u0111\u1ed9ng b\u1edfi nh\u1eadn x\u00e9t tr\u00ean c\u1ee7a Frey. Ph\u1ea7n ch\u1ee9ng minh \u0111\u1ea7u (1) sau m\u1ed9t n\u0103m r\u01b0\u1ee1i \u0111\u00e3 \u0111\u01b0\u1ee3c Ben Ribet c\u1ee7a \u0110\u1ea1i h\u1ecdc Berkeley nhanh ch\u00f3ng gi\u1ea3i quy\u1ebft. Khi nghe tin n\u00e0y, Andrew Wiles, l\u00fac \u0111\u00f3 l\u00e0m gi\u00e1o s\u01b0 \u1edf Princeton, th\u1ea5y nh\u01b0 b\u1ecb \u201c\u0111i\u1ec7n gi\u1eadt\u201d, nh\u01b0 \u00f4ng thu\u1eadt l\u1ea1i (Xem ph\u1ea7n Ph\u1ee5 l\u1ee5c c\u1ee7a s\u00e1ch, ph\u1ecfng v\u1ea5n Wiles), b\u1edfi v\u00ec \u00f4ng l\u00e0 ng\u01b0\u1eddi \u0111\u01b0\u1ee3c r\u00e8n luy\u1ec7n th\u00e0nh m\u1ed9t chuy\u00ean gia kh\u00e1 nhu\u1ea7n nhuy\u1ec5n v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng elliptic v\u00e0 l\u00fd thuy\u1ebft Iwasawa v\u1edbi th\u1ea7y \u0111\u1ee1 \u0111\u1ea7u c\u1ee7a \u00f4ng l\u00e0 John Coates t\u1ea1i \u0110\u1ea1i h\u1ecdc Cambridge, nh\u1eefng c\u00f4ng c\u1ee5 m\u1ea1nh m\u1ebd m\u00e0 \u00f4ng s\u1ebd s\u1eed d\u1ee5ng. Wiles nh\u1eadn ra r\u1eb1ng, b\u00e0i to\u00e1n Fermat \u0111\u00e3 h\u1ebft l\u1ea1c l\u00f5ng v\u00e0 n\u1eb1m \u0111\u00fang trong d\u00f2ng ch\u1ea3y ch\u00ednh c\u1ee7a to\u00e1n h\u1ecdc th\u1ebf gi\u1edbi, v\u00e0 c\u00f3 manh m\u1ed1i c\u1ee5 th\u1ec3 \u0111\u1ec3 ch\u1ee9ng minh. \u0110\u00f3 l\u00e0 n\u0103m 1986, l\u00fac \u00f4ng 33 tu\u1ed5i. T\u1eeb \u0111\u00f3 \u00f4ng quy\u1ebft \u0111\u1ecbnh \u201c\u0111\u00f3ng c\u1eeda ph\u00f2ng\u201d mi\u1ec7t m\u00e0i l\u00e0m vi\u1ec7c 7 n\u0103m li\u1ec1n. Nh\u01b0 v\u1eady, b\u00e0i to\u00e1n Fermat tr\u1edf th\u00e0nh: Gi\u1ea3i quy\u1ebft gi\u1ea3 thuy\u1ebft Taniyama\u2013Shimura. Cho d\u00f9 n\u1ebfu kh\u00f4ng \u0111\u1ea1t t\u1edbi \u0111\u00edch cu\u1ed1i c\u00f9ng \u0111i n\u1eefa, nh\u1eefng c\u00f4ng lao b\u1ecf ra s\u1ebd kh\u00f4ng b\u1ecb ph\u00ed ho\u00e0i, \u00f4ng ngh\u0129. Gi\u1ea5c m\u01a1 thi\u1ebfu ni\u00ean mu\u1ed1n gi\u1ea3i b\u00e0i to\u00e1n Fermat t\u1eeb l\u00fac m\u1edbi 10 tu\u1ed5i c\u1ee7a Andrew b\u1eebng l\u00ean, tr\u1edf th\u00e0nh n\u1ed7i \u00e1m \u1ea3nh v\u00e0 cu\u1ed3ng nhi\u1ec7t \u0111\u1ed1i v\u1edbi \u00f4ng.<\/p>\n

    Ph\u01b0\u01a1ng ph\u00e1p l\u00f4gic Wiles s\u1eed d\u1ee5ng \u1edf \u0111\u00e2y l\u00e0 ph\u00e9p qui n\u1ea1p<\/i> quen thu\u1ed9c trong to\u00e1n h\u1ecdc sau \u0111\u00e2y, r\u1ea5t \u0111\u1eb9p:<\/p>\n

    Gi\u1ea3 s\u1eed ch\u00fang ta mu\u1ed1n ch\u1ee9ng minh m\u1ed9t chu\u1ed7i m\u1ec7nh \u0111\u1ec1, hay c\u00f4ng th\u1ee9c H(n) n\u00e0o \u0111\u00f3, \u0111\u00fang cho m\u1ecdi n = 1, 2, 3, \u2026. Ph\u01b0\u01a1ng ph\u00e1p qui n\u1ea1p n\u00f3i r\u1eb1ng, b\u1ea1n c\u1ea7n ph\u1ea3i ch\u1ee9ng minh \u0111\u01b0\u1ee3c 2 \u0111i\u1ec1u sau \u0111\u00e2y:<\/p>\n

    a) <\/b>M\u1ec7nh \u0111\u1ec1 \u0111\u1ea7u ti\u00ean H(1) l\u00e0 \u0111\u00fang (\u0111i\u1ec1u n\u00e0y th\u01b0\u1eddng d\u1ec5 ki\u1ec3m tra h\u01a1n);<\/p>\n

    b) Cho n b\u1ea5t k\u1ef3. N\u1ebfu gi\u1ea3 thi\u1ebft m\u1ec7nh \u0111\u1ec1 H(n) l\u00e0 \u0111\u00fang, b\u1ea1n ph\u1ea3i suy ra r\u1eb1ng H(n+1) c\u0169ng \u0111\u00fang lu\u00f4n.<\/p>\n

    T\u1eeb \u0111\u00f3 b\u1ea1n c\u00f3 th\u1ec3 an t\u00e2m k\u1ebft lu\u1eadn: T\u1ea5t c\u1ea3 H(n), n = 1, 2, 3 \u2026 \u0111\u1ec1u \u0111\u00fang.<\/p>\n

    Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y tr\u00e1nh vi\u1ec7c ch\u1ee9ng minh tr\u1ef1c ti\u1ebfp H(n) l\u00e0 \u0111\u00fang cho n t\u1ed5ng qu\u00e1t, th\u01b0\u1eddng c\u00f3 th\u1ec3 r\u1ea5t r\u1eafc r\u1ed1i. B\u1ea1n c\u00f3 th\u1ec3 h\u00ecnh dung c\u1edd \u0111\u00f4min\u00f4: n\u1ebfu b\u1ea1n ch\u1ee9ng minh \u0111\u01b0\u1ee3c r\u1eb1ng n\u1ebfu con c\u1edd th\u1ee9 n b\u1ecb \u0111\u1ed5, con c\u1edd ti\u1ebfp th\u1ee9 n+1 c\u0169ng s\u1ebd b\u1ecb \u0111\u1ed5 theo, cho n t\u1ed5ng qu\u00e1t, th\u00ec ch\u1ec9 c\u1ea7n con c\u1edd \u0111\u1ea7u b\u1ecb \u0111\u1ed5 (\u0111i\u1ec1u b\u1ea1n ph\u1ea3i ki\u1ec3m tra), th\u00ec hi\u1ec7u \u1ee9ng d\u00e2y chuy\u1ec1n c\u1ee7a n\u00f3 s\u1ebd l\u00e0 to\u00e0n b\u1ed9 c\u00e1c con c\u1edd c\u0169ng s\u1ebd b\u1ecb \u0111\u1ed5 theo. Cho n\u00ean ph\u01b0\u01a1ng ph\u00e1p qui n\u1ea1p tr\u00ean ch\u00fang ta c\u00f3 th\u1ec3 v\u00ed nh\u01b0 \u201cph\u01b0\u01a1ng ph\u00e1p \u0111\u00f4min\u00f4\u201d. Hay c\u0169ng c\u00f3 th\u1ec3 g\u1ecdi \u201cph\u01b0\u01a1ng ph\u00e1p leo c\u1ea7u thang\u201d: Mu\u1ed1n leo c\u1ea7u thang \u0111\u01b0\u1ee3c b\u1ea5t t\u1eadn, b\u1ea1n ph\u1ea3i c\u00f3 hai \u0111i\u1ec1u: a) \u0111\u1eb7t ch\u00e2n \u0111\u01b0\u1ee3c l\u00ean b\u1eadc thang ban \u0111\u1ea7u; sau \u0111\u00f3, n\u1ebfu gi\u1ea3 thi\u1ebft b\u1ea1n \u0111ang \u1edf b\u1eadc thang n, th\u00ec b\u1ea1n ph\u1ea3i ch\u1ee9ng minh b\u1ea1n c\u00f3 th\u1ec3 leo l\u00ean b\u1eadc thang n + 1 k\u1ebf ti\u1ebfp, cho b\u1ea5t c\u1ee9 tr\u1ecb s\u1ed1 n t\u1ed5ng qu\u00e1t.<\/p>\n

