{"id":16690,"date":"2026-08-04T20:16:11","date_gmt":"2026-08-04T13:16:11","guid":{"rendered":"https:\/\/rosetta.vn\/nguyenxuanxanh\/?p=16690"},"modified":"2026-08-04T20:49:56","modified_gmt":"2026-08-04T13:49:56","slug":"wang-hong-vuong-hong-nu-tu-si-cua-den-tho-toan-hoc","status":"publish","type":"post","link":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wang-hong-vuong-hong-nu-tu-si-cua-den-tho-toan-hoc\/","title":{"rendered":"Wang Hong (V\u01b0\u01a1ng H\u1ed3ng): N\u1eef tu s\u0129 c\u1ee7a \u0111\u1ec1n th\u1edd to\u00e1n h\u1ecdc"},"content":{"rendered":"

“S\u1ed0NG TR\u1eccN V\u1eb8N TRONG TH\u1ebe GI\u1edaI TO\u00c1N H\u1eccC L\u00c0 B\u01af\u1edaC \u0110I TR\u00caN L\u1eb0N RANH MONG MANH”<\/span><\/h1>\n

T\u00e1c gi\u1ea3<\/em>: Natalie Wolchover <\/span><\/p>\n

T\u1ea1p ch\u00ed<\/em> Quanta Magazine <\/span><\/p>\n

\u0110\u1ed7 Th\u1ecb Thu Tr\u00e0, <\/strong>n<\/em><\/span>g\u01b0\u1eddi d\u1ecbch<\/em><\/p>\n

Nguy\u1ec5n Xu\u00e2n Xanh<\/strong> xem l\u1ea1i v\u00e0 gi\u1edbi thi\u1ec7u<\/em><\/span><\/p>\n

\"\"<\/strong><\/p>\n

“H\u00e3y gi\u00e0nh th\u00ec gi\u1edd c\u1ee7a b\u1ea1n \u0111\u1ec3 suy ngh\u0129”<\/span><\/p>\n

\u2014 Wang Hong<\/span><\/strong><\/p>\n\"\"\n

Wang Hong (V\u01b0\u01a1ng H\u1ed3ng) (1991, 35 tu\u1ed5i)<\/p>\n

Acknowledgement, L\u1eddi c\u1ea3m \u01a1n<\/strong><\/em>: Ch\u00fang t\u00f4i h\u1ebft s\u1ee9c c\u1ea3m \u01a1n t\u1ea1p ch\u00ed Quanta Magazine<\/strong><\/span> v\u00e0 t\u00e1c gi\u1ea3 Natalie Wolchover<\/strong> v\u1ec1 b\u00e0i vi\u1ebft xu\u1ea5t s\u1eafc v\u1ec1 nh\u00e0 n\u1eef to\u00e1n h\u1ecdc tuy\u1ec7t v\u1eddi Wang Hong, ng\u01b0\u1eddi v\u1eeba \u0111\u01b0\u1ee3c trao gi\u1ea3i Fields t\u1ea1i Philadelphia, t\u1ea5m g\u01b0\u01a1ng h\u1ebft s\u1ee9c \u0111\u00e1ng ng\u01b0\u1ee1ng m\u1ed9 v\u00e0 truy\u1ec1n c\u1ea3m h\u1ee9ng cho gi\u1edbi tr\u1ebb Vi\u1ec7t Nam. Ch\u00fang t\u00f4i \u0111\u00e3 h\u1ebft s\u1ee9c c\u1ed1 g\u1eafng \u0111\u1ec3 chuy\u1ec3n ng\u1eef, nh\u1ea5t l\u00e0 nh\u1eefng thu\u1eadt ng\u1eef chuy\u00ean m\u00f4n, \u0111\u1ec3 b\u1ea1n \u0111\u1ecdc h\u00ecnh dung \u0111\u01b0\u1ee3c h\u00e0nh tr\u00ecnh l\u1eadp th\u00e2n, nh\u1eefng ch\u1eb7ng \u0111\u01b0\u1eddng khoa h\u1ecdc v\u00e0 nh\u1eefng \u0111\u00f3ng g\u00f3p c\u1ee7a c\u00f4, c\u0169ng nh\u01b0 kh\u00f4ng qu\u00ean gi\u00fap b\u1ea1n \u0111\u1ed9c hi\u1ec3u \u0111\u01b0\u1ee3c intuitive nh\u1eefng \u00fd t\u01b0\u1edfng to\u00e1n h\u1ecd trong context, v\u00e0 c\u00e1ch Wang Hong x\u1eed l\u00fd nh\u1eefng kh\u00f3 kh\u0103n chuy\u00ean m\u00f4n. R\u1ea5t c\u1ea3m \u01a1n Thu Tr\u00e0 \u0111\u00e3 c\u00f3 b\u1ea3n d\u1ecbch r\u1ea5t t\u1ed1t. Nh\u1eefng ch\u1ed7 n\u00e0o c\u00f2n kh\u00f3 hi\u1ec3u, xin \u0111\u1ed9c gi\u1ea3 tham kh\u1ea3o b\u1ea3n g\u1ed1c ti\u1ebfng Anh \u1edf cu\u1ed1i b\u00e0i.\u00a0<\/span><\/span><\/p>\n

Ch\u00fang t\u00f4i c\u0169ng r\u1ea5t c\u1ea3m \u01a1n b\u1ea1n T.M.K.<\/strong> \u0111\u00e3 gi\u00fap ph\u1ea7n x\u1eed l\u00fd \u1ea3nh animated v\u00e0 th\u00f4ng tin b\u00e1o ch\u00ed.<\/span><\/span><\/p>\n

T\u00f4i c\u0169ng c\u00f2n n\u1ee3 b\u1ea1n \u0111\u1ecdc m\u1ed9t L\u1eddi b\u1ea1t<\/em> <\/strong>ch\u01b0a th\u1ec3 vi\u1ebft \u0111\u01b0\u1ee3c h\u00f4m nay. Xin h\u1eb9n l\u1ea1i khi kh\u00e1c.<\/p>\n

 <\/p>\n

L\u1eddi d\u1eabn nh\u1eadp<\/em><\/strong><\/span><\/p>\n

(I)<\/strong><\/span><\/p>\n

Ng\u00e0y 23 th\u00e1ng 7 n\u0103m 2026 t\u1ea1i l\u1ec5 khai m\u1ea1c \u0110\u1ea1i h\u1ed9i To\u00e1n h\u1ecdc Qu\u1ed1c t\u1ebf (ICM, International Congress of Mathematicians) di\u1ec5n ra t\u1ea1i Philadelphia, bang Pennsylvania, Hoa K\u1ef3, Li\u00ean \u0111o\u00e0n To\u00e1n h\u1ecdc Qu\u1ed1c t\u1ebf (IMU, International Mathematical Union) \u0111\u00e3 c\u00f4ng b\u1ed1 b\u1ed1n nh\u00e0 to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c trao Huy ch\u01b0\u01a1ng Fields n\u0103m 2026: Deng Yu, John Pardon, Jacob Tsimerman, and Wang Hong. Hai trong \u0111\u00f3, Deng Yu v\u00e0 Wang Hong, c\u00f3 qu\u1ed1c t\u1ecbch Trung Qu\u1ed1c \u2013 l\u1ea7n \u0111\u1ea7u ti\u00ean. C\u1ea3 hai sinh s\u1ed1ng v\u00e0 l\u00e0m vi\u1ec7c \u1edf Hoa K\u1ef3; ri\u00eang Wang Hong c\u00f2n s\u1ed1ng v\u00e0 l\u00e0m vi\u1ec7c \u1edf Ph\u00e1p, IHES, Institut des Hautes \u00c9tudes Scientifiques (Vi\u1ec7n Nghi\u00ean c\u1ee9u Khoa h\u1ecdc Cao c\u1ea5p). S\u1ef1 ki\u1ec7n c\u00f3 hai nh\u00e0 to\u00e1n h\u1ecdc qu\u1ed1c t\u1ecbch Trung Qu\u1ed1c g\u00e2y s\u1ef1 ch\u00fa \u00fd l\u1edbn trong d\u01b0 lu\u1eadn, v\u00ec n\u00f3 hi\u1ebfm. N\u1ebfu x\u00e1c su\u1ea5t m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c nh\u1eadn gi\u1ea3i Fields, gi\u1ea3 thi\u1ebft 1\/50, t\u1ee9c sau 50 k\u1ef3 ph\u00e1t gi\u1ea3i c\u00f3 m\u1ed9t ng\u01b0\u1eddi qu\u1ed1c t\u1ecbch Trung Qu\u1ed1c, th\u00ec x\u00e1c xu\u1ea5t \u0111\u1ec3 hai ng\u01b0\u1eddi qu\u1ed1c t\u1ecbch Trung Qu\u1ed1c c\u00f9ng l\u00e3nh gi\u1ea3i m\u1ed9t l\u1ea7n l\u00e0 (1\/50)x(1\/50) = 0, 0004, r\u1ea5t nh\u1ecf. V\u1eady m\u00e0 n\u00f3 \u0111\u00e3 x\u1ea3y ra. V\u00e0 \u0111\u00f3 ch\u00ednh l\u00e0 \u0111i\u1ec1u g\u00e2y d\u01b0 lu\u1eadn. N\u01b0\u1edbc M\u1ef9 t\u1ee9c kh\u1eafc tr\u00e0n ng\u1eadp c\u00e1c b\u00e0i b\u00e1o v\u1ec1 s\u1ef1 ki\u1ec7n nh\u01b0 m\u1ed9t tr\u1eadn sao b\u0103ng, \u0111\u1eb7c bi\u1ec7t v\u1ec1 Wang v\u00e0 Deng. Ch\u1ec9 trong hai ng\u00e0y 23\/7 v\u00e0 24\/7 t\u1edd The New York Time<\/em>s \u0111\u0103ng \u0111\u1ebfn 4 b\u00e0i vi\u1ebft, trong \u0111\u00f3 3 b\u00e0i n\u00f3i v\u1ec1 Wang v\u00e0 Deng, b\u00e0i th\u1ee9 t\u01b0 v\u1ec1 c\u1ea3 b\u1ed1n nh\u00e0 \u0111\u01b0\u1ee3c gi\u1ea3i. “Yu Deng d\u1ef1 \u0111o\u00e1n \u0111\u01b0\u1ee3c ho\u1ea1t \u0111\u1ed9ng c\u1ee7a t\u1ed5ng th\u1ec3 (c\u1ee7a h\u1ec7 th\u1ed1ng) d\u1ef1a tr\u00ean nh\u1eefng (ho\u1ea1t \u0111\u1ed9ng c\u1ee7a) th\u00e0nh ph\u1ea7n nh\u1ecf nh\u1ea5t c\u1ee7a n\u00f3”, “M\u1ed9t ng\u00e0y ho\u00e0nh tr\u00e1ng cho To\u00e1n”. “\u00c1nh h\u00e0o quang, s\u1ef1 quy\u1ebfn r\u0169 v\u00e0 m\u1ed9t si\u00eau sao to\u00e1n h\u1ecdc t\u1ea7m c\u1ee1 th\u1ebf gi\u1edbi” l\u00e0 gi\u1eadt t\u00edt c\u1ee7a b\u00e1o The Times Lu\u00e2n \u0111\u00f4n. “\u0110\u1eb7ng V\u0169 (Deng Yu) v\u00e0 V\u01b0\u01a1ng H\u1ed3ng (Wang Hong) l\u00e0 nh\u1eefng ng\u01b0\u1eddi Trung Qu\u1ed1c \u0111\u1ea7u ti\u00ean c\u00f9ng \u0111o\u1ea1t Huy ch\u01b0\u01a1ng Fields; d\u00f9 \u0110\u1eb7ng V\u0169 nh\u1eadn \u0111\u01b0\u1ee3c nhi\u1ec1u l\u1eddi t\u00e1n d\u01b0\u01a1ng \u0111\u1ea7y tr\u00e2n tr\u1ecdng, nh\u01b0ng V\u01b0\u01a1ng H\u1ed3ng m\u1edbi l\u00e0 ng\u01b0\u1eddi \u0111ang tr\u1edf th\u00e0nh t\u00e2m \u0111i\u1ec3m b\u00e0n t\u00e1n c\u1ee7a d\u01b0 lu\u1eadn.” “V\u00e0 trong khi \u0110\u1eb7ng nh\u1eadn \u0111\u01b0\u1ee3c nh\u1eefng l\u1eddi t\u00e1n d\u01b0\u01a1ng \u0111\u1ea7y tr\u00e2n tr\u1ecdng \u2013 th\u1eadm ch\u00ed c\u1ea3 c\u00e1i “vinh d\u1ef1” ch\u1eb3ng m\u1ea5y hay ho l\u00e0 b\u1ecb c\u01a1 quan ki\u1ec3m duy\u1ec7t c\u1ee7a nh\u00e0 n\u01b0\u1edbc Trung qu\u1ed1c “s\u1edd g\u00e1y” \u2013 th\u00ec ch\u00ednh V\u01b0\u01a1ng, 35 tu\u1ed5i, m\u1edbi l\u00e0 ng\u01b0\u1eddi khi\u1ebfn c\u1ea3 Trung Qu\u1ed1c ph\u1ea3i ph\u00e1t cu\u1ed3ng.” C\u00f3 b\u00e1o soi c\u1ea3 c\u00e1c ph\u1ee5 ki\u1ec7n \u0103n m\u1eb7c c\u1ee7a Wang, v\u00e0 c\u00e1c nh\u00e0 s\u1ea3n xu\u1ea5t th\u1eddi trang sau \u0111\u00f3 v\u00e0o cu\u1ed9c \u0111\u1ec3 qu\u1ea3ng b\u00e1 s\u1ea3n ph\u1ea9m.<\/p>\n

Trung Qu\u1ed1c tr\u01b0\u1edbc \u0111\u00f3 \u0111\u00e3 c\u00f3 hai ng\u01b0\u1eddi t\u1eebng \u0111o\u1ea1t Huy ch\u01b0\u01a1ng Fields, l\u00e0 Shing-Tung Yau (Kh\u00e2u Th\u00e0nh \u0110\u1ed3ng, n\u0103m 1982) v\u00e0 Terence Tao (n\u0103m 2006), nh\u01b0ng Shing-Tung Yau\u00a0 ho\u00e0n th\u00e0nh ch\u01b0\u01a1ng tr\u00ecnh gi\u00e1o d\u1ee5c ph\u1ed5 th\u00f4ng v\u00e0 \u0111\u1ea1i h\u1ecdc t\u1ea1i H\u1ed3ng K\u00f4ng, c\u00f2n Terence Tao l\u1edbn l\u00ean t\u1ea1i \u00dac; kh\u00f4ng ai trong h\u1ecd t\u1eebng theo h\u1ecdc trong h\u1ec7 th\u1ed1ng gi\u00e1o d\u1ee5c n\u1ed9i \u0111\u1ecba t\u1ea1i Trung Qu\u1ed1c \u0111\u1ea1i l\u1ee5c. M\u1ed9t ng\u01b0\u1eddi n\u1eefa, thu\u1ed9c l\u1edbp “ti\u1ec1n b\u1ed1i” c\u1ee7a nh\u1eefng t\u00e0i n\u0103ng to\u00e1n h\u1ecdc Trung Qu\u1ed1c l\u00e0 Shiing-Shen Chern (Tr\u1ea7n T\u1ec9nh Th\u00e2n) (1911- 2004). \u00d4ng \u0111\u01b0\u1ee3c m\u1ec7nh danh l\u00e0 “cha \u0111\u1ebb c\u1ee7a h\u00ecnh h\u1ecdc vi ph\u00e2n hi\u1ec7n \u0111\u1ea1i” v\u00e0 \u0111\u01b0\u1ee3c c\u00f4ng nh\u1eadn r\u1ed9ng r\u00e3i l\u00e0 m\u1ed9t nh\u00e0 l\u00e3nh \u0111\u1ea1o trong l\u0129nh v\u1ef1c h\u00ecnh h\u1ecdc c\u0169ng nh\u01b0 l\u00e0 m\u1ed9t trong nh\u1eefng nh\u00e0 to\u00e1n h\u1ecdc v\u0129 \u0111\u1ea1i nh\u1ea5t th\u1ebf k\u1ef7 20. \u00d4ng \u0111\u00e3 gi\u00e0nh \u0111\u01b0\u1ee3c nhi\u1ec1u gi\u1ea3i th\u01b0\u1edfng v\u00e0 s\u1ef1 c\u00f4ng nh\u1eadn, bao g\u1ed3m Gi\u1ea3i Wolf v\u00e0 Gi\u1ea3i Shaw. \u00d4ng t\u1ed1t nghi\u1ec7p th\u1ea1c s\u0129 \u1edf \u0110\u1ea1i h\u1ecdc Thanh Hoa tr\u01b0\u1edbc khi sang ch\u00e2u \u00c2u r\u1ed3i Ph\u00e1p, r\u1ed3i sau \u0111\u00f3 \u0111\u1ebfn Hoa K\u1ef3. Cha c\u1ee7a D\u01b0\u01a1ng Ch\u1ea5n Ninh (Yang Chen-Ning) l\u00e0 D\u01b0\u01a1ng Kh\u1eafc Thu\u1ea7n (Yang Ko-Chuen) \u2013 m\u1ed9t gi\u00e1o s\u01b0 kh\u00e1c t\u1eebng tu nghi\u1ec7p t\u1ea1i Chicago v\u00e0 gi\u1ea3ng d\u1ea1y t\u1ea1i Thanh Hoa nh\u01b0ng chuy\u00ean v\u1ec1 \u0111\u1ea1i s\u1ed1 \u2013 c\u0169ng t\u1eebng d\u1ea1y Chern. \u0110\u1ed3ng th\u1eddi, Chern c\u0169ng l\u00e0 th\u1ea7y d\u1ea1y to\u00e1n b\u1eadc \u0111\u1ea1i h\u1ecdc cho D\u01b0\u01a1ng Ch\u1ea5n Ninh t\u1ea1i Thanh Hoa.<\/p>\n

Wang Hong ch\u1ec9 t\u1ecf ra c\u00f3 n\u0103ng khi\u1ebfu to\u00e1n h\u1ecdc khi gi\u1ea3i \u0111\u01b0\u1ee3c m\u1ed9t b\u00e0i to\u00e1n \u0111\u1ed1 h\u00ecnh h\u1ecdc, tr\u01b0\u1edbc c\u1ea3 b\u1ed1, \u1edf tu\u1ed5i 6. B\u00e0i to\u00e1n n\u00e0y n\u1eb1m trong m\u1ee5c “H\u00e3y c\u00f9ng suy ngh\u0129” trong m\u1ed9t quy\u1ec3n s\u00e1ch gi\u00e1o khoa m\u00e0 c\u00f4 mua \u0111\u1ec3 h\u1ecdc tru\u1edbc: Cho tr\u01b0\u1edbc 7 c\u00e1i c\u00e2y, h\u1ecfi c\u00f3 th\u1ec3 t\u1ea1o ra t\u1ed1i \u0111a bao nhi\u00eau \u0111\u01b0\u1eddng th\u1eb3ng sao cho m\u1ed7i \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua \u0111\u00fang 3 c\u00e1i c\u00e2y? B\u00e0i to\u00e1n n\u00e0y l\u1ea1i thu\u1ed9c lo\u1ea1i h\u00ecnh h\u1ecdc \u0111\u1eb7c th\u00f9 (li\u00ean thu\u1ed9c) c\u00f3 m\u1ed1i li\u00ean h\u1ec7 v\u1edbi b\u00e0i to\u00e1n Kakeya sau n\u00e0y c\u1ee7a c\u00f4. C\u00f4 \u0111\u00e3 v\u00f4 c\u00f9ng th\u00edch th\u00fa v\u00e0 gi\u1ea3i \u0111\u01b0\u1ee3c. (Einstein c\u0169ng t\u1eebng t\u1ef1 t\u1ea1o ra ch\u1ee9ng minh \u0111\u1ecbnh l\u00fd Pythagoras \u1edf tu\u1ed5i 12).<\/p>\n

Wang Hong sinh ra \u1edf thanh ph\u1ed1 Qu\u1ebf L\u00e2m (Guilin), Qu\u1ea3ng T\u00e2y, m\u1ed9t v\u00f9ng \u0111\u1ea5t r\u1ea5t xinh \u0111\u1eb9p. M\u1ed9t c\u00e2u n\u00f3i n\u1ed5i ti\u1ebfng c\u1ee7a Trung Qu\u1ed1c v\u1ec1 phong c\u1ea3nh Qu\u1ebf L\u00e2m l\u00e0: “Phong c\u1ea3nh Qu\u1ebf L\u00e2m \u0111\u1eb9p nh\u1ea5t thi\u00ean h\u1ea1.” Th\u00e0nh ph\u1ed1 n\u00e0y c\u0169ng l\u00e0 n\u01a1i c\u01b0 ng\u1ee5 c\u1ee7a nhi\u1ec1u d\u00e2n t\u1ed9c thi\u1ec3u s\u1ed1. Cha c\u00f4 l\u00e0 ng\u01b0\u1eddi Dao.<\/p>\n

[Tr\u01b0\u1edbc th\u1eddi nh\u00e0 T\u1ea7n, v\u00f9ng Qu\u1ebf L\u00e2m l\u00e0 n\u01a1i sinh s\u1ed1ng c\u1ee7a ng\u01b0\u1eddi B\u00e1ch Vi\u1ec7t. V\u00e0o n\u0103m 314 TCN, m\u1ed9t khu \u0111\u1ecbnh c\u01b0 nh\u1ecf \u0111\u00e3 \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh d\u1ecdc theo b\u1edd s\u00f4ng Ly Giang. H\u1eadu du\u1ec7 c\u1ee7a ng\u01b0\u1eddi B\u00e1ch Vi\u1ec7t c\u1ed5 v\u1eabn sinh s\u1ed1ng t\u1ea1i Qu\u1ebf L\u00e2m v\u00e0 kh\u1eafp v\u00f9ng Qu\u1ea3ng T\u00e2y; ng\u00e0y nay, h\u1ecd ch\u1ee7 y\u1ebfu \u0111\u01b0\u1ee3c \u0111\u1ea1i di\u1ec7n b\u1edfi d\u00e2n t\u1ed9c thi\u1ec3u s\u1ed1 Choang (Zhuang) c\u00f9ng c\u00e1c nh\u00f3m c\u01b0 d\u00e2n b\u1ea3n \u0111\u1ecba kh\u00e1c. Theo c\u00e1c t\u00e0i li\u1ec7u l\u1ecbch s\u1eed khu v\u1ef1c, “ng\u01b0\u1eddi Choang c\u00f3 ngu\u1ed3n g\u1ed1c t\u1eeb ng\u01b0\u1eddi B\u00e1ch Vi\u1ec7t c\u1ed5… v\u1ed1n l\u00e0 nh\u1eefng c\u01b0 d\u00e2n \u0111\u1ea7u ti\u00ean c\u1ee7a v\u00f9ng L\u0129nh Nam”.<\/p>\n

Ng\u00e0y nay, Qu\u1ebf L\u00e2m v\u1eabn c\u00f2n l\u00e0 n\u01a1i sinh s\u1ed1ng c\u1ee7a nhi\u1ec1u nh\u00f3m d\u00e2n t\u1ed9c, ch\u1ee7 y\u1ebfu l\u00e0 ng\u01b0\u1eddi H\u00e1n, ng\u01b0\u1eddi Dao v\u00e0 ng\u01b0\u1eddi Choang, v\u00e0 m\u1ed9t s\u1ed1 kh\u00e1c nh\u01b0 ng\u01b0\u1eddi Mi\u00eau, ng\u01b0\u1eddi \u0110\u1ed9ng v\u00e0 ng\u01b0\u1eddi H\u1ed3i c\u0169ng sinh s\u1ed1ng t\u1ea1i khu v\u1ef1c n\u00e0y, \u0111\u1eb7c bi\u1ec7t l\u00e0 g\u1ea7n c\u00e1c huy\u1ec7n n\u00f4ng th\u00f4n v\u00e0 nh\u1eefng v\u00f9ng c\u00f3 ru\u1ed9ng b\u1eadc thang.]<\/p>\n

N\u0103m 2007, Wang Hong \u2013 khi \u0111\u00f3 m\u1edbi 16 tu\u1ed5i \u2013 \u0111\u00e3 tham gia k\u1ef3 thi tuy\u1ec3n sinh \u0111\u1ea1i h\u1ecdc to\u00e0n qu\u1ed1c (Gaokao, Cao kh\u1ea3o). \u0110i\u1ec3m thi c\u1ee7a c\u00f4 \u0111\u1ea1t 653, m\u1ed9t \u0111i\u1ec3m s\u1ed1 cao.\u00a0 Do \u0111\u01b0\u1ee3c xem thu\u1ed9c nh\u00f3m d\u00e2n t\u1ed9c thi\u1ec3u s\u1ed1 t\u1ea1i Qu\u1ea3ng T\u00e2y, c\u00f4 \u0111\u01b0\u1ee3c c\u1ed9ng th\u00eam 20 \u0111i\u1ec3m \u01b0u ti\u00ean theo ch\u00ednh s\u00e1ch, n\u00e2ng t\u1ed5ng \u0111i\u1ec3m x\u00e9t tuy\u1ec3n \u0111\u1ea1i h\u1ecdc ch\u00ednh th\u1ee9c c\u1ee7a c\u00f4 l\u00ean 673 \u0111i\u1ec3m. Tuy nhi\u00ean c\u00f3 m\u1ed9t sinh vi\u00ean kh\u00e1c c\u00f3 \u0111i\u1ec3m s\u1ed1 v\u01b0\u1ee3t l\u00ean c\u00f4, trong khi quota B\u1eafc \u0110\u1ea1i d\u00e0nh cho Qu\u1ea3ng T\u00e2y ch\u1ec9 l\u00e0 1, n\u00ean c\u00f4 kh\u00f4ng \u0111\u1ea1t nguy\u1ec7n v\u1ecdng, m\u00e0 ph\u1ea3i theo h\u1ecdc ng\u00e0nh Khoa h\u1ecdc \u0111\u1ecba ch\u1ea5t.<\/p>\n

Trong khi \u0111\u00f3, Deng Yu, sinh \u1edf Th\u1ea9m Quy\u1ebfn, ng\u01b0\u1eddi t\u1eebng gi\u00e0nh huy ch\u01b0\u01a1ng v\u00e0ng Olympic To\u00e1n qu\u1ed1c t\u1ebf (IMO) n\u0103m 2006 \u1edf Slovenia, \u0111\u01b0\u1ee3c tuy\u1ec3n th\u1eb3ng v\u00e0o Khoa to\u00e1n B\u1eafc \u0110\u1ea1i. Anh l\u1edbn h\u01a1n Wang Hong hai tu\u1ed5i. Nh\u01b0ng v\u1edbi l\u00f2ng \u0111am m\u00ea to\u00e1n, v\u00e0 n\u1ed7 l\u1ef1c t\u1ed1i \u0111a, c\u00f4 cu\u1ed1i c\u00f9ng \u0111\u01b0\u1ee3c chuy\u1ec3n qua h\u1ecdc Khoa to\u00e1n nh\u01b0 \u00fd nguy\u1ec7n c\u1ee7a c\u00f4. Khoa to\u00e1n c\u1ee7a B\u1eafc \u0110\u1ea1i l\u00e0 r\u1ea5t n\u1ed5i ti\u1ebfng, \u0111\u01b0\u1ee3c tuy\u1ec3n v\u00e0o \u0111\u00f3 l\u00e0 vinh d\u1ef1 l\u1edbn, v\u00e0 c\u00f3 c\u01a1 h\u1ed9i ph\u00e1t tri\u1ec3n t\u1ed1t.<\/p>\n

Hong Wang nh\u1eadn b\u1eb1ng c\u1eed nh\u00e2n to\u00e1n h\u1ecdc t\u1ea1i B\u1eafc \u0110\u1ea1i v\u00e0o n\u0103m 2011. Sau \u0111\u00f3, c\u00f4 chuy\u1ec3n \u0111\u1ebfn Ph\u00e1p, l\u00fac ch\u01b0a bi\u1ebft m\u1ed9t ch\u1eef Ph\u00e1p l\u00e0 g\u00ec, nh\u01b0ng ch\u1ec9 ba n\u0103m sau, c\u00f4 t\u1ed1t nghi\u1ec7p Tr\u01b0\u1eddng B\u00e1ch khoa Paris (\u00c9cole Polytechnique, kh\u00f3a X2010) v\u00e0 nh\u1eadn b\u1eb1ng th\u1ea1c s\u0129 to\u00e1n h\u1ecdc t\u1ea1i \u0110\u1ea1i h\u1ecdc Paris-Saclay v\u00e0o n\u0103m 2014. Con \u0111\u01b0\u1eddng c\u00f4 ng\u00e0y c\u00e0ng m\u1edf r\u1ed9ng t\u1eeb \u0111\u00f3.<\/p>\n

N\u0103m 2014, c\u00f4 \u0111\u01b0\u1ee3c chuy\u1ec3n \u0111\u1ebfn MIT l\u00e0m nghi\u00ean c\u1ee9u sinh ti\u1ebfn s\u0129, d\u01b0\u1edbi s\u1ef1 h\u01b0\u1edbng d\u1eabn c\u1ee7a Larry Guth, ng\u01b0\u1eddi d\u1eabn d\u1eaft r\u1ea5t quan tr\u1ecdng cho s\u1ef1 nghi\u1ec7p c\u00f4, v\u00e0 c\u00f4 \u0111\u00e3 ho\u00e0n th\u00e0nh lu\u1eadn \u00e1n ti\u1ebfn s\u0129 (c\u00f3 t\u1ef1a \u0111\u1ec1 “A restriction estimate in R\u00b3\u201d) n\u0103m 2019. \u1ede \u0111\u00e2y, c\u00f4 b\u1eaft \u0111\u1ea7u nghi\u00ean c\u1ee9u c\u00e1c b\u00e0i to\u00e1n thu\u1ed9c l\u0129nh v\u1ef1c gi\u1ea3i t\u00edch Fourier.<\/p>\n