    Ch\u1ee9ng minh \u0111\u01b0\u1ee3c b\u01b0\u1edbc a) Wiles c\u1ea7n 2 n\u0103m. C\u00f2n b) \u00f4ng ph\u1ea3i c\u1ea7n th\u00eam 5 n\u0103m li\u1ec1n. T\u1ed5ng c\u1ed9ng 7 n\u0103m. \u00d4ng ph\u1ea3i d\u00f9ng nhi\u1ec1u c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc chuy\u00ean ng\u00e0nh, trong \u0111\u00f3 c\u00f3 thuy\u1ebft nh\u00f3m Galois c\u1ee7a th\u1ebf k\u1ef7 19. Th\u00e1ng 7, 1993 \u00f4ng tuy\u00ean b\u1ed1 \u0111\u00e3 gi\u1ea3i quy\u1ebft xong, th\u1ebf gi\u1edbi hoan h\u00f4 vang d\u1ed9i. Nh\u01b0ng sau \u0111\u00f3, th\u00e1ng 8, ng\u01b0\u1eddi ta \u0111\u00e3 ph\u00e1t hi\u1ec7n c\u00f3 m\u1ed9t l\u1ed7 h\u1ed5ng trong ch\u1ee9ng minh. Tin nh\u01b0 s\u00e9t \u0111\u00e1nh qua \u0111\u1ea7u! Bao nhi\u00eau c\u00f4ng lao c\u00f3 th\u1ec3 \u201c\u0111\u1ed5 s\u00f4ng \u0111\u1ed5 bi\u1ec3n\u201d. Nh\u01b0ng kh\u00f4ng, \u00f4ng h\u1ebft s\u1ee9c tin t\u01b0\u1edfng v\u00e0o l\u00f4gic trong ch\u1ee9ng minh c\u1ee7a m\u00ecnh, v\u00e0 tin ch\u1eafc r\u1eb1ng \u00f4ng \u0111\u00e3 \u0111i \u0111\u00fang \u0111\u01b0\u1eddng, c\u00f4ng lao \u00f4ng kh\u00f4ng th\u1ec3 ph\u00ed ho\u00e0i, v\u00ec \u0111\u00f3 l\u00e0 nh\u1eefng b\u01b0\u1edbc ph\u00e1t tri\u1ec3n r\u1ea5t \u0111\u1eb9p, cho d\u00f9 \u00f4ng kh\u00f4ng \u0111\u1ea1t m\u1ee5c ti\u00eau cu\u1ed1i c\u00f9ng, cho d\u00f9 c\u00f2n thi\u1ebfu c\u00f4ng c\u1ee5 n\u00e0o \u0111\u00f3 \u0111\u1ec3 \u0111i \u0111\u1ebfn \u0111\u00edch \u0111i n\u1eefa.<\/p>\n

    Wiles \u0111\u00e3 b\u1ecf ra 8 th\u00e1ng li\u1ec1n, v\u1edbi s\u1ef1 gi\u00fap \u0111\u1ee1 c\u1ee7a m\u1ed9t h\u1ecdc tr\u00f2 c\u1ee7a \u00f4ng, Richard Taylor t\u1eeb Cambridge. M\u1ed9t c\u00f4ng vi\u1ec7c v\u00f4 c\u00f9ng gian nan. V\u00e0 khi t\u01b0\u1edfng b\u1ecf cu\u1ed9c, \u0111\u1ea7u h\u00e0ng v\u1edbi s\u1ed1 ph\u1eadn, th\u00ec, trong s\u1ef1 b\u00ecnh t\u0129nh nh\u00ecn th\u1eb3ng v\u00e0o s\u1ef1 vi\u1ec7c m\u1ed9t l\u1ea7n n\u1eefa \u0111\u1ec3 hi\u1ec3u t\u1ea1i sao th\u1ea5t b\u1ea1i tr\u01b0\u1edbc khi x\u1ebfp l\u1ea1i, th\u00e1ng 9, 1994 \u00f4ng nh\u1eadn ra l\u1ed1i tho\u00e1t! \u00d4ng v\u00e0 Taylor ng\u1ed3i l\u1ea1i v\u00e0 vi\u1ebft l\u1ed1i tho\u00e1t \u1ea5y th\u00e0nh m\u1ed9t ch\u01b0\u01a1ng \u0111\u1ed9c l\u1eadp v\u00e0 sau n\u00e0y \u0111\u01b0\u1ee3c c\u00f4ng b\u1ed1 ri\u00eang k\u00e8m v\u00e0o b\u1ea3n ch\u1ee9ng minh c\u1ee7a Wiles. Th\u00e1ng 3, 1995, Wiles ch\u00ednh th\u1ee9c c\u00f4ng b\u1ed1 ho\u00e0n t\u1ea5t tr\u1ecdn v\u1eb9n c\u00f4ng tr\u00ecnh ch\u1ee9ng minh c\u1ee7a b\u00e0i to\u00e1n Fermat. Ng\u00e0y \u00f4ng ch\u1ee9ng minh xong, c\u0169ng l\u00e0 ng\u00e0y v\u1ee3 \u00f4ng, Nada c\u00f3 sinh nh\u1eadt, v\u00e0 \u0111\u00f3 l\u00e0 m\u00f3n qu\u00e0 \u00f4ng \u0111\u00e3 t\u1eb7ng v\u1ee3, \u0111i\u1ec1u \u00f4ng \u0111\u00e3 th\u1ea5t h\u1ee9a m\u1ed9t n\u0103m tr\u01b0\u1edbc. Th\u00e1ng 5, 1995, ch\u1ee9ng minh \u0111\u01b0\u1ee3c ch\u00ednh th\u1ee9c c\u00f4ng b\u1ed1 tr\u00ean t\u1ea1p ch\u00ed Annals of Mathematics<\/i>, trong \u0111\u00f3 c\u00f3 b\u00e0i ri\u00eang c\u1ee7a \u00f4ng v\u00e0 Taylor d\u00e0nh cho vi\u1ec7c tu ch\u1ec9nh. L\u00fac \u0111\u00f3 \u00f4ng 42 tu\u1ed5i. Chi\u1ebfc c\u1ea7u Taniyama\u2013Shimura gi\u1eefa hai mi\u1ec1n to\u00e1n h\u1ecdc kh\u00e1c nhau \u0111\u01b0\u1ee3c th\u00f4ng.<\/p>\n