T\u1eeb 2019 \u0111\u1ebfn 2021, Wang Hong l\u00e0m vi\u1ec7c t\u1ea1i Princeton v\u1edbi t\u01b0 c\u00e1ch l\u00e0 nghi\u00ean c\u1ee9u sinh sau ti\u1ebfn s\u0129 t\u1ea1i Vi\u1ec7n Nghi\u00ean c\u1ee9u Cao c\u1ea5p (Institute for Advanced Study). L\u0129nh v\u1ef1c tr\u1ecdng t\u00e2m: “Gi\u1ea3i t\u00edch Fourier v\u00e0 c\u00e1c m\u1ed1i li\u00ean h\u1ec7 v\u1edbi c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc”.<\/p>\n

Th\u00e1ng 7 n\u0103m 2021, Wang Hong chuy\u1ec3n \u0111\u1ebfn \u0110\u1ea1i h\u1ecdc California, Los Angeles (UCLA), \u0111\u1ea3m nhi\u1ec7m v\u1ecb tr\u00ed Gi\u00e1o s\u01b0 h\u1ed7 tr\u1ee3 t\u1ea1i Khoa To\u00e1n h\u1ecdc c\u1ee7a UCLA. C\u00f4 l\u00e0m vi\u1ec7c \u0111\u00fang hai n\u0103m, t\u1eeb 2021 \u0111\u1ebfn 2023, tr\u01b0\u1edbc khi chuy\u1ec3n sang \u0110\u1ea1i h\u1ecdc New York (NYU).<\/p>\n

Sau khi ho\u00e0n th\u00e0nh ch\u01b0\u01a1ng tr\u00ecnh nghi\u00ean c\u1ee9u sau ti\u1ebfn s\u0129 t\u1ea1i Vi\u1ec7n Nghi\u00ean c\u1ee9u Cao c\u1ea5p (Institute for Advanced Study) \u1edf Princeton, c\u00f4 tr\u1edf th\u00e0nh Gi\u00e1o s\u01b0 Tr\u1ee3 l\u00fd t\u1ea1i UCLA v\u00e0o n\u0103m 2021. N\u0103m 2023 c\u00f4 gia nh\u1eadp Vi\u1ec7n Courant c\u1ee7a NYU.<\/p>\n

N\u0103m 2022, Wang Hong \u0111\u00e3 \u0111\u01b0\u1ee3c trao Gi\u1ea3i th\u01b0\u1edfng Maryam Mirzakhani New Frontiers nh\u1edd nh\u1eefng “ti\u1ebfn b\u1ed9 trong c\u00e1c b\u00e0i to\u00e1n: gi\u1ea3 thuy\u1ebft h\u1ea1n ch\u1ebf (Fourier restriction conjecture, l\u00fac c\u00f4 l\u00e0m lu\u1eadn \u00e1n ti\u1ebfn s\u0129), gi\u1ea3 thuy\u1ebft l\u00e0m tr\u01a1n c\u1ee5c b\u1ed9 (local smoothing conjecture, th\u1ef1c hi\u1ec7n v\u1edbi Larry Guth v\u00e0 Ruixiang Zhang n\u0103m 2019), v\u00e0 c\u00e1c v\u1ea5n \u0111\u1ec1 li\u00ean quan.” T\u1eeb \u0111\u00f3, v\u00e0 nh\u1ea5t l\u00e0 sau khi c\u00f4 v\u00e0 nh\u00e0 to\u00e1n h\u1ecdc Josua Zahl gi\u1ea3i \u0111\u01b0\u1ee3c b\u00e0i to\u00e1n Kakeya ba chi\u1ec1u, c\u00f4 nh\u1eadn \u0111\u01b0\u1ee3c lo\u1ea1t ph\u1ea7n th\u01b0\u1edfng danh gi\u00e1:<\/p>\n

Frontier of Science Award (2023, 2025)<\/em><\/p>\n

Antonio Ambrosetti Medal (2025)<\/em><\/p>\n

Ostrowski Prize (2025)<\/em><\/p>\n

Salem Prize (2025)<\/em><\/p>\n

International Congress of Chinese Mathematicians Gold Medal of Mathematics (2025)<\/em><\/p>\n

Association for Women in Mathematics Sadosky Research Prize in Analysis (2026)<\/em><\/p>\n

New Horizons in Mathematics Prize (2026)<\/em><\/p>\n

Clay Research Award (2026)<\/em><\/p>\n

Th\u00e0nh t\u1ef1u c\u1ed1t l\u00f5i \u0111\u01b0a c\u00f4 \u0111\u1ebfn b\u1ee5c vinh quang l\u00e0 b\u00e0i nghi\u00ean c\u1ee9u d\u00e0i 127 trang do c\u00f4 \u0111\u1ed3ng t\u00e1c gi\u1ea3 c\u00f9ng Gi\u00e1o s\u01b0 Joshua Zahl thu\u1ed9c \u0110\u1ea1i h\u1ecdc British Columbia (Canada), \u0111\u01b0\u1ee3c c\u00f4ng b\u1ed1 v\u00e0o th\u00e1ng 2 n\u0103m 2025 v\u1edbi ti\u00eau \u0111\u1ec1: “A Rigorous Proof of the 3-D Kakeya Conjecture” (Ch\u1ee9ng minh ch\u1eb7t ch\u1ebd v\u1ec1 Gi\u1ea3 thuy\u1ebft Kakeya trong kh\u00f4ng gian 3 chi\u1ec1u). \u00d4ng Emmanuel Ullmo, Gi\u00e1m \u0111\u1ed1c Vi\u1ec7n Nghi\u00ean c\u1ee9u Khoa h\u1ecdc Cao c\u1ea5p (IHES), nh\u1eadn \u0111\u1ecbnh r\u1eb1ng \u0111\u00e2y l\u00e0 m\u1ed9t k\u1ebft qu\u1ea3 mang \u00fd ngh\u0129a quan tr\u1ecdng, \u0111\u1ee7 s\u1ee9c \u0111\u1ecbnh h\u00ecnh l\u1ea1i c\u1ee5c di\u1ec7n c\u1ee7a to\u00e0n b\u1ed9 l\u0129nh v\u1ef1c nghi\u00ean c\u1ee9u n\u00e0y.<\/p>\n

(II)<\/strong><\/span><\/p>\n

Gi\u1ea3 thuy\u1ebft Kakeya (1917)<\/strong><\/span><\/h3>\n

 <\/p>\n

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Wang Hong \u0111ang thuy\u1ebft gi\u1ea3ng t\u1ea1i H\u1ed9i ngh\u1ecb Modern Trends in Fourier Analysis<\/em>\u00a0\u1edf\u00a0Centre de Recerca Matem\u00e0tica, 2025<\/p>\n

Gi\u1ea3 thuy\u1ebft Kakeya b\u1eaft ngu\u1ed3n t\u1eeb m\u1ed9t c\u00e2u h\u1ecfi do nh\u00e0 to\u00e1n h\u1ecdc Nh\u1eadt B\u1ea3n S\u014dichi Kakeya \u0111\u1eb7t ra v\u00e0o n\u0103m 1917: li\u1ec7u m\u1ed9t chi\u1ebfc kim (hay \u0111o\u1ea1n th\u1eb3ng) c\u00f3 th\u1ec3 xoay theo m\u1ecdi h\u01b0\u1edbng \u0111\u1ec3 qu\u00e9t qua m\u1ed9t v\u00f9ng kh\u00f4ng gian c\u00f3 th\u1ec3 t\u00edch nh\u1ecf t\u00f9y \u00fd hay kh\u00f4ng? Gi\u1ea3 thuy\u1ebft Kakeya trong m\u1eb7t ph\u1eb3ng kh\u00f4ng qu\u00e1 kh\u00f3. V\u00e0o nh\u1eefng n\u0103m 1970, Davies v\u00e0 sau \u0111\u00f3 l\u00e0 C\u00f3rdoba \u0111\u00e3 \u0111\u01b0a ra hai ch\u1ee9ng minh r\u1ea5t kh\u00e1c nhau cho th\u1ea5y m\u1ecdi t\u1eadp Kakeya ph\u1eb3ng \u0111\u1ec1u c\u00f3 s\u1ed1 chi\u1ec1u b\u1eb1ng 2. B\u00e0i to\u00e1n trong kh\u00f4ng gian ba chi\u1ec1u tuy nhi\u00ean kh\u00f3 h\u01a1n nhi\u1ec1u.<\/p>\n

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S\u014dichi Kakeya (1886 \u2013 1947), ng\u01b0\u1eddi \u0111\u01b0a ra gi\u1ea3 thuy\u1ebft l\u00fac m\u1edbi 31 tu\u1ed5i. Nh\u1eadt B\u1ea3n l\u00e0 qu\u1ed1c gia ngo\u00e0i ph\u01b0\u01a1ng T\u00e2y c\u00f3 nhi\u1ec1u \u0111\u00f3ng g\u00f3p quan tr\u1ecdng cho to\u00e1n h\u1ecdc hi\u1ec7n \u0111\u1ea1i.Xem th\u00eam: https:\/\/rosetta.vn\/nguyenxuanxanh\/yutaka-taniyama-va-thoi-dai-cua-anh\/.<\/p>\n

Trong su\u1ed1t 50 n\u0103m qua, nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 nghi\u00ean c\u1ee9u Gi\u1ea3 thuy\u1ebft Kakeya trong kh\u00f4ng gian ba chi\u1ec1u (v\u00e0 c\u1ea3 c\u00e1c chi\u1ec1u l\u1edbn h\u01a1n). Qua nh\u1eefng n\u1ed7 l\u1ef1c \u0111\u00f3, ng\u01b0\u1eddi ta \u0111\u00e3 ph\u00e1t hi\u1ec7n ra nh\u1eefng m\u1ed1i li\u00ean h\u1ec7 s\u00e2u s\u1eafc gi\u1eefa b\u00e0i to\u00e1n n\u00e0y v\u1edbi c\u00e1c v\u1ea5n \u0111\u1ec1 thu\u1ed9c l\u0129nh v\u1ef1c ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ea1o h\u00e0m ri\u00eang (PDE), t\u1ed5 h\u1ee3p s\u1ed1 h\u1ecdc, l\u00fd thuy\u1ebft s\u1ed1, v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c. C\u00e1c k\u1ebft qu\u1ea3 t\u1eebng ph\u1ea7n v\u1ec1 Gi\u1ea3 thuy\u1ebft Kakeya \u0111\u00e3 d\u1eabn \u0111\u1ebfn nh\u1eefng b\u01b0\u1edbc \u0111\u1ed9t ph\u00e1 ngo\u1ea1n m\u1ee5c trong vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n kh\u00e1c. M\u1ed9t v\u00ed d\u1ee5 \u0111\u1eb7c bi\u1ec7t \u1ea5n t\u01b0\u1ee3ng l\u00e0 l\u00fd thuy\u1ebft Kakeya \u0111a tuy\u1ebfn t\u00ednh c\u1ee7a Bennett, Carbery v\u00e0 Tao \u0111\u00e3 d\u1eabn \u0111\u1ebfn vi\u1ec7c gi\u1ea3i quy\u1ebft gi\u1ea3 thuy\u1ebft ch\u00ednh t\u1ed3n t\u1ea1i t\u1eeb l\u00e2u trong \u0111\u1ecbnh l\u00fd gi\u00e1 tr\u1ecb trung b\u00ecnh Vinogradov thu\u1ed9c l\u0129nh v\u1ef1c l\u00fd thuy\u1ebft s\u1ed1 gi\u1ea3i t\u00edch.<\/p>\n

Th\u1ea7y c\u1ee7a Wang, Larry Guth nh\u1edb l\u1ea1i: \u201cKhi c\u00f2n l\u00e0 m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb v\u00e0 b\u1eaft \u0111\u1ea7u h\u1ee9ng th\u00fa v\u1edbi b\u00e0i to\u00e1n Kakeya, t\u00f4i th\u1ea5y n\u00f3 c\u00f3 v\u1ebb \u0111\u01a1n gi\u1ea3n v\u00e0 mang t\u00ednh h\u00ecnh h\u1ecdc \u0111\u1ebfn m\u1ee9c t\u00f4i th\u1ef1c s\u1ef1 ng\u1ea1c nhi\u00ean khi bi\u1ebft n\u00f3 l\u1ea1i kh\u00f3 gi\u1ea3i quy\u1ebft \u0111\u1ebfn v\u1eady.” Nhi\u1ec1u n\u0103m sau, Wang \u2013 nghi\u00ean c\u1ee9u sinh c\u1ee7a \u00f4ng \u2013 c\u0169ng b\u1ecb thu h\u00fat b\u1edfi ch\u00ednh s\u1ef1 \u0111\u01a1n gi\u1ea3n \u0111\u1ea7y \u0111\u00e1nh l\u1eeba \u1ea5y. \u201cB\u1ea1n c\u00f3 th\u1ec3 h\u00ecnh dung c\u1ee5 th\u1ec3 v\u1ec1 c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng trong b\u00e0i to\u00e1n n\u00e0y. N\u00f3 kh\u00f4ng qu\u00e1 \u0111\u00e1ng s\u1ee3 nh\u01b0 c\u00e1c l\u00fd thuy\u1ebft to\u00e1n h\u1ecdc kh\u00e1c,\u201d Wang n\u00f3i. Nh\u01b0ng \u201cT\u00f4i ch\u1ec9 mu\u1ed1n hi\u1ec3u t\u1ea1i sao n\u00f3 l\u1ea1i kh\u00f3 \u0111\u1ebfn th\u1ebf.\u201d<\/p>\n

\"\"<\/p>\n

Joshua Zahl, nh\u00e0 to\u00e1n h\u1ecdc t\u1ea1i \u0110\u1ea1i h\u1ecdc British Columbia (Canada), \u0111\u1ed3ng t\u00e1c gi\u1ea3 c\u1ee7a ch\u1ee9ng minh. (Paul Joseph)<\/p>\n