    ***<\/span><\/p>\n

    B\u00e0i to\u00e1n Fermat \u0111\u1ea7y k\u1ecbch t\u00ednh v\u00e0 huy\u1ec1n b\u00ed. N\u00f3 cho th\u1ea5y chi\u1ec1u s\u00e2u kh\u1ee7ng khi\u1ebfp c\u1ee7a b\u00e0i to\u00e1n, v\u00e0 s\u1ef1 ki\u00ean nh\u1eabn c\u1ee7a con ng\u01b0\u1eddi, v\u00e0 r\u1eb1ng to\u00e1n h\u1ecdc t\u1ef1 n\u00f3, m\u1ed9t l\u00fac n\u00e0o \u0111\u00f3, kh\u00e9p k\u00edn v\u00f2ng tri th\u1ee9c l\u1ea1i. N\u00f3 c\u0169ng cho th\u1ea5y tr\u00ed tu\u1ec7 con ng\u01b0\u1eddi l\u00e0 v\u0129 \u0111\u1ea1i. Wiles \u0111ang s\u1ed1ng trong th\u1eddi \u0111\u1ea1i m\u00e1y t\u00ednh v\u1edbi tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o c\u00f3 th\u1ec3 \u0111\u00e1nh b\u1ea1i c\u00e1c \u0111\u1ea1i ki\u1ec7n t\u01b0\u1edbng c\u1edd vua, c\u1edd v\u00e2y, c\u00f3 th\u1ec3 g\u00f3p ph\u1ea7n v\u00e0o vi\u1ec7c gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n, nh\u01b0 b\u00e0i to\u00e1n b\u1ed1n m\u00e0u m\u00e0 kh\u00f4ng ai c\u00f3 th\u1ec3 ki\u1ec3m tra \u0111\u01b0\u1ee3c kh\u1ed1i l\u01b0\u1ee3ng tr\u01b0\u1eddng h\u1ee3p qu\u00e1 \u0111\u1ed3 s\u1ed9. Nh\u01b0ng Wiles ch\u1ee9ng minh r\u1eb1ng tr\u00ed tu\u1ec7 con ng\u01b0\u1eddi v\u1eabn l\u00e0 c\u00e1i g\u00ec \u0111\u00f3 kh\u00f4ng th\u1ec3 thay th\u1ebf \u0111\u01b0\u1ee3c. \u00d4ng ch\u1ec9 l\u00e0m vi\u1ec7c b\u1eb1ng b\u00fat ch\u00ec, gi\u1ea5y, t\u01b0 duy l\u00f4gic, tr\u1ef1c gi\u00e1c nh\u01b0 t\u1eeb h\u01a1n hai ngh\u00ecn n\u0103m tr\u01b0\u1edbc c\u1ee7a con ng\u01b0\u1eddi. Wiles \u0111\u01b0\u1ee3c sinh ra t\u1ea1i Cambridge, Anh, v\u00e0 khi l\u1edbn l\u00ean, t\u1ed1t nghi\u1ec7p c\u1eed nh\u00e2n t\u1ea1i \u0110\u1ea1i h\u1ecdc Oxford, r\u1ed3i ti\u1ebfn s\u0129 t\u1ea1i \u0110\u1ea1i h\u1ecdc Cambridge. Kho\u1ea3ng 300 n\u0103m tr\u01b0\u1edbc Newton \u0111\u00e3 h\u1ecdc v\u00e0 t\u1ed1t nghi\u1ec7p th\u1ea1c s\u1ef9 t\u1ea1i \u0110\u1ea1i h\u1ecdc Cambridge. \u201cB\u1eb1ng t\u01b0 duy thu\u1ea7n t\u00fay, b\u1eb1ng s\u1ef1 t\u1eadp trung tinh th\u1ea7n, \u0111i\u1ec1u b\u00ed \u1ea9n, \u00f4ng (Newton) tin, s\u1ebd b\u1ed9c l\u1ed9 ra cho ng\u01b0\u1eddi \u0111\u00e3 \u0111\u01b0\u1ee3c \u2018th\u1ecd ph\u00e1p\u2019 (initiate)\u201d, nh\u01b0 nh\u00e0 kinh t\u1ebf John Maynard Keynes vi\u1ebft v\u1ec1 Newton. Ph\u1ea3i ch\u0103ng Wiles \u0111\u00e3 \u0111\u01b0\u1ee3c \u201cth\u1ecd ph\u00e1p\u201d v\u00e0o l\u00fac \u00f4ng b\u1eaft g\u1eb7p b\u00e0i to\u00e1n Fermat \u1edf tu\u1ed5i l\u00ean m\u01b0\u1eddi trong m\u1ed9t ng\u00e0y \u0111\u1ecbnh m\u1ec7nh t\u1ea1i th\u01b0 vi\u1ec7n tr\u00ean \u0111\u01b0\u1eddng Milton, v\u00e0 t\u1eeb \u0111\u00f3, ti\u1ec1m th\u1ee9c c\u1ee7a \u00f4ng ho\u1ea1t \u0111\u1ed9ng v\u00e0 d\u1eabn d\u1eaft \u00e2m th\u1ea7m, r\u1ed3i \u00f4ng \u0111\u01b0\u1ee3c th\u1ea7y m\u00ecnh truy\u1ec1n cho c\u00f4ng c\u1ee5 c\u1ea7n thi\u1ebft sau n\u00e0y, hay \u00f4ng \u0111\u00e3 \u0111\u01b0\u1ee3c ti\u1ec1m th\u1ee9c d\u1eabn d\u1eaft (?), \u0111\u1ec3 30 n\u0103m sau \u00f4ng gi\u1ea3i m\u00e3 b\u00e0i to\u00e1n Fermat ho\u00e0n to\u00e0n? N\u1ebfu Newton \u0111\u1ee9ng tr\u00ean vai nh\u1eefng ng\u01b0\u1eddi kh\u1ed5ng l\u1ed3, th\u00ec \u0111i\u1ec1u \u0111\u00f3 c\u0169ng t\u01b0\u01a1ng t\u1ef1 \u0111\u00fang \u0111\u1ed1i v\u1edbi Wiles.<\/p>\n

    \"\"

    B\u00e0i to\u00e1n Fermat v\u00e0 Andrew Wiles, ng\u01b0\u1eddi \u201cch\u1ebf ng\u1ef1\u201d (\u1ea3nh n\u0103m 1998,Charles Rex Arbogast\/AP (Nature)).<\/p><\/div>\n