N\u0103m 2025, Wang Hong v\u00e0 Josua Zahl cu\u1ed1i c\u00f9ng \u0111\u1ea1t \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 \u0111\u1ed9t ph\u00e1 v\u00e0 t\u1ea7m c\u1ee1 sau khi \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng trong kh\u00f4ng gian ba chi\u1ec1u, b\u1ea5t k\u1ef3 t\u1eadp h\u1ee3p Kakeya n\u00e0o nh\u01b0 v\u1eady c\u0169ng ph\u1ea3i c\u00f3 s\u1ed1 chi\u1ec1u Hausdorff v\u00e0 s\u1ed1 chi\u1ec1u Minkowski \u0111\u00fang b\u1eb1ng 3. N\u00f3i c\u00e1ch kh\u00e1c: t\u1eadp h\u1ee3p \u0111\u00f3 c\u00f3 th\u1ec3 m\u1ecfng, nh\u01b0ng kh\u00f4ng th\u1ec3 nh\u1ecf b\u00e9 v\u1ec1 m\u1eb7t th\u1ec3 t\u00edch. Ch\u00fang ta c\u00f3 th\u1ec3 ph\u00e1t bi\u1ec3u:<\/p>\n

\u0110\u1ecbnh l\u00fd. B\u1ea5t c\u1ee9 t\u1eadp h\u1ee3p Kakeya K\u2286\u211d\u00b3<\/span> \u0111\u1ec1u c\u00f3 th\u1ee9 nguy\u00ean 3.\u00a0<\/strong><\/p>\n

Th\u1ee9 nguy\u00ean <\/i>(dimensions) \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 s\u1ed1 chi\u1ec1u Minkowski ho\u1eb7c s\u1ed1 chi\u1ec1u Hausdorff.<\/p>\n

C\u00f4ng tr\u00ecnh c\u1ee7a Wang – Zahl ph\u1ea3n \u00e1nh m\u1ed9t s\u1ef1 chuy\u1ec3n d\u1ecbch r\u1ed9ng h\u01a1n trong l\u0129nh v\u1ef1c gi\u1ea3i t\u00edch \u0111i\u1ec1u h\u00f2a, k\u1ebft h\u1ee3p s\u1ef1 am hi\u1ec3u s\u00e2u s\u1eafc v\u1ec1 h\u00ecnh h\u1ecdc v\u1edbi c\u00e1c c\u00f4ng c\u1ee5 gi\u1ea3i t\u00edch m\u1ea1nh m\u1ebd. Nets Katz, chuy\u00ean gia t\u1eadp h\u1ee3p Kakeya t\u1ea1i \u0110\u1ea1i h\u1ecdc Rice, nh\u1eadn \u0111\u1ecbnh, l\u1eddi gi\u1ea3i cho gi\u1ea3 thuy\u1ebft Kakeya l\u00e0 m\u1ed9t th\u00e0nh t\u1ef1u hi\u1ebfm c\u00f3 trong th\u1ebf k\u1ef7, v\u00e0 Wang \u0111\u00e3 \u0111\u00f3ng vai tr\u00f2 then ch\u1ed1t trong th\u00e0nh t\u1ef1u \u0111\u00f3. \u201cT\u00f4i th\u1ef1c s\u1ef1 tin r\u1eb1ng t\u1eeb \u0111\u00e2y s\u1ebd n\u1ea3y sinh m\u1ed9t kh\u1ed1i l\u01b0\u1ee3ng \u00fd t\u01b0\u1edfng \u0111\u1ee7 l\u1edbn \u0111\u1ec3 t\u1ea1o ra cu\u1ed9c c\u00e1ch m\u1ea1ng cho to\u00e0n b\u1ed9 l\u0129nh v\u1ef1c n\u00e0y,\u201d Jonathan Hickman nh\u00e0 to\u00e1n h\u1ecdc \u1edf \u0110\u1ea1i h\u1ecdc Edinburgh, nh\u1eadn \u0111\u1ecbnh. \u201c\u0110\u00e2y th\u1ef1c s\u1ef1 l\u00e0 m\u1ed9t giai \u0111o\u1ea1n v\u00f4 c\u00f9ng th\u00fa v\u1ecb.\u201d<\/p>\n

Xem th\u00eam t\u01b0 li\u1ec7u:<\/p>\n

    \n
  1. \n

    Kakeya set: https:\/\/en.wikipedia.org\/wiki\/Kakeya_set\u00a0<\/span><\/span><\/p>\n<\/li>\n

  2. The Kakeya Conjecture: where does it come from and why is it important?: https:\/\/arxiv.org\/html\/2512.09842v1<\/li>\n
  3. \n

    New Proof Threads the Needle on a Sticky Geometry Problem: https:\/\/www.quantamagazine.org\/new-proof-threads-the-needle-on-a-sticky-geometry-problem-20230711\/<\/p>\n<\/li>\n

  4. \n

    \u2018Once in a Century\u2019 Proof Settles Math\u2019s Kakeya Conjecture: https:\/\/www.quantamagazine.org\/once-in-a-century-proof-settles-maths-kakeya-conjecture-20250314\/<\/p>\n<\/li>\n<\/ol>\n

    (III)<\/strong><\/span><\/p>\n

    Qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y c\u1ee7a n\u1eef t\u00e1c gi\u1ea3 Natalie Wolchover, t\u1ea1p ch\u00ed Quanta Magazine, ch\u00fang ta c\u00f3 th\u1ec3 theo d\u00f5i s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a V\u01b0\u01a1ng H\u1ed3ng t\u1eeb con ng\u01b0\u1eddi t\u01b0\u01a1ng \u0111\u1ed1i b\u00ecnh th\u01b0\u1eddng \u0111\u1ebfn l\u00fac c\u00f4 tr\u1edf th\u00e0nh \u201cthi\u00ean t\u00e0i to\u00e1n h\u1ecdc\u201d \u2013 m\u1ed9t c\u00e1ch t\u1ef1 nhi\u00ean. T\u1eeb th\u1eddi trung h\u1ecdc, c\u00f4 kh\u00f4ng n\u1eb1m trong danh s\u00e1ch c\u00e1c trung t\u00e2m luy\u1ec7n thi Olympic, c\u00f3 l\u1ebd v\u00ec b\u1ed1 m\u1eb9 c\u00f4 mong mu\u1ed1n c\u00f4 c\u00f3 m\u1ed9t \u201ccu\u1ed9c s\u1ed1ng v\u00e0 ph\u00e1t tri\u1ec3n b\u00ecnh th\u01b0\u1eddng\u201d. Cha m\u1eb9 c\u00f4 kh\u00f4ng bao gi\u1edd g\u00e2y \u00e1p l\u1ef1c h\u1ecdc t\u1eadp qu\u00e1 m\u1ee9c l\u00ean c\u00f4. Sau gi\u1edd h\u1ecdc, Hong Wang th\u01b0\u1eddng \u0111\u1ecdc th\u1ea7n tho\u1ea1i Hy L\u1ea1p, Harry Potter v\u00e0 Ch\u00faa t\u1ec3 nh\u1eefng chi\u1ebfc nh\u1eabn, ch\u01a1i b\u00f3ng b\u00e0n v\u00e0 c\u1ea7u l\u00f4ng; c\u00f2n v\u00e0o bu\u1ed5i t\u1ed1i, c\u1ea3 gia \u0111\u00ecnh th\u01b0\u1eddng c\u00f9ng nhau \u0111i d\u1ea1o gi\u1eefa khung c\u1ea3nh n\u00fai \u0111\u00e1 v\u00f4i \u0111\u1eb7c tr\u01b0ng c\u1ee7a Qu\u1ebf L\u00e2m.<\/p>\n

    Nh\u1eefng cu\u1ed9c \u0111i d\u1ea1o \u0111\u01b0\u1ee3c ti\u1ebfp t\u1ee5c trong \u0111\u1eddi c\u00f4 l\u00e0 nh\u1eefng gi\u1edd ph\u00fat gi\u1ea3i stress, l\u00e0m cho \u0111\u1ea7u \u00f3c c\u00f4 tho\u00e1ng \u0111\u1ea1t, t\u1eadp trung n\u0103ng l\u01b0\u1ee3ng m\u1edbi, v\u00e0 m\u00e0i d\u0169a c\u00e1i nh\u00ecn. N\u00f3 c\u00f3 c\u00e1c d\u1ee5ng nh\u01b0 m\u1ed9t c\u1eed thi\u1ec1n.<\/p>\n

    \u0110am m\u00ea to\u00e1n h\u1ecdc \u0111\u00e3 thu h\u00fat c\u00f4 ra kh\u1ecfi th\u1ebf gi\u1edbi th\u1ebf t\u1ee5c tr\u01b0\u1edbc m\u1eb7t c\u1ee7a ng\u01b0\u1eddi ph\u00e0m \u0111\u1ec3 s\u1ed1ng trong th\u1ebf gi\u1edbi tr\u1ea7m t\u01b0 v\u1ec1 nh\u1eefng v\u1ea5n \u0111\u1ec1 to\u00e1n h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng. C\u00f4 \u0111\u01b0\u1ee3c bi\u1ebft c\u00f3 \u00edch th\u00fa vui c\u1ee7a ng\u01b0\u1eddi th\u1ebf gian. Th\u00fa vui c\u1ee7a c\u00f4 l\u00e0 t\u01b0\u01a1ng t\u00e1c v\u1edbi v\u00e0 tr\u1ea7m t\u01b0 v\u1ec1 nh\u1eefng \u0111\u1ed1i t\u01b0\u1ee3ng to\u00e1n h\u1ecdc. Cogito ergo sum<\/em>. S\u1ee9c m\u1ea1nh c\u1ee7a tr\u1ea7m t\u01b0 \u0111\u00e3 l\u00e0m cho nh\u1eefng l\u1edbp che ch\u1eafn t\u1ea7m nh\u00ecn l\u1ea7n l\u01b0\u1ee3c s\u1ee5p \u0111\u1ed5, m\u1edf ra nh\u1eefng c\u00e1nh c\u1eeda m\u1edbi c\u1ee7a \u00e1nh s\u00e1ng. S\u1ef1 b\u1ec1n ch\u00ed, \u00f3c t\u01b0\u1edfng t\u01b0\u1ee3ng m\u1ea1nh m\u1ebd v\u00e0 s\u1ef1 l\u00e0m ch\u1ee7 c\u00e1c k\u1ef9 thu\u1eadt to\u00e1n m\u1edbi m\u1ebb ph\u1ee9c t\u1ea1p, \u0111\u00e3 thay \u0111\u1ed5i t\u1ea5t c\u1ea3. C\u00f4 kh\u00f4ng m\u00e0n ai \u0111\u00f3 nhanh h\u01a1n c\u00f4, kh\u00f4ng sao, c\u00f4 n\u00f3i, “it doesn’t matter”. C\u00f4 kh\u00f4ng ch\u1ea1y \u0111ua v\u1edbi ng\u01b0\u1eddi kh\u00e1c. Tinh th\u1ea7n n\u00e0y gi\u1ed1ng tinh th\u1ea7n c\u1ee7a Albert Einstein.<\/p>\n

    \u0110\u1ecdc b\u00e0i vi\u1ebft c\u1ee7a Natalie Wolchover ta c\u00f3 th\u1ec3 th\u1ea5y, n\u1ec1n to\u00e1n h\u1ecdc ph\u01b0\u01a1ng T\u00e2y v\u1eabn c\u00f2n c\u1ef1c k\u1ef3 m\u1ea1nh m\u1ebd v\u00e0 s\u00f4i \u0111\u1ed9ng t\u1ea1i c\u00e1c trung t\u00e2m \u0111\u1ea1i h\u1ecdc v\u00e0 vi\u1ec7n nghi\u00ean c\u1ee9u. Wang nh\u1ea5n m\u1ea1nh gi\u00e1 tr\u1ecb c\u1ee7a nh\u1eefng d\u1ecbp g\u1eb7p g\u1ee1 t\u1ea1i c\u00e1c h\u1ed9i ngh\u1ecb. “B\u1ea1n n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c nh\u1eefng g\u00ec \u0111ang di\u1ec5n ra trong l\u0129nh v\u1ef1c n\u00e0y, c\u00f3 nh\u1eefng cu\u1ed9c tr\u00f2 chuy\u1ec7n ng\u1eabu h\u1ee9ng v\u00e0 g\u1eb7p g\u1ee1 c\u00e1c c\u1ed9ng s\u1ef1 ti\u1ec1m n\u0103ng; \u0111\u00f3 l\u00e0 m\u1ed9t ph\u1ea7n c\u1ed1t y\u1ebfu c\u1ee7a c\u00f4ng vi\u1ec7c nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc,” c\u00f4 chia s\u1ebb. “Nh\u1eefng kho\u1ea3nh kh\u1eafc nh\u01b0 th\u1ebf n\u00e0y kh\u00f4ng bao gi\u1edd l\u00e0 th\u00e0nh qu\u1ea3 c\u1ee7a ri\u00eang m\u1ed9t c\u00e1 nh\u00e2n. Ch\u00fang l\u00e0 k\u1ebft tinh c\u1ee7a nhi\u1ec1u n\u0103m g\u1eb7p g\u1ee1 t\u00ecnh c\u1edd v\u00e0 nh\u1eefng c\u00e2u h\u1ecfi b\u1ea5t ng\u1edd \u0111\u00e3 d\u1eabn l\u1ed1i ta \u0111i \u0111\u00fang h\u01b0\u1edbng. T\u00f4i v\u00f4 c\u00f9ng may m\u1eafn khi \u0111\u01b0\u1ee3c s\u00e1t c\u00e1nh c\u00f9ng nh\u1eefng \u0111\u1ed3ng nghi\u1ec7p xu\u1ea5t s\u1eafc trong su\u1ed1t ch\u1eb7ng \u0111\u01b0\u1eddng s\u1ef1 nghi\u1ec7p c\u1ee7a m\u00ecnh, v\u00e0 vinh d\u1ef1 n\u00e0y thu\u1ed9c v\u1ec1 h\u1ecd c\u0169ng nhi\u1ec1u nh\u01b0 thu\u1ed9c v\u1ec1 t\u00f4i s\u1ef1 t\u1ed5ng h\u1ee3p c\u1ee7a bao cu\u1ed9c g\u1eb7p g\u1ee1, h\u1ecdc h\u1ecfi t\u1eeb b\u1ea1n b\u00e8.” M\u1ed9t th\u00e1i \u0111\u1ed9 r\u1ea5t khi\u00eam nh\u01b0\u1eddng v\u00e0 bi\u1ebft \u01a1n. D\u0129 nhi\u00ean, c\u00e1c tr\u01b0\u1eddng, vi\u1ec7n m\u00e0 Wang v\u00e0 Deng \u0111\u00e3 \u0111i qua, c\u0169ng \u0111\u1ec1u h\u1ebft s\u1ee9c h\u00e3nh di\u1ec7n v\u1ec1 s\u1ef1 \u0111\u00f3ng g\u00f3p c\u1ee7a h\u1ecd.<\/p>\n

    Ph\u01b0\u01a1ng T\u00e2y kh\u00f4ng nh\u1eefng v\u1eabn l\u00e0 trung t\u00e2m h\u1ecdc thu\u1eadt th\u1ebf gi\u1edbi, m\u00e0 c\u00f2n l\u00e0 m\u00f4i tr\u01b0\u1eddng nu\u00f4i d\u01b0\u1ee1ng v\u00e0 ph\u00e1t tri\u1ec3n t\u00e0i n\u0103ng t\u1ed1t nh\u1ea5t, v\u1ec1 v\u1eadt ch\u1ea5t l\u1eabn tinh th\u1ea7n, v\u1ec1 t\u1ef1 do t\u01b0 bi\u1ec7n nh\u01b0 m\u1ed9t m\u1ea1ng l\u01b0\u1edbi vi\u1ec7n h\u00e0n l\u00e2m Plato kh\u1ed5ng l\u1ed3. C\u00f3 nhi\u1ec1u ng\u01b0\u1eddi h\u1ecfi: N\u1ebfu nh\u1eefng t\u00e0i n\u0103ng nh\u01b0 Wang Hong v\u00e0 Deng Yu, ti\u1ebfp t\u1ee5c \u1edf l\u1ea1i nghi\u00ean c\u1ee9u t\u1ea1i Trung Qu\u1ed1c, th\u00ec h\u1ecd c\u00f3 c\u01a1 may ph\u00e1t huy t\u00e0i n\u0103ng r\u1ef1c r\u1ee1 \u0111\u1ec3 \u0111\u01b0\u1ee3c trao gi\u1ea3i Fields hay kh\u00f4ng? Shing-Tung Yau t\u1eebng n\u1ed7 l\u1ef1c h\u1ebft s\u1ee9c \u0111\u1ec3 n\u00e2ng cao n\u0103ng l\u1ef1c s\u00e1ng t\u1ea1o c\u1ee7a c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c trong n\u01b0\u1edbc, nh\u01b0ng \u0111\u1ebfn nay ch\u01b0a th\u00e0nh c\u00f4ng m\u1ea5y. C\u1ea3 hai, Yang Hong v\u00e0 Deng Yu, trong nh\u1eefng ph\u00e1t bi\u1ec3u c\u1ee7a m\u00ecnh trong l\u1ec5 trao gi\u1ea3i, nh\u01b0 ng\u01b0\u1eddi ta ghi nh\u1eadn, \u0111\u1ec1u kh\u00f4ng nh\u1eafc t\u1edbi B\u1eafc \u0110\u1ea1i. C\u00f3 l\u1ebd h\u1ecd t\u1ef1 c\u1ea3m nh\u1eadn s\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa h\u1ecdc thu\u1eadt Trung Qu\u1ed1c v\u00e0 ph\u01b0\u01a1ng T\u00e2y th\u1eadt h\u1ebft s\u1ee9c to l\u1edbn l\u00e0m cho tr\u1ecdng t\u00e2m c\u1ee7a s\u1ef1 ph\u00e1t tri\u1ec3n \u0111\u1ed1i v\u1edbi h\u1ecd h\u1ea7u nh\u01b0 ho\u00e0n to\u00e0n n\u1eb1m t\u1ea1i c\u00e1c tr\u01b0\u1eddng, vi\u1ec7n ph\u01b0\u01a1ng T\u00e2y. M\u1ea1ng l\u01b0\u1edbi \u0111\u00f3 c\u00f3 nhi\u1ec1u b\u1eadc th\u1ea7y d\u1eabn d\u1eaft, \u0111\u1ed3ng nghi\u1ec7p h\u1ecdc thu\u1eadt \u0111\u1ec3 t\u01b0\u01a1ng t\u00e1c, c\u1ed9ng t\u00e1c, nh\u00e0 nghi\u00ean c\u1ee9u h\u01b0\u1edfng \u0111\u01b0\u1ee3c m\u1ed9t ch\u1ebf \u0111\u1ed9 qu\u1ea3n tr\u1ecb h\u1ebft s\u1ee9c c\u1edfi m\u1edf trong khoa h\u1ecdc, \u0111\u01b0\u1ee3c h\u1ed7 tr\u1ee3 b\u1edfi c\u00e1c qu\u1ef9 t\u01b0 nh\u00e2n nh\u00e2n \u00e1i, cu\u1ed9c s\u1ed1ng \u0111\u01b0\u1ee3c ho\u00e0n to\u00e0n b\u1ea3o \u0111\u1ea3m. Con ng\u01b0\u1eddi \u1edf \u0111\u00f3 \u0111\u01b0\u1ee3c trao quy\u1ec1n t\u1ef1 do, v\u00e0 \u0111\u01b0\u1ee3c tin t\u01b0\u1edfng. M\u1ed9t n\u1ec1n h\u1ecdc thu\u1eadt mu\u1ed1n ph\u00e1t \u0111\u1ea1i c\u1ea7n c\u00f3 \u0111i\u1ec1u ki\u1ec7n cu\u1ed9c s\u1ed1ng \u0111\u01b0\u1ee3c b\u1ea3o \u0111\u1ea3m, l\u00e0 n\u01a1i giao l\u01b0u c\u1ee7a nhi\u1ec1u lu\u1ed3ng v\u0103n h\u00f3a th\u1ebf gi\u1edbi, v\u00e0 nh\u1ea5t l\u00e0 c\u00f3 \u0111\u1ea7y \u0111\u1ee7 t\u1ef1 do h\u1ecdc thu\u1eadt. \u0110\u00f3 ch\u00ednh l\u00e0 nh\u1eefng \u0111i\u1ec1u ki\u1ec7n m\u00e0 Melitus \u1edf v\u00f9ng \u0111\u1ea5t Ionia c\u1ee7a Hy L\u1ea1p \u0111\u00e3 t\u1eebng c\u00f3 \u0111\u1ec3 ph\u00e1t tri\u1ec3n h\u1ecdc thu\u1eadt \u0111\u1ea7u ti\u00ean c\u1ee7a th\u1ebf gi\u1edbi hai ngh\u00ecn s\u00e1u tr\u0103m n\u0103m tr\u01b0\u1edbc. Ch\u00e2u \u1eacu \u0111\u00e3 lu\u00f4n lu\u00f4n h\u1ed9i \u0111\u1ee7 nh\u1eefng y\u1ebfu t\u1ed1 \u0111\u00f3 trong su\u1ed1t s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a m\u00ecnh.<\/p>\n

    Tuy th\u1ebf, m\u00f4i tr\u01b0\u1eddng ph\u01b0\u01a1ng T\u00e2y kh\u00f4ng ph\u1ea3i ho\u00e0n to\u00e0n l\u00fd t\u01b0\u1edfng v\u00e0 ho\u00e0n h\u1ea3o. N\u00f3 v\u1eabn g\u00e2y s\u1ee9c \u00e9p l\u00ean c\u00e1c nh\u00e0 khoa h\u1ecdc r\u1ea5t l\u1edbn: “Publish or Perish” l\u00e0 “ch\u00e2m ng\u00f4n” c\u0169ng r\u1ea5t \u0111\u00e1ng s\u1ee3. Einstein r\u1ea5t \u00fd th\u1ee9c \u0111i\u1ec1u \u0111\u00f3, v\u00e0 th\u01b0\u1eddng khuy\u00ean c\u00e1c nh\u00e0 v\u1eadt l\u00fd tr\u1ebb, r\u1eb1ng h\u1ecd n\u00ean t\u00ecm m\u1ed9t vi\u1ec7c l\u00e0m b\u1ea3o \u0111\u1ea3m \u0111\u01b0\u1ee3c cu\u1ed9c s\u1ed1ng nh\u01b0ng v\u1eabn c\u00f2n d\u01b0 th\u1eddi gi\u1edd \u0111\u1ec3 theo \u0111u\u1ed5i nghi\u00ean c\u1ee9u khoa h\u1ecdc c\u1ee7a m\u00ecnh, gi\u1ed1ng nh\u01b0 b\u1ea3n th\u00e2n \u00f4ng t\u1eebng l\u00e0m vi\u1ec7c nhi\u1ec1u n\u0103m \u1edf S\u1edf c\u1ea5p b\u1eb1ng s\u00e1ng ch\u1ebf m\u00e0 v\u1eabn c\u00f2n th\u00ec gi\u1edd \u0111\u1ec3 l\u00e0m nghi\u00ean c\u1ee9u cho \u0111\u1ebfn khi \u00f4ng th\u0103ng hoa.<\/p>\n

    M\u1eb7c d\u00f9 th\u1ebf, hi\u1ec7n t\u1ea1i kh\u00f4ng c\u00f3 m\u00f4i tr\u01b0\u1eddng h\u1ecdc thu\u1eadt n\u00e0o t\u1ed1t h\u01a1n m\u00f4i tr\u01b0\u1eddng ph\u01b0\u01a1ng T\u00e2y.<\/p>\n

    (IV)<\/span><\/strong><\/p>\n

    Hai n\u1ec1n v\u0103n minh \u0110\u00f4ng, T\u00e2y kh\u00e1c nhau r\u1ea5t c\u0103n b\u1ea3n. M\u1ed9t b\u00ean d\u1ef1a tr\u00ean t\u00ednh khoa h\u1ecdc, t\u1ef1 do, \u0111\u1ed5i m\u1edbi s\u00e1ng t\u1ea1o v\u00e0 m\u1ed9t b\u00ean d\u1ef1a tr\u00ean nho gi\u00e1o nh\u01b0 m\u1ed9t \u00fd th\u1ee9c h\u1ec7 duy nh\u1ea5t. \u0110\u1ea7u thi\u00ean ni\u00ean k\u1ef7 th\u1ee9 hai, ph\u01b0\u01a1ng T\u00e2y x\u00e2y d\u1ef1ng m\u1ea1ng l\u01b0\u1edbi \u0111\u1ea1i h\u1ecdc \u0111\u01b0\u1ee3m tinh th\u1ea7n l\u00fd t\u00ednh, khoa h\u1ecdc, tri\u1ebft h\u1ecdc, t\u00ecm t\u00f2i, t\u01b0 bi\u1ec7n. M\u1ed9t cu\u1ed9c d\u1ecbch thu\u1eadt v\u0129 \u0111\u1ea1i di\u1ec5n ra c\u1ee7a nh\u1eefng t\u00e1c ph\u1ea9m Hy l\u1ea1p, v\u00e0 \u1ea2 r\u1eadp, k\u00e9o d\u00e0i c\u1ea3 hai tr\u0103m n\u0103m. Trung Hoa c\u00f9ng l\u00fac \u0111\u00f3 c\u0169ng x\u00e2y d\u1ef1ng \u0111\u1ea1i h\u1ecdc, nh\u01b0ng l\u1ea5y T\u1ee9 th\u01b0 Ng\u0169 kinh l\u00e0m n\u1ec1n t\u1ea3ng. \u0110\u00f3 l\u00e0 s\u1ef1 kh\u00e1c bi\u1ec7t.<\/p>\n

    Ph\u01b0\u01a1ng T\u00e2y ch\u1ecbu \u1ea3nh h\u01b0\u1edfng to l\u1edbn c\u1ee7a t\u00f4n gi\u00e1o, nh\u01b0ng \u0111\u00e3 tho\u00e1t ra kh\u1ecfi s\u1ef1 r\u00e0ng bu\u1ed9c gi\u00e1o \u0111i\u1ec1u, kinh vi\u1ec7n, \u0111\u1ec3 cu\u1ed1i c\u00f9ng c\u00f3 khoa h\u1ecdc hi\u1ec7n \u0111\u1ea1i th\u1ebf k\u1ef7 XVII. Ph\u01b0\u01a1ng \u0110\u00f4ng v\u1eabn s\u1ed1ng v\u1edbi nho gi\u00e1o cho \u0111\u1ebfn khi c\u00e1c \u0111\u1ebf ch\u1ebf s\u1ee5p \u0111\u1ed5.<\/p>\n

    Khoa h\u1ecdc Hy l\u1ea1p c\u1ed5 \u0111\u1ea1i \u0111\u00e3 th\u00e2m nh\u1eadp v\u00e0o ch\u00e2u \u00c2u th\u00f4ng qua gi\u00e1o d\u1ee5c khai ph\u00f3ng (liberal education). \u0110\u00e2y l\u00e0 gi\u00e1o d\u1ee5c bao g\u1ed3m n\u1ed9i dung c\u0103n b\u1ea3n c\u1ee7a b\u1ea3y m\u00f4n h\u1ecdc khai ph\u00f3ng: ng\u1eef ph\u00e1p, logic (bi\u1ec7n ch\u1ee9ng), h\u00f9ng bi\u1ec7n, h\u1ecdp th\u00e0nh trivium<\/em>, v\u00e0 s\u1ed1 h\u1ecdc, h\u00ecnh h\u1ecdc, \u00e2m nh\u1ea1c v\u00e0 thi\u00ean v\u0103n h\u1ecdc h\u1ecdp th\u00e0nh quadrivium<\/em>. Gi\u00e1o d\u1ee5c n\u00e0y \u0111\u00e3 t\u1ed3n t\u1ea1i t\u1eeb th\u1eddi Hy l\u1ea1p c\u1ed5 \u0111\u1ea1i, gi\u00fap con ng\u01b0\u1eddi bi\u1ebft t\u01b0 duy, l\u00fd lu\u1eadn, ti\u1ebfp thu khoa h\u1ecdc, c\u00f3 t\u01b0 duy ph\u1ea3n bi\u1ec7n, bi\u1ebft nh\u1eadn th\u1ee9c, \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 h\u1ecdc ti\u1ebfp cao h\u01a1n. Gi\u00e1o d\u1ee5c \u0111\u00f3 l\u00e0 c\u1ea3nh c\u1eeda m\u1edf v\u00e0o con \u0111\u01b0\u1eddng khoa h\u1ecdc, v\u00e0 h\u1ecdc thu\u1eadt n\u00f3i chung.<\/p>\n