    ***<\/span><\/p>\n

    M\u1ed9t Pythagorean<\/i>, m\u1ed9t Platonist<\/i>. Wiles l\u00e0 m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc l\u00fd thuy\u1ebft. To\u00e1n h\u1ecdc c\u1ee7a \u00f4ng r\u1ea5t tr\u1eebu t\u01b0\u1ee3ng. L\u00fd thuy\u1ebft v\u00e0 tr\u1eebu t\u01b0\u1ee3ng l\u00e0 hai \u0111\u1eb7c t\u00ednh c\u1ee7a n\u1ec1n to\u00e1n h\u1ecdc v\u00e0 t\u01b0 duy ph\u01b0\u01a1ng T\u00e2y. Alfred North Whitehead, m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc \u0111\u1ed3ng h\u01b0\u01a1ng c\u1ee7a Wiles v\u00e0 t\u1eebng \u0111\u01b0\u1ee3c \u0111\u00e0o t\u1ea1o \u1edf \u0110\u1ea1i h\u1ecdc Cambridge, ca ng\u1ee3i n\u0103ng l\u1ef1c t\u01b0 duy tr\u1eebu t\u01b0\u1ee3ng c\u1ee7a con ng\u01b0\u1eddi: \u201cKhoa h\u1ecdc c\u1ee7a to\u00e1n thu\u1ea7n t\u00fay (l\u00fd thuy\u1ebft), trong nh\u1eefng s\u1ef1 ph\u00e1t tri\u1ec3n hi\u1ec7n \u0111\u1ea1i c\u1ee7a n\u00f3, c\u00f3 th\u1ec3 kh\u1eb3ng \u0111\u1ecbnh l\u00e0 s\u1ef1 s\u00e1ng t\u1ea1o \u0111\u1ed9c \u0111\u00e1o nh\u1ea5t c\u1ee7a tr\u00ed tu\u1ec7 con ng\u01b0\u1eddi.\u201d T\u01b0 duy tr\u1eebu t\u01b0\u1ee3ng b\u1eaft \u0111\u1ea7u t\u1eeb nh\u1eefng ng\u01b0\u1eddi Hy L\u1ea1p th\u1ebf k\u1ef7 th\u1ee9 6 tr\u01b0\u1edbc C\u00f4ng nguy\u00ean. H\u1ecd l\u1ed9t b\u1ecf c\u00e1i v\u1ecf v\u1eadt ch\u1ea5t kh\u1ecfi c\u00e1c kh\u00e1i ni\u1ec7m c\u1ed1t l\u00f5i ch\u1ee9a \u0111\u1ef1ng b\u00ean trong. H\u1ecd ch\u1eaft l\u1ecdc kh\u00e1i ni\u1ec7m (concept), \u00fd ni\u1ec7m (idea) t\u1eeb th\u1ef1c t\u1ea1i v\u1eadt l\u00fd. Kh\u00e1i ni\u1ec7m m\u1edbi l\u00e0 c\u00e1i c\u00f3 t\u00ednh ph\u1ed5 qu\u00e1t, trong khi v\u1eadt ch\u1ea5t th\u00ec thay \u0111\u1ed5i v\u00e0 kh\u00f4ng b\u1ec1n v\u1eefng. T\u01b0 duy v\u1edbi nh\u1eefng kh\u00e1i ni\u1ec7m gi\u00fap h\u1ecd \u0111\u1ea1t t\u1edbi t\u00ednh t\u1ed5ng qu\u00e1t (generality), t\u1eeb \u0111\u00f3 h\u1ecd c\u00f3 tri\u1ebft h\u1ecdc. Pythagoras tuy\u00ean t\u1ed1 \u201cT\u00f4i l\u00e0 m\u1ed9t nh\u00e0 tri\u1ebft h\u1ecdc\u201d. \u00d4ng \u0111i t\u1eeb con s\u1ed1 \u0111\u1ec3 hi\u1ec3u th\u1ebf gi\u1edbi, kh\u00f4ng m\u00e0ng th\u1ebf gi\u1edbi v\u1eadt ch\u1ea5t. T\u01b0 duy khoa h\u1ecdc, to\u00e1n h\u1ecdc, tr\u1eebu t\u01b0\u1ee3ng, c\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1i \u0111\u1eb9p t\u1ef1 th\u00e2n. Pythagoras t\u1eeb nh\u00e0 to\u00e1n h\u1ecdc tr\u1edf th\u00e0nh nh\u00e0 tri\u1ebft h\u1ecdc. Plato ng\u01b0\u1ee3c l\u1ea1i, \u00f4ng l\u00e0 nh\u00e0 tri\u1ebft h\u1ecdc tr\u1edf th\u00e0nh ng\u01b0\u1eddi \u0111\u00e1nh gi\u00e1 cao vai tr\u00f2 c\u1ee7a to\u00e1n h\u1ecdc \u0111\u1ed1i v\u1edbi tri\u1ebft h\u1ecdc. T\u01b0 duy to\u00e1n h\u1ecdc chu\u1ea9n b\u1ecb cho con ng\u01b0\u1eddi b\u01b0\u1edbc v\u00e0o th\u1ebf gi\u1edbi c\u1ee7a c\u00e1c forms \u2013 m\u00f4 th\u1ee9c \u2212 cao h\u01a1n, \u0111\u1ed9c l\u1eadp v\u1edbi th\u1ebf gi\u1edbi v\u1eadt ch\u1ea5t lu\u00f4n lu\u00f4n bi\u1ebfn \u0111\u1ed5i. Con \u0111\u01b0\u1eddng c\u1ee9u r\u1ed7i \u0111\u1ec3 \u0111\u1ea1t t\u1edbi Ch\u00e2n \u2013 Thi\u1ec7n \u2013 M\u1ef9 \u0111i ngang qua to\u00e1n h\u1ecdc. H\u1ecdc to\u00e1n l\u00e0 s\u1ef1 \u201cth\u1ecd ph\u00e1p\u201d v\u00e0o Tinh th\u1ea7n c\u1ee7a Th\u01b0\u1ee3ng \u0110\u1ebf. H\u00ecnh h\u1ecdc c\u00f3 t\u00e1c d\u1ee5ng d\u1eabn d\u1eaft linh h\u1ed3n \u0111\u1ebfn ch\u00e2n l\u00fd, v\u00e0 t\u1ea1o ra tinh th\u1ea7n tri\u1ebft h\u1ecdc. \u0110i\u1ec3m, \u0111\u01b0\u1eddng th\u1eb3ng, tam gi\u00e1c, h\u00ecnh vu\u00f4ng v\u00e0 nh\u01b0 th\u1ebf ti\u1ebfp t\u1ee5c, l\u00e0 nh\u1eefng \u0111\u1ed1i t\u01b0\u1ee3ng c\u1ee7a t\u01b0 duy thu\u1ea7n t\u00fay. S\u1ed1 h\u1ecdc, c\u0169ng theo Platon, \u201cc\u00f3 t\u00e1c d\u1ee5ng r\u1ea5t l\u1edbn v\u00e0 n\u00e2ng cao, bu\u1ed9c linh h\u1ed3n l\u00fd lu\u1eadn v\u1ec1 nh\u1eefng con s\u1ed1 tr\u1eebu t\u01b0\u1ee3ng, v\u00e0 ch\u1ed1ng l\u1ea1i \u1ea3nh h\u01b0\u1edfng c\u1ee7a th\u1ebf gi\u1edbi c\u1ee7a c\u00e1c v\u1eadt th\u1ec3 h\u1eefu h\u00ecnh th\u00e2m nh\u1eadp v\u00e0o l\u00fd lu\u1eadn.\u201d Platon khuy\u00ean \u201cnh\u1eefng ng\u01b0\u1eddi \u0111\u00f3ng vai ch\u00ednh y\u1ebfu c\u1ee7a Nh\u00e0 n\u01b0\u1edbc ch\u00fang ta n\u00ean \u0111i h\u1ecdc s\u1ed1 h\u1ecdc, kh\u00f4ng ph\u1ea3i nh\u01b0 t\u00e0i t\u1eed, m\u00e0 h\u1ecd ph\u1ea3i h\u1ecdc cho \u0111\u1ebfn \u0111\u1ed9 h\u1ecd nh\u00ecn th\u1ea5y b\u1ea3n ch\u1ea5t c\u1ee7a s\u1ed1 b\u1eb1ng c\u00e1i \u0111\u1ea7u th\u00f4i.\u201d Platon khuy\u00ean nh\u1eefng nh\u00e0 l\u00e3nh \u0111\u1ea1o t\u01b0\u01a1ng lai c\u1ea7n ph\u1ea3i h\u1ecdc m\u01b0\u1eddi n\u0103m, t\u1eeb tu\u1ed5i 20 \u0111\u1ebfn tu\u1ed5i 30, c\u00e1c khoa h\u1ecdc ch\u00ednh x\u00e1c nh\u01b0 s\u1ed1 h\u1ecdc, h\u00ecnh h\u1ecdc, thi\u00ean v\u0103n l\u00e0m c\u0103n b\u1ea3n. (M. Kline) Hy L\u1ea1p l\u00e0 d\u00e2n t\u1ed9c \u0111\u1ea7u ti\u00ean c\u00f3 tinh th\u1ea7n \u201cth\u01b0\u1ee3ng t\u00f4n tr\u00ed tu\u1ec7\u201d. \u201cNh\u1eefng g\u00ec ch\u00fang t\u00f4i nh\u1eefng ng\u01b0\u1eddi Hy L\u1ea1p nh\u1eadn \u0111\u01b0\u1ee3c, ch\u00fang t\u00f4i \u0111\u1ec1u c\u1ea3i ti\u1ebfn v\u00e0 ho\u00e0n thi\u1ec7n\u201d, nh\u01b0 c\u00e2u n\u00f3i n\u1ed5i ti\u1ebfng c\u1ee7a Platon. \u0110\u00fang nh\u01b0 th\u1ebf, h\u1ecd ho\u00e0n thi\u1ec7n b\u1eb1ng nh\u1eefng t\u01b0 duy tr\u1eebu t\u01b0\u1ee3ng \u1edf giai t\u1ea7ng cao. Andrew Wiles l\u00e0 m\u1ed9t trong nh\u1eefng ng\u01b0\u1eddi g\u00f3p ph\u1ea7n ho\u00e0n thi\u1ec7n nh\u1eefng g\u00ec nh\u1eadn \u0111\u01b0\u1ee3c c\u00f2n dang d\u1edf.<\/p>\n

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    Nh\u1eefng nh\u00e0 to\u00e1n h\u1ecdc theo h\u1ecdc thuy\u1ebft (t\u00e2n-) Platon cho r\u1eb1ng ch\u00e2n l\u00fd to\u00e1n h\u1ecdc \u0111\u00e3 c\u00f3 s\u1eb5n, c\u0169ng nh\u01b0 th\u1ebf gi\u1edbi v\u1eadt l\u00fd, \u0111\u1ed9c l\u1eadp v\u1edbi con ng\u01b0\u1eddi, t\u1eeb m\u1ed9t quy\u1ec1n n\u0103ng l\u00e0 \u201clinh h\u1ed3n th\u1ebf gi\u1edbi\u201d. Con ng\u01b0\u1eddi ch\u1ec9 \u0111i t\u00ecm v\u00e0 kh\u00e1m ph\u00e1, kh\u00f4ng s\u00e1ng t\u1ea1o ra c\u00e1i m\u1edbi. \u201cM\u1eb7c d\u00f9 ch\u00e2n l\u00fd ch\u01b0a \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ed1i v\u1edbi ch\u00fang ta, nh\u01b0ng n\u00f3 t\u1ed3n t\u1ea1i tr\u01b0\u1edbc<\/i> (pre-exists<\/i>), v\u00e0 \u00e1p \u0111\u1eb7t l\u00ean ch\u00fang ta con \u0111\u01b0\u1eddng ch\u00fang ta ph\u1ea3i \u0111i theo, m\u1ed9t c\u00e1ch kh\u00f4ng th\u1ec3 kh\u00e1c h\u01a1n\u201d nh\u01b0 nh\u00e0 to\u00e1n h\u1ecdc Jacques Hadamard (1865-1963) ph\u00e1t bi\u1ec3u. To\u00e1n h\u1ecdc \u0111i t\u00ecm th\u1ef1c t\u1ebf \u0111\u00edch th\u1ef1c (true reality) t\u1eeb nh\u1eefng th\u1ef1c th\u1ec3 \u00fd ni\u1ec7m (ideal entities). Th\u1ebf gi\u1edbi c\u1ee7a Platon l\u00e0 th\u1ebf gi\u1edbi c\u1ee7a c\u00e1c th\u1ef1c th\u1ec3 \u00fd ni\u1ec7m, tr\u1eebu t\u01b0\u1ee3ng c\u00f3 s\u1eb5n, kh\u00f4ng n\u1eb1m trong kinh nghi\u1ec7m, v\u00e0 \u0111\u1ed9c l\u1eadp v\u1edbi con ng\u01b0\u1eddi. Kh\u00f4ng ph\u1ea3i t\u1ea5t c\u1ea3, nh\u01b0ng nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc tin nh\u01b0 th\u1ebf. \u201cT\u00f4i tin r\u1eb1ng s\u1ed1 v\u00e0 h\u00e0m s\u1ed1 c\u1ee7a gi\u1ea3i t\u00edch kh\u00f4ng ph\u1ea3i s\u1ea3n ph\u1ea9m t\u00f9y ti\u1ec7n c\u1ee7a tr\u00ed tu\u1ec7 ch\u00fang ta: t\u00f4i tin r\u1eb1ng ch\u00fang t\u1ed3n t\u1ea1i b\u00ean ngo\u00e0i ch\u00fang ta, nh\u01b0 c\u00f9ng t\u00ednh ch\u1ea5t c\u1ee7a s\u1ef1 t\u1ea5t y\u1ebfu, nh\u01b0 c\u00e1c v\u1eadt th\u1ec3 c\u1ee7a th\u1ef1c th\u1ec3 kh\u00e1ch quan; v\u00e0 ch\u00fang ta t\u00ecm th\u1ea5y, ho\u1eb7c kh\u00e1m ph\u00e1 ch\u00fang v\u00e0 nghi\u00ean c\u1ee9u ch\u00fang nh\u01b0 c\u00e1c nh\u00e0 v\u1eadt l\u00fd, h\u00f3a h\u1ecdc v\u00e0 nh\u00e0 \u0111\u1ed9ng v\u1eadt h\u1ecdc l\u00e0m\u201d nh\u01b0 nh\u00e0 to\u00e1n h\u1ecdc Charles Hermite (1822-1901) vi\u1ebft. \u0110\u1ed1i v\u1edbi \u00f4ng, c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u201cl\u00e0 nh\u1eefng ng\u01b0\u1eddi \u0111\u1ea7y t\u1edb h\u01a1n l\u00e0 nh\u1eefng ng\u01b0\u1eddi ch\u1ee7 trong to\u00e1n h\u1ecdc.\u201d Georg Cantor, cha \u0111\u1ebb c\u1ee7a thuy\u1ebft t\u1eadp h\u1ee3p, c\u0169ng tin nh\u01b0 th\u1ebf: nh\u00e0 to\u00e1n h\u1ecdc kh\u00f4ng ph\u00e1t minh nh\u01b0ng kh\u00e1m ph\u00e1 c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 \u0111\u1ecbnh l\u00fd. Ch\u00fang t\u1ed3n t\u1ea1i \u0111\u1ed9c l\u1eadp v\u1edbi t\u01b0 duy con ng\u01b0\u1eddi. Cantor xem \u00f4ng l\u00e0 m\u1ed9t \u201cng\u01b0\u1eddi b\u00e1o c\u00e1o\u201d v\u00e0 \u201cth\u01b0 k\u00fd\u201d. (M. Kline) Tuy con ng\u01b0\u1eddi c\u00f3 quy\u1ec1n t\u1ef1 do s\u00e1ng t\u1ea1o \u0111\u1ec3 \u0111i \u0111\u1ebfn kh\u00e1m ph\u00e1 ch\u00e2n l\u00fd, nh\u01b0ng s\u00e1ng t\u1ea1o ph\u1ea3i ph\u00f9 h\u1ee3p v\u1edbi ch\u00e2n l\u00fd \u0111\u00edch th\u1ef1c ti\u1ec1n \u0111\u1ecbnh. Einstein c\u0169ng nh\u1eafc \u0111\u1ebfn Pythagoras v\u00e0 Platon khi \u00f4ng n\u00f3i v\u1ec1 th\u00e1i \u0111\u1ed9 tri\u1ebft h\u1ecdc c\u1ea7n thi\u1ebft c\u1ee7a ng\u01b0\u1eddi l\u00e0m khoa h\u1ecdc: \u201cAnh ta ngay c\u1ea3 c\u00f3 th\u1ec3 tr\u1edf th\u00e0nh m\u1ed9t Platonist (ng\u01b0\u1eddi theo thuy\u1ebft Platon) hay Pythagorean (m\u00f4n \u0111\u1ec7 c\u1ee7a tr\u01b0\u1eddng ph\u00e1i Pythagoras) trong ch\u1eebng m\u1ef1c anh ta xem quan \u0111i\u1ec3m c\u1ee7a t\u00ednh \u0111\u01a1n gi\u1ea3n l\u00f4gic nh\u01b0 l\u00e0 c\u00f4ng c\u1ee5 h\u1eefu hi\u1ec7u v\u00e0 kh\u00f4ng th\u1ec3 thi\u1ebfu trong nghi\u00ean c\u1ee9u c\u1ee7a anh ta.\u201d<\/p>\n