    M\u1ea5y th\u1eadp ni\u00ean qua, Trung Qu\u1ed1c \u0111\u00e3 n\u1ed7 l\u1ef1c c\u1ea3i c\u00e1ch v\u00e0 n\u00e2ng c\u1ea5p c\u00e1c \u0111\u1ea1i h\u1ecdc h\u00e0ng \u0111\u1ea7u c\u1ee7a h\u1ecd hy v\u1ecdng ngang b\u1eb1ng v\u1edbi c\u00e1c \u0111\u1ea1i h\u1ecdc M\u1ef9 v\u00e0 ph\u01b0\u01a1ng T\u00e2y. D\u01b0\u1edbi th\u1eddi T\u1ed5ng b\u00ed th\u01b0 Giang Tr\u1ea1ch D\u00e2n, h\u1ecd \u0111\u00e3 tri\u1ec3n khai hai ch\u01b0\u01a1ng tr\u00ecnh tr\u1ecdng \u0111i\u1ec3m l\u00e0 D\u1ef1 \u00e1n 211 (t\u1eeb n\u0103m 1995) v\u00e0 D\u1ef1 \u00e1n 985 (t\u1eeb th\u00e1ng 5 n\u0103m 1998) v\u1edbi t\u1ed5ng ngu\u1ed3n v\u1ed1n \u0111\u1ea7u t\u01b0 ban \u0111\u1ea7u \u01b0\u1edbc t\u00ednh kho\u1ea3ng h\u01a1n 4 t\u1ef7 USD t\u1eeb ng\u00e2n s\u00e1ch trung \u01b0\u01a1ng v\u00e0 \u0111\u1ecba ph\u01b0\u01a1ng cho giai \u0111o\u1ea1n \u0111\u1ea7u, sau \u0111\u00f3 ti\u1ebfp t\u1ee5c \u0111\u01b0\u1ee3c r\u00f3t th\u00eam h\u00e0ng ch\u1ee5c t\u1ef7 nh\u00e2n d\u00e2n t\u1ec7 trong c\u00e1c giai \u0111o\u1ea1n ti\u1ebfp theo. H\u1ecd xem \u0111\u1ea1i h\u1ecdc l\u00e0 \u0111\u1ed9ng l\u1ef1c c\u1ee7a \u0111\u1ed5i m\u1edbi s\u00e1ng t\u1ea1o kh\u00f4ng th\u1ec3 thi\u1ebfu. C\u00e1nh c\u1eeda \u0111\u1ea1i h\u1ecdc m\u1edf r\u1ed9ng \u0111\u1ec3 \u0111\u00f3n ti\u1ebfp h\u1ecdc gi\u1ea3 ph\u01b0\u01a1ng T\u00e2y. M\u1ed9t d\u00f2ng th\u00e1c nh\u00e0 khoa h\u1ecdc ph\u01b0\u01a1ng T\u00e2y \u0111\u00e3 \u0111\u1ed5 v\u1ec1 c\u00e1c \u0111\u1ea1i h\u1ecdc Trung Qu\u1ed1c. Theo th\u1ed1ng k\u00ea ch\u00ednh th\u1ee9c, con s\u1ed1 n\u00e0y l\u00ean t\u1edbi kho\u1ea3ng 18.000. Ch\u01b0\u01a1ng tr\u00ecnh “Ng\u00e0n nh\u00e2n t\u00e0i”: \u0111\u00e3 thu h\u00fat h\u01a1n 7.000 nh\u00e0 nghi\u00ean c\u1ee9u v\u00e0 khoa h\u1ecdc \u0111\u1ec9nh cao trong giai \u0111o\u1ea1n 2011 \u0111\u1ebfn n\u0103m 2017, bao g\u1ed3m h\u00e0ng ch\u1ee5c nh\u00e0 khoa h\u1ecdc ph\u01b0\u01a1ng T\u00e2y gi\u1ea3i Nobel. Th\u00e2t ra, kh\u00f4ng ph\u1ea3i m\u1edbi. Nh\u1eadt B\u1ea3n th\u1eddi Minh Tr\u1ecb c\u0169ng \u0111\u00e3 t\u1eebng l\u00e0m nh\u01b0 th\u1ebf \u0111\u1ec3 x\u00e2y d\u1ef1ng h\u1ec7 th\u1ed1ng \u0111\u1ea1i h\u1ecdc, nghi\u00ean c\u1ee9u c\u1ee7a h\u1ecd.<\/p>\n

    Tuy nhi\u00ean, c\u00e1ch qu\u1ea3n tr\u1ecb \u0111\u1ea1i h\u1ecdc v\u00e0 con ng\u01b0\u1eddi, t\u00ednh minh b\u1ea1ch, li\u00eam ch\u00ednh, kh\u00f4ng kh\u00ed t\u1ef1 do h\u1ecdc thu\u1eadt ch\u01b0a gi\u1ed1ng truy\u1ec1n th\u1ed1ng ph\u01b0\u01a1ng T\u00e2y. B\u1ea3n th\u00e2n Shing-Tung Yau, ng\u01b0\u1eddi v\u00f4 c\u00f9ng nhi\u1ec7t t\u00ecnh v\u1edbi qu\u00ea h\u01b0\u01a1ng \u00f4ng, \u0111\u01b0\u1ee3c gi\u1edbi l\u00e3nh \u0111\u1ea1o c\u1ea5p cao \u0111\u00f3n ti\u1ebfp n\u1ed3ng h\u1eadu v\u00e0 nh\u00e0 n\u01b0\u1edbc huy \u0111\u1ed9ng \u0111\u01b0\u1ee3c ngu\u1ed3n l\u1ef1c to l\u1edbn \u0111\u1ec3 x\u00e2y d\u1ef1ng c\u00e1c c\u01a1 s\u1edf nghi\u00ean c\u1ee9u \u0111\u1eb3ng c\u1ea5p, nh\u01b0 \u201cTrung t\u00e2m Khoa h\u1ecdc To\u00e1n h\u1ecdc Yau\u201d t\u1ea1i \u0110\u1ea1i h\u1ecdc Thanh Hoa \u2013 n\u01a1i \u00f4ng chuy\u1ec3n \u0111\u1ebfn l\u00e0m vi\u1ec7c to\u00e0n th\u1eddi gian. \u00d4ng \u0111\u00e3 \u0111\u00e0o t\u1ea1o v\u00e0 d\u1eabn d\u1eaft th\u00e0nh c\u00f4ng nhi\u1ec1u nh\u00e0 to\u00e1n h\u1ecdc xu\u1ea5t s\u1eafc c\u1ee7a Trung Qu\u1ed1c. Nh\u01b0ng \u00f4ng c\u0169ng c\u00f3 nh\u1eefng cu\u1ed9c tranh c\u00e3i gay g\u1eaft c\u00f4ng khai v\u1edbi c\u00e1c c\u01a1 s\u1edf nghi\u00ean c\u1ee9u trong n\u01b0\u1edbc, ti\u00eau bi\u1ec3u l\u00e0 \u0110\u1ea1i h\u1ecdc B\u1eafc Kinh, khi ch\u1ec9 tr\u00edch t\u00ecnh tr\u1ea1ng \u201ckh\u00e9p k\u00edn mang t\u00ednh quan li\u00eau, n\u1ea1n b\u00e8 ph\u00e1i v\u00e0 s\u1ef1 thi\u1ebfu minh b\u1ea1ch trong quy tr\u00ecnh b\u00ecnh duy\u1ec7t\u201d. \u00d4ng c\u00f4ng khai nh\u1eadn \u0111\u1ecbnh r\u1eb1ng nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc c\u1ee7a Trung Qu\u1ed1c c\u00f2n \u201cthua k\u00e9m so v\u1edbi c\u00e1c chu\u1ea9n m\u1ef1c l\u1ecbch s\u1eed c\u1ee7a ph\u01b0\u01a1ng T\u00e2y\u201d.<\/p>\n

    T\u1edd TIMES Anh qu\u1ed1c ghi l\u1ea1i, khi \u0111\u01b0\u1ee3c ph\u1ecfng v\u1ea5n cho t\u00e0i kho\u1ea3n m\u1ea1ng x\u00e3 h\u1ed9i c\u1ee7a khoa To\u00e1n \u0110\u1ea1i h\u1ecdc B\u1eafc Kinh, Deng Yu cho bi\u1ebft \u00f4ng khuy\u00ean t\u1ea5t c\u1ea3 c\u00e1c h\u1ecdc gi\u1ea3 n\u00ean c\u00f3 \u201c\u00edt nh\u1ea5t m\u1ed9t tr\u1ea3i nghi\u1ec7m du h\u1ecdc to\u00e0n di\u1ec7n trong su\u1ed1t s\u1ef1 nghi\u1ec7p h\u1ecdc thu\u1eadt c\u1ee7a m\u00ecnh\u201d. \u0110o\u1ea1n v\u0103n n\u00e0y sau \u0111\u00f3 \u0111\u00e3 b\u1ecb x\u00f3a.<\/p>\n

    (V)<\/strong><\/span><\/p>\n

    Trong \u0111\u1ec1n th\u1edd to\u00e1n h\u1ecdc n\u1eef c\u00f3 th\u00eam t\u00ean tu\u1ed5i Wang Hong nh\u01b0 m\u1ed9t icon, b\u00ean c\u1ea1nh nh\u1eefng thi\u00ean t\u00e0i kh\u00e1c nh\u01b0 Hypatia c\u1ee7a Alexandria Hy l\u1ea1p h\u00f3a (kho\u1ea3ng 360-415 sau CN), nh\u00e0 to\u00e1n h\u1ecdc n\u1eefa ng\u01b0\u1eddi M\u1ef9 g\u1ed1c Ba T\u01b0 Maryam Mirzakhani (Fields, 2014), Maryna Viazovska c\u1ee7a Ukraina (Fields, 2022), v\u00e0 nhi\u1ec1u nh\u00e0 n\u1eef to\u00e1n h\u1ecdc kh\u00e1c c\u1ee7a th\u1ebf gi\u1edbi Claire Voisin (Gi\u1ea3i Shaw, 2017, Gi\u1ea3i Crafoord, 2024), Karen Uhlenbeck (Gi\u1ea3i Abel, 2019), Ingrid Daubechies ng\u01b0\u1eddi B\u1ec9 (Gi\u1ea3i Wolf, 2023).<\/p>\n

    Ngo\u00e0i ra l\u1ecbch s\u1eed c\u00f3 hai nh\u00e0 to\u00e1n h\u1ecdc quan tr\u1ecdng n\u1eefa: Sophie Germain c\u1ee7a Ph\u00e1p, Sofia Kovalevskaja c\u1ee7a Nga th\u1ebf k\u1ef7 XIX, v\u00e0 Emmy Noether c\u1ee7a \u0110\u1ee9c n\u1eeda \u0111\u1ea7u th\u1ebf k\u1ef7 XX.<\/p>\n

    \"\"\u00a0 \u00a0 \u00a0 \u00a0\"\"<\/p>\n

    Hypatia v\u00e0 Emmy Noether<\/p>\n

    \"\"\u00a0 \u00a0\u00a0 \"\"<\/p>\n

    Maryam Mirzakhani v\u00e0 Maryna Viazovska<\/p>\n

    (VI)<\/strong><\/span><\/p>\n

    C\u00e2u chuy\u1ec7n c\u1ee7a Wang Hong l\u00e0 minh ch\u1ee9ng tuy\u1ec7t v\u1eddi cho s\u1ef1 ki\u00ean tr\u00ec b\u1ec1n b\u1ec9 trong s\u1ef1 l\u1eb7ng l\u1ebd, v\u1edbi kh\u1ea3 n\u0103ng t\u1eadp trung cao \u0111\u1ed9, v\u00e0 vi\u1ec7c c\u00f4 v\u01b0\u01a1n l\u00ean kh\u1ecfi nh\u1eefng s\u1ef1 \u1ed3n \u00e0o c\u1ee7a cu\u1ed9c s\u1ed1ng \u0111\u1ec3 nh\u00ecn th\u1ea5y \u00e1nh s\u00e1ng \u0111\u1ec3 theo \u0111u\u1ed5i to\u00e1n h\u1ecdc v\u00e0 c\u1ed1ng hi\u1ebfn.<\/p>\n

    Einstein c\u00f3 ph\u00e1t bi\u1ec3u v\u1ec1 tri\u1ebft l\u00fd c\u1ee7a nh\u1eefng ng\u01b0\u1eddi ch\u1ecdn l\u1ed1i s\u1ed1ng s\u1ed1ng thu\u1ea7n khi\u1ebft d\u00e0nh cho khoa h\u1ecdc trong b\u00e0i \u0111i\u1ebfu v\u0103n cho Emmy Noether m\u1ea5t n\u0103m 1935 nh\u01b0 sau:<\/p>\n

    Nh\u1eefng n\u1ed7 l\u1ef1c c\u1ee7a ph\u1ea7n l\u1edbn con ng\u01b0\u1eddi \u0111\u01b0\u1ee3c ti\u00eau pha v\u00e0o s\u1ef1 chi\u1ebfn \u0111\u1ea5u cho mi\u1ebfng \u0103n h\u00e0ng ng\u00e0y, nh\u01b0ng ph\u1ea7n l\u1edbn nh\u1eefng ai, ho\u1eb7c b\u1eb1ng s\u1ef1 may m\u1eafn, hay m\u1ed9t \u0111\u1eb7c \u00e2n tr\u1eddi cho, \u0111\u01b0\u1ee3c l\u00e0m nh\u1eb9 b\u1edbt trong cu\u1ed9c chi\u1ebfn \u0111\u1ea5u, b\u1ecb thu h\u00fat v\u00e0o s\u1ef1 c\u1ea3i thi\u1ec7n ti\u1ebfp t\u1ee5c s\u1ed1 ph\u1eadn h\u1ecd tr\u00ean th\u1ebf gian. D\u01b0\u1edbi nh\u1eefng n\u1ed7 l\u1ef1c h\u01b0\u1edbng v\u1ec1 s\u1ef1 t\u00edch l\u0169y c\u00e1c t\u00e0i s\u1ea3n th\u1ebf gian th\u01b0\u1eddng l\u00e0 \u1ea3o t\u01b0\u1edfng cho r\u1eb1ng \u0111\u00f3 l\u00e0 c\u1ee9u c\u00e1nh quan tr\u1ecdng v\u00e0 \u0111\u00e1ng mong m\u1ecfi nh\u1ea5t; nh\u01b0ng may m\u1eafn thay, c\u00f3 m\u1ed9t thi\u1ec3u s\u1ed1 g\u1ed3m nh\u1eefng ng\u01b0\u1eddi s\u1edbm nh\u1eadn th\u1ee9c trong \u0111\u1eddi h\u1ecd r\u1eb1ng nh\u1eefng tr\u1ea3i nghi\u1ec7m \u0111\u1eb9p \u0111\u1ebd v\u00e0 l\u00e0m h\u00e0i l\u00f2ng nh\u1ea5t m\u1edf ra cho nh\u00e2n lo\u1ea1i kh\u00f4ng ph\u1ea3i xu\u1ea5t ph\u00e1t t\u1eeb b\u00ean ngo\u00e0i, m\u00e0 g\u1eafn li\u1ec1n v\u1edbi s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a c\u1ea3m x\u00fac ri\u00eang c\u00e1 nh\u00e2n, suy ngh\u0129 v\u00e0 h\u00e0nh \u0111\u1ed9ng. Nh\u1eefng nh\u00e0 ngh\u1ec7 s\u0129, nh\u00e0 nghi\u00ean c\u1ee9u, hay nh\u00e0 t\u01b0 t\u01b0\u1edfng \u0111\u00edch th\u1ef1c lu\u00f4n lu\u00f4n l\u00e0 nh\u1eefng ng\u01b0\u1eddi lo\u1ea1i n\u00e0y. Cu\u1ed9c \u0111\u1eddi c\u1ee7a nh\u1eefng c\u00e1 nh\u00e2n n\u00e0y, d\u00f9 di\u1ec5n ra \u00e2m th\u1ea7m th\u1ebf n\u00e0o, nh\u1eefng th\u00e0nh qu\u1ea3 c\u1ee7a n\u1ed7 l\u1ef1c h\u1ecd l\u00e0 nh\u1eefng \u0111\u00f3ng g\u00f3p qu\u00fd b\u00e1u nh\u1ea5t m\u00e0 m\u1ed9t th\u1ebf h\u1ec7 c\u00f3 th\u1ec3 xem nh\u01b0 di s\u1ea3n c\u1ee7a nh\u1eefng ng\u01b0\u1eddi n\u1ed1i nghi\u1ec7p c\u1ee7a n\u00f3.<\/p>\n