    H\u1ecdc thuy\u1ebft Platon (Platonism) l\u00e0 d\u00f2ng tri\u1ebft h\u1ecdc c\u00f3 \u1ea3nh h\u01b0\u1edfng m\u1ea1nh l\u00ean c\u00e1c nh\u00e0 khoa h\u1ecdc v\u00e0 to\u00e1n h\u1ecdc sau khi c\u00e1c t\u00e1c ph\u1ea9m c\u1ee7a Platon \u0111\u01b0\u1ee3c d\u1ecbch \u0111\u1ea7y \u0111\u1ee7 sang ti\u1ebfng Latinh v\u00e0o th\u1ebf k\u1ef7 15 c\u1ee7a Ph\u1ee5c H\u01b0ng, ph\u1ed5 bi\u1ebfn r\u1ed9ng r\u00e3i v\u00e0o ch\u00e2u \u00c2u Kit\u00f4 gi\u00e1o. N\u00f3 \u201ct\u1ea1o h\u1ed3n\u201d cho c\u00e1c m\u00f4n khoa h\u1ecdc t\u1ef1 nhi\u00ean v\u00e0 to\u00e1n h\u1ecdc, kh\u1eafc ph\u1ee5c ch\u1ee7 ngh\u0129a duy l\u00fd kh\u00f4 khan c\u1ee7a Aristote, v\u00e0 ch\u1ee7 ngh\u0129a c\u01a1 gi\u1edbi c\u1ee9ng nh\u1eafc, mechanism \u0111ang l\u00ean, \u0111\u1ea1i bi\u1ec3u l\u00e0 Descartes v\u00e0 Mersenne. V\u1edbi quan ni\u1ec7m nh\u01b0 \u201ch\u1ed3n th\u1ebf gi\u1edbi\u201d (world-soul), hay \u201cTh\u1ec3 Duy nh\u1ea5t\u201d (\u201cOne\u201d), n\u00f3 g\u1ea7n g\u0169i v\u1edbi Kit\u00f4 gi\u00e1o, nh\u01b0ng kh\u00f4ng ph\u1ea3i l\u00e0 t\u00f4n gi\u00e1o. N\u00f3 c\u0169ng c\u00f3 n\u00e9t \u201cma thu\u1eadt\u201d (magic), ph\u00f9 h\u1ee3p v\u1edbi tr\u00e0o l\u01b0u c\u1ee7a thu\u1eadt gi\u1ea3 kim (alchemy). H\u1ec7 t\u01b0 t\u01b0\u1edfng Platon \u1ea3nh h\u01b0\u1edfng s\u00e2u s\u1eafc l\u00ean nh\u1eefng nh\u00e0 khoa h\u1ecdc l\u1edbn nh\u01b0 Galilei, Kepler v\u00e0 Newton. Th\u1ebf k\u1ef7 17, t\u1eeb nh\u1eefng n\u0103m 1630-1680, Cambridge c\u00f3 m\u1ed9t nh\u00f3m h\u1ecdc gi\u1ea3 ch\u1ecbu \u1ea3nh h\u01b0\u1edfng c\u1ee7a h\u1ec7 t\u01b0 t\u01b0\u1edfng Platon, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 Cambridge Platonists. H\u1ecd, trong nhi\u1ec1u th\u1ee9, \u0111\u1ec1 cao l\u00fd t\u00ednh v\u00e0 mu\u1ed1n dung h\u1ee3p l\u00fd t\u00ednh v\u00e0 \u0111\u1ee9c tin, tri\u1ebft l\u00fd t\u1ef1 nhi\u00ean m\u1edbi (khoa h\u1ecdc m\u1edbi) v\u00e0 thi\u00ean kh\u1ea3i Kit\u00f4 gi\u00e1o, trong s\u1ef1 h\u00e0i h\u00f2a c\u1ee7a v\u0169 tr\u1ee5.<\/p>\n

    Newton \u0111\u01b0a ra c\u00e1ch di\u1ec5n gi\u1ea3i c\u01a1 ch\u1ebf ho\u1ea1t \u0111\u1ed9ng c\u1ee7a v\u0169 tr\u1ee5 nh\u01b0 nh\u1eefng nguy\u00ean l\u00fd c\u01a1 h\u1ecdc, nh\u01b0ng t\u1eeb ch\u1ed1i nh\u1eefng \u201cnguy\u00ean c\u1edb ban \u0111\u1ea7u\u201d (first causes) c\u1ee7a s\u1ef1 h\u00ecnh th\u00e0nh v\u0169 tr\u1ee5 l\u00e0 c\u01a1 h\u1ecdc thu\u1ea7n t\u00fay. Ch\u00fang c\u00f3 g\u1ed1c r\u1ec5 s\u00e2u xa h\u01a1n, m\u00e0 khoa h\u1ecdc c\u1ea7n ph\u1ea3i t\u00ecm ki\u1ebfm. Newton tin r\u1eb1ng Ch\u00faa \u0111\u00e3 \u0111\u1eb7t nh\u1eefng \u0111\u1ea7u m\u1ed1i huy\u1ec1n b\u00ed (magic clues) l\u00ean th\u1ebf gi\u1edbi, \u0111\u1ec3 cho ph\u00e9p c\u00e1c \u201chuynh \u0111\u1ec7 b\u00ed truy\u1ec1n\u201d (esoteric brethen) l\u00e0m m\u1ed9t cu\u1ed9c s\u0103n l\u00f9ng kho b\u00e1u, nh\u01b0 nh\u00e0 kinh t\u1ebf John Maynard Keynes di\u1ec5n t\u1ea3 h\u00ecnh t\u01b0\u1ee3ng. Nh\u1eefng \u0111\u1ea7u m\u1ed1i huy\u1ec1n b\u00ed n\u00e0y m\u1ed9t ph\u1ea7n \u0111\u01b0\u1ee3c t\u00ecm th\u1ea5y tr\u00ean tr\u1eddi nh\u01b0 nh\u1eefng ch\u1ee9ng c\u1ee9 hi\u1ec3n nhi\u00ean, Keynes vi\u1ebft ti\u1ebfp, nh\u01b0ng m\u1ed9t ph\u1ea7n trong nh\u1eefng t\u01b0 li\u1ec7u v\u00e0 truy\u1ec1n th\u1ed1ng \u0111\u00e3 \u0111\u01b0\u1ee3c c\u00e1c huynh \u0111\u1ec7 truy\u1ec1n l\u1ea1i trong m\u1ed9t chu\u1ed7i kh\u00f4ng \u0111\u1ee9t \u0111o\u1ea1n t\u1eeb s\u1ef1 kh\u1ea3i huy\u1ec1n b\u00ed m\u1eadt ban \u0111\u1ea7u t\u1ea1i Babylon. Newton nh\u00ecn v\u0169 tr\u1ee5 nh\u01b0 m\u1ed9t m\u1eadt m\u00e3<\/i> (cryptogram) \u0111\u01b0\u1ee3c \u0110\u1ea5ng to\u00e0n n\u0103ng t\u1ea1o ra, v\u00e0 c\u0169ng nh\u01b0 th\u1ebf, to\u00e1n vi t\u00edch ph\u00e2n c\u0169ng l\u00e0 m\u1ed9t m\u1eadt m\u00e3 \u0111\u00e3 \u0111\u01b0\u1ee3c \u00f4ng kh\u00e1m ph\u00e1. Th\u1ebf gi\u1edbi kh\u00f4ng \u0111\u01a1n gi\u1ea3n l\u00e0 m\u1ed9t c\u01a1 ch\u1ebf c\u01a1 h\u1ecdc thu\u1ea7n t\u00fay. N\u00f3 c\u00f3 m\u1ed9t \u201clinh h\u1ed3n\u201d.<\/p>\n

    C\u00f3 th\u1ec3 nh\u00ecn, b\u00e0i to\u00e1n c\u1ee7a Fermat c\u0169ng thu\u1ed9c d\u1ea1ng \u201cm\u1eadt m\u00e3\u201d, m\u00e0 d\u00f2ng su\u1ed1i to\u00e1n h\u1ecdc \u0111\u00e3 khai s\u00e1ng t\u1eeb ngu\u1ed3n \u1edf Babylon, ti\u1ebfp t\u1ee5c ch\u1ea3y qua c\u00e1c th\u1ebf k\u1ef7, \u0111\u1ec3 \u0111\u1ebfn th\u1ebf k\u1ef7 20, mang theo nhi\u1ec1u ph\u00f9 sa, v\u1edbi s\u1ef1 ti\u1ebfp s\u1ee9c c\u1ee7a c\u00e1c \u201chuynh \u0111\u1ec7\u201d to\u00e1n h\u1ecdc bao \u0111\u1eddi, v\u00e0 khi \u0111\u1ea7y \u0111\u1ee7, Andrew Wiles, ng\u01b0\u1eddi th\u1eeba h\u01b0\u1edfng nh\u1eefng tri th\u1ee9c c\u1ea7n thi\u1ebft \u0111\u00f3, vi\u1ebft l\u00ean m\u1ed9t b\u1ea3n giao h\u01b0\u1edfng c\u1ee7a ch\u1ee9ng minh \u0111i\u1ec1u b\u00ed \u1ea9n. Cho n\u00ean, trong m\u1ed9t ch\u1eebng m\u1ef1c nh\u1ea5t \u0111\u1ecbnh, Andrew Wiles c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c xem l\u00e0 m\u1ed9t t\u00edn \u0111\u1ed3 c\u1ee7a Pythagore v\u00e0 m\u1ed9t ng\u01b0\u1eddi theo thuy\u1ebft Platon. Ch\u1eb3ng ph\u1ea3i c\u00f3 c\u00e1i g\u00ec \u201cti\u1ec1n \u0111\u1ecbnh\u201d hay sao?<\/p>\n