    (Trong\u00a0K\u1ef7 ni\u1ec7m 100 n\u0103m \u0111\u1ecbnh l\u00fd Emmy Noether<\/em>)<\/a><\/p>\n

    Nh\u1eefng \u0111i\u1ec1u \u0111\u00f3 c\u0169ng c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng cho Wang Hong. T\u1ea1i sao c\u00f3 nh\u1eefng ng\u01b0\u1eddi th\u00e0nh c\u00f4ng l\u1edbn, v\u1edbi nh\u1eefng gi\u00e1 tr\u1ecb tr\u00ed tu\u1ec7 l\u1edbn? B\u00e0n v\u1ec1 s\u1ef1 th\u00e0nh c\u00f4ng c\u1ee7a ng\u01b0\u1eddi Do Th\u00e1i, Einstein \u0111\u01b0a ra quan \u0111i\u1ec3m: th\u00f4ng minh l\u00e0 \u00edt, m\u00e0 v\u0103n h\u00f3a \u2013 v\u0103n h\u00f3a bi\u1ebft ng\u01b0\u1ee1ng m\u1ed9 nh\u1eefng gi\u00e1 tr\u1ecb cao \u2013 l\u00e0 nhi\u1ec1u. \u00d4ng vi\u1ebft:<\/p>\n

    N\u00e9t \u0111\u1eb7c tr\u01b0ng th\u1ee9 hai c\u1ee7a truy\u1ec1n th\u1ed1ng Do Th\u00e1i l\u00e0 s\u1ef1 \u0111\u00e1nh gi\u00e1 cao m\u1ecdi lo\u1ea1i\u00a0kh\u00e1t v\u1ecdng tr\u00ed tu\u1ec7<\/em>\u00a0v\u00e0\u00a0lao \u0111\u1ed9ng tinh th\u1ea7n<\/em>. Ch\u00ednh do s\u1ef1 tr\u00e2n qu\u00fd n\u00e0y m\u00e0 theo t\u00f4i nh\u1eefng ng\u01b0\u1eddi Do Th\u00e1i \u0111\u00e3 \u0111\u00f3ng g\u00f3p v\u00e0o t\u1ea5t c\u1ea3 nh\u1eefng ti\u1ebfn b\u1ed9 c\u1ee7a nh\u1eadn th\u1ee9c tr\u00ed th\u1ee9c theo ngh\u0129a r\u1ed9ng nh\u1ea5t c\u1ee7a t\u1eeb tr\u00ean m\u1ed9t quy m\u00f4 m\u00e0, n\u1ebfu ch\u00fa \u00fd \u0111\u1ebfn s\u1ed1 l\u01b0\u1ee3ng t\u01b0\u01a1ng \u0111\u1ed1i nh\u1ecf v\u00e0 nh\u1eefng tr\u1edf ng\u1ea1i b\u00ean ngo\u00e0i \u0111\u00e1ng k\u1ec3 h\u1ecd ph\u1ea3i \u0111\u1ed1i m\u1eb7t, nh\u1eefng th\u1ee9 kh\u00f4ng ng\u1eebng l\u00e0 l\u1ef1c c\u1ea3n tr\u00ean con \u0111\u01b0\u1eddng h\u1ecd kh\u1eafp m\u1ecdi n\u01a1i, r\u1ea5t x\u1ee9ng \u0111\u00e1ng v\u1edbi s\u1ef1 c\u00f4ng nh\u1eadn c\u1ee7a t\u1ea5t c\u1ea3 nh\u1eefng ng\u01b0\u1eddi ch\u00e2n th\u1eadt. T\u00f4i tin r\u1eb1ng \u0111i\u1ec1u n\u00e0y kh\u00f4ng ph\u1ea3i do m\u1ed9t s\u1ef1 gi\u00e0u c\u00f3 c\u00e1c t\u00e0i n\u0103ng thi\u00ean ph\u00fa n\u00e0o, m\u00e0 do s\u1ef1 th\u1eadt r\u1eb1ng s\u1ef1\u00a0tr\u00e2n qu\u00fd th\u00e0nh t\u1ef1u tinh th\u1ea7n<\/em>\u00a0\u1edf nh\u1eefng ng\u01b0\u1eddi Do Th\u00e1i \u0111\u00e3 t\u1ea1o ra m\u1ed9t b\u1ea7u kh\u00f4ng kh\u00ed l\u00e0m thu\u1eadn l\u1ee3i \u0111\u1eb7c bi\u1ec7t cho s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a c\u00e1c t\u00e0i n\u0103ng c\u00f3 th\u1ec3 c\u00f3. \u0110\u1ed3ng th\u1eddi, \u00f3c ph\u00ea ph\u00e1n m\u1ea1nh m\u1ebd c\u1ee7a h\u1ecd gi\u00fap ng\u0103n ng\u1eeba s\u1ef1 ch\u1ea1y theo b\u1ea5t c\u1ee9 m\u1ed9t quy\u1ec1n uy n\u00e0o m\u1ed9t c\u00e1ch m\u00f9 qu\u00e1ng. (nghi\u00eang \u0111\u01b0\u1ee3c th\u00eam v\u00e0o)<\/p>\n

    (Einstein, 1938, trong s\u00e1ch\u00a0T\u1eeb nh\u1eefng n\u0103m sau c\u1ee7a \u0111\u1eddi t\u00f4i<\/em>, 2025)<\/p>\n

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

    \u2b50 \u2b50\u2b50<\/p>\n

    “S\u1ed0NG TR\u1eccN V\u1eb8N TRONG TH\u1ebe GI\u1edaI TO\u00c1N H\u1eccC L\u00c0 B\u01af\u1edaC \u0110I TR\u00caN L\u1eb0N RANH MONG MANH”<\/span><\/h1>\n

    T\u00e1c gi\u1ea3<\/em>: Natalie Wolchover<\/span><\/p>\n

     <\/p>\n

    \"\"<\/p>\n

    Trong b\u1ee9c \u1ea3nh n\u00e0y, V\u01b0\u01a1ng H\u1ed3ng \u0111ang vi\u1ebft m\u1ed9t b\u00e0i b\u00e1o nghi\u00ean c\u1ee9u m\u1edbi t\u1ea1i Vi\u1ec7n Nghi\u00ean c\u1ee9u Khoa h\u1ecdc Cao c\u1ea5p (IHES) \u1edf Ph\u00e1p.\u00a0\u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    S\u1ef1 t\u1eadp trung, d\u1ea5n th\u00e2n v\u00e0 tr\u1ef1c quan s\u1eafc b\u00e9n \u0111\u00e3 mang l\u1ea1i m\u1ed9t ch\u1ee9ng minh “tr\u0103m n\u0103m c\u00f3 m\u1ed9t”. V\u01b0\u01a1ng H\u1ed3ng (Hong Wang) gi\u1edd \u0111\u00e2y l\u00e0 ng\u01b0\u1eddi ph\u1ee5 n\u1eef th\u1ee9 ba gi\u00e0nh \u0111\u01b0\u1ee3c Huy ch\u01b0\u01a1ng Fields trong su\u1ed1t l\u1ecbch s\u1eed 90 n\u0103m c\u1ee7a gi\u1ea3i th\u01b0\u1edfng danh gi\u00e1 n\u00e0y.<\/p>\n

    Ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 t\u01b0\u1edfng t\u01b0\u1ee3ng r\u1eb1ng, \u0111\u1ed1i v\u1edbi m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc, vi\u1ec7c ch\u1ee9ng minh \u0111\u01b0\u1ee3c m\u1ed9t \u0111\u1ecbnh l\u00fd v\u0129 \u0111\u1ea1i l\u00e0 m\u1ed9t tr\u1ea3i nghi\u1ec7m ng\u1eadp tr\u00e0n h\u1ea1nh ph\u00fac. Nh\u01b0ng v\u1edbi V\u01b0\u01a1ng H\u1ed3ng, m\u1ecdi chuy\u1ec7n l\u1ea1i kh\u00f4ng h\u1eb3n nh\u01b0 v\u1eady. V\u00e0o th\u00e1ng 2 n\u0103m 2025, V\u01b0\u01a1ng H\u1ed3ng c\u00f9ng c\u1ed9ng s\u1ef1 Joshua Zahl \u0111\u00e3 c\u00f4ng b\u1ed1 m\u1ed9t b\u1ea3n ch\u1ee9ng minh d\u00e0i 127 trang cho m\u1ed9t gi\u1ea3 thuy\u1ebft \u0111\u00e3 t\u1ed3n t\u1ea1i t\u1eeb l\u00e2u, n\u1eb1m \u1edf giao \u0111i\u1ec3m c\u1ee7a nhi\u1ec1u nh\u00e1nh to\u00e1n h\u1ecdc. Hai ng\u01b0\u1eddi \u0111\u00e3 d\u00e0nh nhi\u1ec1u th\u00e1ng ki\u1ec3m tra k\u1ef9 l\u01b0\u1ee1ng c\u00f4ng tr\u00ecnh c\u1ee7a m\u00ecnh, \u0111\u1ed3ng th\u1eddi g\u1eedi b\u1ea3n th\u1ea3o cho m\u1ed9t s\u1ed1 \u0111\u1ed3ng nghi\u1ec7p tin c\u1eady xem tr\u01b0\u1edbc, r\u1ed3i m\u1edbi c\u00f3 \u0111\u1ee7 d\u0169ng kh\u00ed \u0111\u1ec3 c\u00f4ng b\u1ed1. \u0110i\u1ec1u khi\u1ebfn V\u01b0\u01a1ng H\u1ed3ng lo l\u1eafng kh\u00f4ng ph\u1ea3i l\u00e0 c\u00e1c l\u1eadp lu\u1eadn c\u00f3 sai s\u00f3t, m\u00e0 l\u00e0 ch\u00fang c\u00f3 th\u1ec3 ch\u01b0a \u0111\u01b0\u1ee3c di\u1ec5n \u0111\u1ea1t th\u1eadt ho\u00e0n h\u1ea3o, v\u00e0 v\u00ec th\u1ebf ch\u01b0a \u0111\u1ee7 r\u00f5 r\u00e0ng.<\/p>\n

    Kh\u00f4ng c\u00f3 sai s\u00f3t n\u00e0o \u0111\u01b0\u1ee3c ph\u00e1t hi\u1ec7n; l\u1eadp lu\u1eadn trong b\u1ea3n ch\u1ee9ng minh d\u1ea7n \u0111\u01b0\u1ee3c hi\u1ec3u th\u1ea5u \u0111\u00e1o v\u00e0 \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y l\u1ea1i m\u1ed9t c\u00e1ch m\u1ea1ch l\u1ea1c h\u01a1n, cho \u0111\u1ebfn khi m\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u tin t\u01b0\u1edfng v\u00e0o t\u00ednh \u0111\u00fang \u0111\u1eafn c\u1ee7a n\u00f3. V\u01b0\u01a1ng H\u1ed3ng v\u00e0 Zahl \u0111\u00e3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c gi\u1ea3 thuy\u1ebft Kakeya trong kh\u00f4ng gian ba chi\u1ec1u.<\/p>\n

    B\u1ea3n ch\u1ee9ng minh n\u00e0y \u0111\u00e3 mang v\u1ec1 cho V\u01b0\u01a1ng H\u1ed3ng, nh\u00e0 to\u00e1n h\u1ecdc \u0111\u1ebfn t\u1eeb Qu\u1ebf L\u00e2m, Trung Qu\u1ed1c, m\u1ed9t chu\u1ed7i c\u00e1c gi\u1ea3i th\u01b0\u1edfng li\u00ean ti\u1ebfp: Gi\u1ea3i Salem, Gi\u1ea3i Ostrowski v\u00e0 Huy ch\u01b0\u01a1ng V\u00e0ng To\u00e1n h\u1ecdc c\u1ee7a \u0110\u1ea1i h\u1ed9i Qu\u1ed1c t\u1ebf c\u00e1c Nh\u00e0 To\u00e1n h\u1ecdc Trung Qu\u1ed1c trong n\u0103m 2025; Huy ch\u01b0\u01a1ng Antonio Ambrosetti, Gi\u1ea3i Sadosky, Gi\u1ea3i Nghi\u00ean c\u1ee9u Clay v\u00e0 Gi\u1ea3i New Horizons in Mathematics trong n\u1eeda \u0111\u1ea7u n\u0103m 2026; v\u00e0 cu\u1ed1i c\u00f9ng l\u00e0 Huy ch\u01b0\u01a1ng Fields 2026, \u0111\u01b0\u1ee3c xem l\u00e0 cao qu\u00fd nh\u1ea5t trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc, d\u00e0nh cho nh\u1eefng nh\u00e0 to\u00e1n h\u1ecdc d\u01b0\u1edbi 40 tu\u1ed5i c\u00f3 nh\u1eefng th\u00e0nh t\u1ef1u xu\u1ea5t s\u1eafc. \u1ede tu\u1ed5i 35, V\u01b0\u01a1ng H\u1ed3ng – gi\u00e1o s\u01b0 to\u00e1n h\u1ecdc t\u1ea1i \u0110\u1ea1i h\u1ecdc New York (NYU) v\u00e0 Vi\u1ec7n Nghi\u00ean c\u1ee9u Khoa h\u1ecdc Cao c\u1ea5p (IHES) c\u1ee7a Ph\u00e1p – l\u00e0 ng\u01b0\u1eddi ph\u1ee5 n\u1eef th\u1ee9 ba trong l\u1ecbch s\u1eed 90 n\u0103m c\u1ee7a gi\u1ea3i Fields \u0111\u01b0\u1ee3c nh\u1eadn Huy ch\u01b0\u01a1ng n\u00e0y.<\/p>\n

    S\u1ef1 n\u1ed5i ti\u1ebfng c\u0169ng \u0111\u1ed3ng ngh\u0129a v\u1edbi vi\u1ec7c V\u01b0\u01a1ng H\u1ed3ng ng\u00e0y c\u00e0ng nh\u1eadn \u0111\u01b0\u1ee3c nhi\u1ec1u l\u1eddi m\u1eddi m\u00e0 c\u00f4 kh\u00f3 l\u00f2ng t\u1eeb ch\u1ed1i: c\u00e1c bu\u1ed5i thuy\u1ebft tr\u00ecnh, c\u00e1c chuy\u1ebfn \u0111i v\u00e0 c\u00e1c cu\u1ed9c ph\u1ecfng v\u1ea5n. Nh\u1eefng vi\u1ec7c n\u00e0y l\u1ea5n \u00e1t qu\u1ef9 th\u1eddi gian m\u00e0 c\u00f4 c\u00f3 th\u1ec3 d\u00e0nh cho nghi\u00ean c\u1ee9u c\u00e1ch nh\u1eefng \u1ed1ng (tubes) d\u00e0i v\u00e0 m\u1ea3nh, h\u01b0\u1edbng theo c\u00e1c ph\u01b0\u01a1ng kh\u00e1c nhau, c\u00f3 th\u1ec3 ch\u1ed3ng l\u1ea5n l\u00ean nhau nh\u01b0 th\u1ebf n\u00e0o.<\/p>\n\"\"\n