    ***<\/span><\/p>\n

    Ti\u1ebfn s\u0129 L\u00ea Quang \u00c1nh, h\u1ecdc tr\u00f2 khoa to\u00e1n c\u1ee7a GS. \u0110\u1eb7ng \u0110\u00ecnh \u00c1ng c\u1ee7a \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc S\u00e0i G\u00f2n nh\u1eefng n\u0103m 1960 \u0111\u1ea7y k\u1ef7 ni\u1ec7m, l\u00e0 ng\u01b0\u1eddi k\u1ec3 l\u1ea1i c\u00e2u chuy\u1ec7n l\u1ecbch s\u1eed to\u00e1n h\u1ecdc t\u1eeb th\u1eddi Babylon li\u00ean quan \u0111\u1ebfn \u0110\u1ecbnh l\u00fd sau c\u00f9ng c\u1ee7a Fermat nh\u01b0 m\u1ed9t \u201cm\u1eadt m\u00e3\u201d cho ch\u00fang ta nghe. \u00d4ng k\u1ec3 r\u1ea5t s\u00e2u s\u1eafc, r\u1ea5t c\u00f3 duy\u00ean, c\u00f3 h\u1ed3n, v\u1edbi nhi\u1ec1u chi ti\u1ebft l\u1ecbch s\u1eed gi\u00fap ng\u01b0\u1eddi \u0111\u1ecdc hi\u1ec3u \u0111\u01b0\u1ee3c s\u1ee3i chu\u1ed7i \u0111\u1ebfn ng\u1ecdn ng\u00e0nh. B\u1ea1n \u0111\u1ecdc s\u1ebd lu\u00f4n lu\u00f4n ng\u1ea1c nhi\u00ean m\u1ed9t c\u00e1ch th\u00fa v\u1ecb t\u1eeb chuy\u1ec7n n\u00e0y \u0111\u1ebfn chuy\u1ec7n kh\u00e1c. M\u1ed7i ch\u01b0\u01a1ng, hay \u0111\u1ec1 t\u00e0i, l\u00e0 m\u1ed9t c\u00e2u chuy\u1ec7n h\u1ea5p d\u1eabn t\u1ef1 n\u00f3. Ng\u01b0\u1eddi ta t\u01b0\u1edfng \u00f4ng \u0111\u01b0\u1ee3c t\u1eafm m\u00ecnh trong d\u00f2ng su\u1ed1i t\u1eeb thu\u1edf Babylon \u1ea5y v\u00e0 ch\u1ea3y \u0111\u1ebfn ng\u00e0y nay. \u0110\u00e3 c\u00f3 hai quy\u1ec3n s\u00e1ch xu\u1ea5t s\u1eafc v\u1ec1 \u0110\u1ecbnh l\u00fd cu\u1ed1i c\u00f9ng c\u1ee7a Fermat, m\u1ed9t c\u1ee7a Simon Singh (do Ph\u1ea1m V\u0103n Thi\u1ec1u v\u00e0 Ph\u1ea1m Vi\u1ec7t H\u01b0ng d\u1ecbch), v\u00e0 m\u1ed9t c\u1ee7a Amir Aczel (do Tr\u1ea7n v\u0103n Nhung, \u0110\u1ed7 Trung H\u1eadu, Nguy\u1ec5n Kim Chi d\u1ecbch), nh\u01b0ng b\u1ea1n \u0111\u1ecdc s\u1ebd t\u00ecm th\u1ea5y t\u00ednh \u0111\u1ed9c \u0111\u00e1o, kh\u00e1c bi\u1ec7t v\u00e0 m\u1edbi m\u1ebb trong ph\u1ea7n k\u1ec3 chuy\u1ec7n c\u1ee7a \u00f4ng \u1edf \u0111\u00e2y. \u00d4ng vi\u1ebft \u0111\u01b0\u1ee3c nh\u01b0 th\u1ebf, v\u1eeba s\u1eafc, v\u1eeba nh\u00e2n v\u0103n, v\u1eeba c\u00f3 t\u00ednh h\u1ecdc thu\u1eadt, v\u1eeba truy\u1ec1n c\u1ea3m, tr\u00ean h\u1ebft v\u00e0 tr\u01b0\u1edbc h\u1ebft, l\u00e0 v\u00ec \u00f4ng c\u00f3 t\u00ecnh y\u00eau \u0111\u00edch th\u1ef1c cho to\u00e1n h\u1ecdc. \u00d4ng r\u1eddi tr\u01b0\u1eddng \u0110\u1ea1i h\u1ecdc S\u00e0i G\u00f2n, nh\u01b0ng kh\u00f4ng r\u1eddi to\u00e1n h\u1ecdc. \u00d4ng r\u1eddi \u0111\u1ea5t n\u01b0\u1edbc, nh\u01b0ng kh\u00f4ng xa to\u00e1n h\u1ecdc. T\u00ecnh y\u00eau n\u00e0y kh\u00f4ng h\u1ec1 v\u01a1i \u0111i b\u1edfi ngo\u1ea1i c\u1ea3nh, m\u00e0 ng\u01b0\u1ee3c l\u1ea1i, \u00f4ng ng\u00e0y c\u00e0ng c\u1ee7ng c\u1ed1 tri th\u1ee9c m\u00ecnh, \u0111\u1ec3 \u201cg\u1eebng c\u00e0ng gi\u00e0 c\u00e0ng cay\u201d, v\u00e2ng, \u201cc\u00e0ng \u0111\u1eadm \u0111\u00e0\u201d n\u1eefa. \u00d4ng t\u1ef1 vun b\u1ed3i t\u00ecnh y\u00eau \u1ea5y m\u1ed9t c\u00e1ch th\u1ea7m l\u1eb7ng v\u00e0 li\u00ean t\u1ee5c. \u00d4ng nh\u01b0 ng\u01b0\u1eddi si t\u00ecnh trao c\u1ea3 t\u00ecnh y\u00eau cho m\u1ed9t ng\u01b0\u1eddi con g\u00e1i quy\u1ebfn r\u0169, m\u1ed9t c\u00e1ch \u0111\u01a1n ph\u01b0\u01a1ng, v\u00f4 \u0111i\u1ec1u ki\u1ec7n. Gi\u1ed1ng nh\u01b0 nh\u00e0 th\u01a1 Dante. Ch\u1ec9 nh\u00ecn th\u1ea5y n\u00e0ng Beatrice m\u1ed9t l\u1ea7n tr\u00ean c\u1ea7u Vecchio b\u1eaft qua s\u00f4ng Arno \u1edf Florence tr\u01b0\u1edbc n\u0103m 1300 m\u00e0 ngu\u1ed3n c\u1ea3m h\u1ee9ng c\u1ee7a \u00f4ng \u0111\u00e3 d\u00e2ng tr\u00e0o v\u00e0 tr\u1edf th\u00e0nh b\u1ea5t t\u1eed. \u0110\u00f3 ch\u00ednh l\u00e0 t\u00ecnh y\u00eau. V\u00e0 quy\u1ec3n s\u00e1ch n\u00e0y ch\u00ednh l\u00e0 s\u1ef1 th\u1ec3 hi\u1ec7n t\u00ecnh y\u00eau s\u00e2u s\u1eafc \u0111\u00f3. Xin gi\u1edbi thi\u1ec7u n\u1ed3ng nhi\u1ec7t v\u1edbi b\u1ea1n \u0111\u1ecdc.<\/p>\n

    Ngo\u00e0i ra, trong ph\u1ea7n Ph\u1ee5 l\u1ee5c, ch\u00fang t\u00f4i \u0111\u00ednh k\u00e8m m\u1ed9t b\u00e0i ph\u1ecfng v\u1ea5n c\u1ee7a NOVA (m\u1ed9t ch\u01b0\u01a1ng tr\u00ecnh truy\u1ec1n h\u00ecnh M\u1ef9 v\u1ec1 khoa h\u1ecdc) v\u1edbi Andrew Wiles, trong \u0111\u00f3 \u00f4ng thu\u1eadt l\u1ea1i h\u00e0nh tr\u00ecnh v\u00e0 nh\u1eefng c\u1ea3m x\u00fac, t\u00e2m l\u00fd c\u1ee7a \u00f4ng, t\u1eeb gi\u1edd ph\u00fat \u0111\u1ea7u khi \u0111\u01b0\u1ee3c \u201ckhai ng\u1ed9\u201d cho \u0111\u1ebfn ph\u00fat cu\u1ed1i \u201cgi\u00e1c ng\u1ed9\u201d. Th\u00eam n\u1eefa, ch\u00fang t\u00f4i xin gi\u1edbi thi\u1ec7u b\u00e0i vi\u1ebft c\u1ee7a nh\u00e0 to\u00e1n h\u1ecdc Goro Shimura k\u1ec3 l\u1ea1i cu\u1ed9c \u0111\u1eddi to\u00e1n h\u1ecdc c\u1ee7a ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh t\u00e0i n\u0103ng c\u1ee7a \u00f4ng, Yutaka Taniyama, \u0111\u00e3 t\u1ef1 s\u00e1t bi th\u1ea3m \u1edf tu\u1ed5i 31 sau khi \u00f4ng trao l\u1ea1i cho Shimura \u00fd t\u01b0\u1edfng mang t\u00ean ti\u00ean \u0111o\u00e1n Taniyama-Shimura. B\u00e0i vi\u1ebft cho \u0111\u1ecdc gi\u1ea3 th\u1ea5y b\u1ed1i c\u1ea3nh x\u00e3 h\u1ed9i c\u1ee7a n\u01b0\u1edbc Nh\u1eadt sau Th\u1ebf chi\u1ebfn II, v\u00e0 s\u1ef1 ph\u1ea5n \u0111\u1ea5u v\u01b0\u01a1n l\u00ean c\u1ee7a nh\u1eefng nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb trong c\u1ea3nh ch\u1eadt v\u1eadt \u0111\u00f3, c\u0169ng nh\u01b0 nh\u1eefng \u0111\u1eb7c t\u00ednh c\u1ee7a t\u00e0i n\u0103ng v\u1eafn s\u1ed1 sau khi \u0111\u00e3 c\u1ed1ng hi\u1ebfn ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n Fermat m\u1ed9t c\u00e1ch kh\u00f4ng \u00fd th\u1ee9c. C\u00e1i ch\u1ebft t\u1ef1 ch\u1ecdn c\u1ee7a Taniyama th\u1eadt v\u00f4 c\u00f9ng kh\u00f3 hi\u1ec3u. \u201cGi\u1ed1ng nh\u01b0 Th\u01b0\u1ee3ng \u0110\u1ebf \u0111\u00e3 thi\u1ebft k\u1ebf anh ph\u1ea3i l\u00e0m m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc trinh khi\u1ebft, ch\u1ee9 kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t ng\u01b0\u1eddi \u0111\u00e0n \u00f4ng c\u1ee7a gia \u0111\u00ecnh\u201d, Shimura vi\u1ebft. R\u1ed3i ch\u1ec9 v\u00e0i tu\u1ea7n sau, Mikaso, v\u1ecb h\u00f4n th\u00ea s\u1eafp c\u01b0\u1edbi, c\u0169ng t\u1ef1 s\u00e1t theo, t\u1ea1i c\u00f9ng c\u0103n h\u1ed9 v\u1eeba thu\u00ea \u0111\u1ec3 l\u00e0m t\u1ed5 \u1ea5m s\u1eafp t\u1edbi cho hai ng\u01b0\u1eddi. C\u00f4 \u0111\u1ec3 l\u1ea1i m\u1ed9t l\u00e1 th\u01b0, kh\u00f4ng bao gi\u1edd \u0111\u01b0\u1ee3c c\u00f4ng b\u1ed1, nh\u01b0ng Shimura \u0111\u01b0\u1ee3c bi\u1ebft c\u00f3 \u0111o\u1ea1n sau \u0111\u00e2y: \u201cCh\u00fang t\u00f4i \u0111\u00e3 h\u1ee9a v\u1edbi nhau r\u1eb1ng b\u1ea5t c\u1ee9 n\u01a1i n\u00e0o ch\u00fang t\u00f4i \u0111\u1ebfn, ch\u00fang t\u00f4i s\u1ebd kh\u00f4ng bao gi\u1edd \u0111\u1ec3 b\u1ecb chia ly. B\u00e2y gi\u1edd anh \u1ea5y \u0111\u00e3 \u0111i r\u1ed3i, t\u00f4i c\u0169ng ph\u1ea3i \u0111i c\u00f9ng v\u1edbi anh \u1ea5y th\u00f4i.\u201d<\/p>\n

    Ch\u1eb3ng ph\u1ea3i th\u00eam m\u1ed9t c\u00e2u chuy\u1ec7n \u201cti\u1ec1n \u0111\u1ecbnh\u201d hay sao? Taniyama v\u1eeba trao thanh ki\u1ebfm b\u00e1u r\u1ed3i bi\u1ebfn m\u1ea5t. Galois c\u0169ng th\u1ebf. Minkowski c\u0169ng th\u1ebf, sau khi trao l\u1ea1i kh\u00f4ng gian b\u1ed1n chi\u1ec1u Minkowski c\u1ee7a thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i, c\u0169ng \u0111\u1ed9t ng\u1ed9t ra \u0111i. Ch\u1eb3ng ph\u1ea3i l\u00e0 nh\u1eefng \u0111i\u1ec1u huy\u1ec1n b\u00ed hay sao? Chi\u1ebfc xe vinh quang c\u1ee7a to\u00e1n h\u1ecdc k\u00e9o qua nhi\u1ec1u quan t\u00e0i c\u1ee7a nh\u1eefng ng\u01b0\u1eddi hy sinh, v\u00ec l\u00fd do n\u00e0y, l\u00fd do kh\u00e1c, nh\u01b0 m\u1ed9t \u201cb\u1ea3n thi\u1ebft k\u1ebf\u201d c\u1ee7a tinh th\u1ea7n v\u0169 tr\u1ee5.<\/p>\n

    Ngo\u00e0i ra, xin b\u1ea1n \u0111\u1ecdc xem th\u00eam quy\u1ec3n Thi\u00ean t\u00e0i v\u00e0 S\u1ed1 ph\u1eadn<\/i> c\u0169ng c\u1ee7a TS. L\u00ea Quang \u00c1nh bi\u00ean so\u1ea1n do T\u1ee7 s\u00e1ch Sputnik ph\u00e1t h\u00e0nh. M\u1ed9t c\u00f4ng tr\u00ecnh nghi\u00ean c\u1ee9u xu\u1ea5t s\u1eafc.<\/p>\n

     <\/p>\n

    Xem th\u00eam c\u00e2u chuy\u1ec7n g\u1eafn li\u1ec1n v\u1edbi l\u1eddi gi\u1ea3i c\u1ee7a \u0111\u1ecbnh l\u00fd Fermat:<\/em><\/span><\/p>\n

    YUTAKA TANIYAMA V\u00c0 TH\u1edcI \u0110\u1ea0I C\u1ee6A ANH<\/a><\/h3>\n

    6 Th\u00e1ng B\u1ea3y, 2022<\/p>\n

    Nguy\u1ec5n Xu\u00e2n Xanh<\/strong><\/span><\/p>\n

    Gi\u00e1ng Sinh 2017<\/p>\n

    \n","protected":false},"excerpt":{"rendered":"

    \u0110\u1ecaNH L\u00dd CU\u1ed0I C\u00d9NG C\u1ee6A FERMAT Nguy\u1ec5n Xu\u00e2n Xanh gi\u1edbi thi\u1ec7u v\u00e0 d\u1eabn nh\u1eadp   C\u1ee9u c\u00e1nh duy nh\u1ea5t c\u1ee7a n\u1ec1n khoa h\u1ecdc l\u00e0 ni\u1ec1m vinh d\u1ef1 c\u1ee7a tr\u00ed tu\u1ec7 con ng\u01b0\u1eddi. C. G. J. Jacobi 1830 T\u00f4i b\u1ecb \u00e1m \u1ea3nh b\u1edfi b\u00e0i to\u00e1n n\u00e0y \u0111\u1ebfn n\u1ed7i l\u00fac n\u00e0o t\u00f4i c\u0169ng ngh\u0129 \u0111\u1ebfn n\u00f3, khi<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"jetpack_post_was_ever_published":false},"categories":[3],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts\/1178"}],"collection":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/comments?post=1178"}],"version-history":[{"count":7,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts\/1178\/revisions"}],"predecessor-version":[{"id":8804,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts\/1178\/revisions\/8804"}],"wp:attachment":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/media?parent=1178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/categories?post=1178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/tags?post=1178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}