    Nh\u1eefng cu\u1ed9c \u0111i b\u1ed9 l\u00fac s\u00e1ng s\u1edbm gi\u00fap V\u01b0\u01a1ng H\u1ed3ng gi\u1ea3i t\u1ecfa b\u1edbt \u00e1p l\u1ef1c v\u00e0 s\u1ef1 ho\u00e0i nghi v\u1ec1 b\u1ea3n th\u00e2n v\u1ed1n lu\u00f4n \u0111i k\u00e8m v\u1edbi c\u00f4ng vi\u1ec7c nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc.\u00a0\u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    \u0110\u00f3 ch\u00ednh l\u00e0 v\u1ea5n \u0111\u1ec1 c\u1ed1t l\u00f5i c\u1ee7a c\u00e1c b\u00e0i to\u00e1n d\u1ea1ng Kakeya \u2013 l\u0129nh v\u1ef1c chuy\u00ean m\u00f4n c\u1ee7a V\u01b0\u01a1ng H\u1ed3ng. \u0110\u00e2y l\u00e0 m\u1ed9t nh\u00f3m c\u00e1c b\u00e0i to\u00e1n v\u00e0 gi\u1ea3 thuy\u1ebft to\u00e1n h\u1ecdc n\u1eb1m ngay t\u1ea1i giao \u0111i\u1ec3m c\u1ee7a ba l\u0129nh v\u1ef1c l\u1edbn, bao g\u1ed3m gi\u1ea3i t\u00edch \u0111i\u1ec1u h\u00f2a (nghi\u00ean c\u1ee9u c\u00e1ch t\u00edn hi\u1ec7u ph\u00e2n gi\u1ea3i th\u00e0nh c\u00e1c t\u1ea7n s\u1ed1 c\u1ea5u th\u00e0nh), l\u00fd thuy\u1ebft \u0111\u1ed9 \u0111o h\u00ecnh h\u1ecdc (nghi\u00ean c\u1ee9u h\u00ecnh d\u1ea1ng v\u00e0 k\u00edch th\u01b0\u1edbc c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng kh\u00f4ng nh\u1eb5n), v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ea1o h\u00e0m ri\u00eang (m\u00f4 t\u1ea3 nh\u1eefng h\u1ec7 th\u1ed1ng bi\u1ebfn \u0111\u1ed5i \u0111\u1ed3ng th\u1eddi theo nhi\u1ec1u c\u00e1ch kh\u00e1c nhau). B\u00ean c\u1ea1nh \u0111\u00f3, l\u0129nh v\u1ef1c n\u00e0y c\u00f2n c\u00f3 m\u1ed1i li\u00ean h\u1ec7 ch\u1eb7t ch\u1ebd v\u1edbi l\u00fd thuy\u1ebft s\u1ed1, to\u00e1n t\u1ed5 h\u1ee3p, v\u00e0 nhi\u1ec1u ng\u00e0nh to\u00e1n h\u1ecdc kh\u00e1c. Nh\u00e0 to\u00e1n h\u1ecdc Pablo Shmerkin, \u0110\u1ea1i h\u1ecdc British Columbia (Canada) nh\u1eadn x\u00e9t: \u201cCh\u00ednh t\u1ea5t c\u1ea3 nh\u1eefng m\u1ed1i li\u00ean h\u1ec7 \u0111\u00f3 \u0111\u00e3 khi\u1ebfn cho l\u0129nh v\u1ef1c n\u00e0y \u0111\u01b0\u1ee3c xem l\u00e0 gi\u1eef v\u1ecb tr\u00ed trung t\u00e2m c\u1ee7a to\u00e1n h\u1ecdc, \u0111\u1ed3ng th\u1eddi c\u0169ng l\u00e0 l\u00fd do v\u00ec sao V\u01b0\u01a1ng H\u1ed3ng \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 cao \u0111\u1ebfn v\u1eady.\u201d<\/p>\n

    Khi kh\u00f4ng ph\u1ea3i b\u1eadn r\u1ed9n v\u1edbi nh\u1eefng chuy\u1ebfn \u0111i, V\u01b0\u01a1ng H\u1ed3ng l\u00e0m vi\u1ec7c v\u1edbi s\u1ef1 t\u1eadn t\u1ee5y v\u00e0 k\u1ef7 lu\u1eadt ch\u1eb3ng kh\u00e1c n\u00e0o m\u1ed9t n\u1eef tu d\u00f2ng k\u00edn ho\u1eb7c m\u1ed9t v\u1eadn \u0111\u1ed9ng vi\u00ean \u0111\u1ec9nh cao. Shukun Wu, c\u1ed9ng s\u1ef1 c\u1ee7a c\u00f4 t\u1ea1i \u0110\u1ea1i h\u1ecdc Indiana, nh\u1eadn x\u00e9t: “C\u00f4 \u1ea5y m\u00ea to\u00e1n \u0111\u1ebfn cu\u1ed3ng nhi\u1ec7t. C\u00f4 \u1ea5y ch\u1eafc ch\u1eafn l\u00e0 m\u1ed9t trong nh\u1eefng ng\u01b0\u1eddi t\u1eadn t\u00e2m nh\u1ea5t m\u00e0 t\u00f4i t\u1eebng g\u1eb7p.” V\u01b0\u01a1ng H\u1ed3ng kh\u01b0\u1edbc t\u1eeb vi\u1ec7c d\u00e0nh th\u1eddi gian cho nh\u1eefng th\u00fa vui d\u1ec5 ng\u1ed1n th\u1eddi gian nh\u01b0 \u0111\u1ecdc s\u00e1ch hay nu\u00f4i th\u00fa c\u01b0ng, m\u1eb7c d\u00f9 c\u00f4 v\u1eabn lu\u00f4n d\u00e0nh th\u1eddi gian cho b\u1ea1n b\u00e8, t\u1eadp yoga v\u00e0 \u0111i b\u1ed9 l\u00fac s\u00e1ng s\u1edbm \u0111\u1ec3 ng\u1eafm nh\u1eefng ch\u00fa ch\u00f3 \u1edf C\u00f4ng vi\u00ean Washington Square. T\u1ea5t c\u1ea3 nh\u1eefng ho\u1ea1t \u0111\u1ed9ng n\u00e0y gi\u00fap c\u00f4 gi\u1ea3m b\u1edbt c\u0103ng th\u1eb3ng c\u0169ng nh\u01b0 c\u1ea3m gi\u00e1c ho\u00e0i nghi b\u1ea3n th\u00e2n v\u1ed1n lu\u00f4n \u0111\u1ed3ng h\u00e0nh v\u1edbi c\u00f4ng vi\u1ec7c nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc.<\/p>\n

    Khao kh\u00e1t c\u00f3 \u0111\u01b0\u1ee3c s\u1ef1 t\u1ef1 tin v\u00e0o ki\u1ebfn th\u1ee9c v\u00e0 n\u0103ng l\u1ef1c c\u1ee7a b\u1ea3n th\u00e2n d\u01b0\u1eddng nh\u01b0 \u0111\u00e3 \u0111\u1ecbnh h\u00ecnh cu\u1ed9c \u0111\u1eddi V\u01b0\u01a1ng H\u1ed3ng. Ch\u1eb3ng h\u1ea1n nh\u01b0, ch\u00ednh \u0111i\u1ec1u \u0111\u00f3 \u0111\u00e3 thu h\u00fat c\u00f4 \u0111\u1ebfn v\u1edbi to\u00e1n h\u1ecdc: l\u0129nh v\u1ef1c m\u00e0 v\u1edbi c\u00f4 l\u00e0 \u00edt c\u00f3 ch\u1ed7 cho s\u1ef1 ho\u00e0i nghi nh\u1ea5t. D\u00f9 c\u00f4 ch\u01b0a bao gi\u1edd d\u00e0nh th\u1eddi gian \u0111\u1ec3 \u0103n m\u1eebng ch\u1ee9ng minh mang \u00fd ngh\u0129a c\u1ed9t m\u1ed1c c\u1ee7a m\u00ecnh, c\u0169ng nh\u01b0 kh\u00f4ng h\u1ec1 c\u1ea3m th\u1ea5y h\u00e3nh di\u1ec7n h\u01a1n v\u1ec1 b\u1ea3n th\u00e2n sau th\u00e0nh t\u1ef1u \u0111\u00f3, \u00edt nh\u1ea5t gi\u1edd \u0111\u00e2y V\u01b0\u01a1ng H\u1ed3ng c\u00f3 th\u1ec3 kh\u1eb3ng \u0111\u1ecbnh v\u1edbi s\u1ef1 ch\u1eafc ch\u1eafn tuy\u1ec7t \u0111\u1ed1i r\u1eb1ng c\u00e1c \u1ed1ng \u01b0\u1edbng theo m\u1ecdi ph\u01b0\u01a1ng trong kh\u00f4ng gian ba chi\u1ec1u kh\u00f4ng th\u1ec3 ch\u1ed3ng l\u1ea5n l\u00ean nhau qu\u00e1 nhi\u1ec1u.<\/p>\n

    Mu\u00f4n v\u00e0n \u0111i\u1ec1u k\u1ef3 di\u1ec7u<\/strong><\/span><\/p>\n

    Ban \u0111\u1ea7u c\u00f2n \u0111\u00f4i ch\u00fat d\u00e8 d\u1eb7t nh\u01b0ng r\u1ed3i nhanh ch\u00f3ng tr\u1edf n\u00ean c\u1edfi m\u1edf h\u01a1n, V\u01b0\u01a1ng H\u1ed3ng \u0111eo c\u1eb7p k\u00ednh g\u1ecdng panto v\u00e2n \u0111\u1ed3i m\u1ed3i v\u00e0 \u0111eo nh\u1eabn \u1edf c\u1ea3 hai ng\u00f3n tr\u1ecf. Chi\u1ebfc nh\u1eabn b\u1ea1c \u1edf tay tr\u00e1i v\u00e0 chi\u1ebfc nh\u1eabn v\u00e0ng \u1edf tay ph\u1ea3i th\u1ec9nh tho\u1ea3ng l\u1ea1i xu\u1ea5t hi\u1ec7n trong khung h\u00ecnh cu\u1ed9c g\u1ecdi video. T\u1eeb B\u1edd T\u00e2y n\u01b0\u1edbc M\u1ef9, n\u01a1i c\u00f4 d\u00e0nh v\u00e0i th\u00e1ng \u0111\u1ec3 gh\u00e9 th\u0103m c\u00e1c c\u1ed9ng s\u1ef1 v\u00e0 b\u1ea1n b\u00e8, V\u01b0\u01a1ng H\u1ed3ng k\u1ec3 r\u1eb1ng nh\u1eefng n\u0103m \u0111\u1ea7u \u0111\u1eddi c\u1ee7a m\u00ecnh tr\u00f4i qua kh\u00e1 v\u00f4 t\u01b0.<\/p>\n

    \u1ede th\u00e0nh ph\u1ed1 Qu\u1ebf L\u00e2m v\u00e0o nh\u1eefng n\u0103m 1990, sau gi\u1edd h\u1ecdc V\u01b0\u01a1ng H\u1ed3ng th\u01b0\u1eddng v\u1ec1 nh\u00e0 \u0111\u1ecdc s\u00e1ch (t\u1eeb th\u1ea7n tho\u1ea1i Hy L\u1ea1p, Harry Potter<\/em> \u0111\u1ebfn Ch\u00faa t\u1ec3 nh\u1eefng chi\u1ebfc nh\u1eabn<\/em>), xem truy\u1ec1n h\u00ecnh ho\u1eb7c ch\u01a1i b\u00f3ng b\u00e0n v\u00e0 c\u1ea7u l\u00f4ng. D\u00f9 \u0111\u1ec1u l\u00e0 gi\u00e1o vi\u00ean, cha m\u1eb9 c\u00f4 kh\u00f4ng h\u1ec1 g\u00e2y \u00e1p l\u1ef1c v\u1ec1 th\u00e0nh t\u00edch h\u1ecdc t\u1eadp. M\u1ed7i t\u1ed1i, c\u1ea3 gia \u0111\u00ecnh c\u00f4 c\u00f9ng nhau \u0111i d\u1ea1o quanh Qu\u1ebf L\u00e2m, th\u01b0\u1eddng \u0111\u01b0\u1ee3c m\u1ec7nh danh l\u00e0 th\u00e0nh ph\u1ed1 \u0111\u1eb9p nh\u1ea5t Trung Qu\u1ed1c, v\u1edbi nh\u1eefng ng\u1ecdn n\u00fai xanh bi\u1ebfc d\u1ed1c \u0111\u1ee9ng bao quanh v\u00e0 m\u1ed9t d\u00f2ng s\u00f4ng u\u1ed1n l\u01b0\u1ee3n ch\u1ea3y qua.<\/p>\n\"\"\n

    Khi c\u00f2n nh\u1ecf \u1edf Qu\u1ebf L\u00e2m, to\u00e1n h\u1ecdc ch\u1ec9 l\u00e0 m\u1ed9t trong r\u1ea5t nhi\u1ec1u s\u1edf th\u00edch c\u1ee7a V\u01b0\u01a1ng H\u1ed3ng, nh\u01b0ng c\u00f4 \u0111\u00e3 s\u1edbm b\u1ed9c l\u1ed9 n\u0103ng khi\u1ebfu n\u1ed5i b\u1eadt v\u1edbi m\u00f4n h\u1ecdc n\u00e0y.\u00a0\u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    C\u00f4 nh\u1edb c\u00f3 m\u1ed9t c\u00e2u \u0111\u1ed1 \u1edf cu\u1ed1i m\u1ed9t ch\u01b0\u01a1ng s\u00e1ch nh\u01b0 sau: L\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 tr\u1ed3ng b\u1ea3y c\u00e1i c\u00e2y th\u00e0nh nhi\u1ec1u h\u00e0ng nh\u1ea5t c\u00f3 th\u1ec3, v\u1edbi ba c\u00e2y \u1edf m\u1ed7i h\u00e0ng? C\u0169ng gi\u1ed1ng nh\u01b0 c\u00e1c b\u00e0i to\u00e1n d\u1ea1ng Kakeya m\u00e0 sau n\u00e0y c\u00f4 theo \u0111u\u1ed5i, c\u00e2u \u0111\u1ed1 n\u00e0y thu\u1ed9c l\u0129nh v\u1ef1c h\u00ecnh h\u1ecdc li\u00ean thu\u1ed9c (incidence geometry), hay l\u00e0 nghi\u00ean c\u1ee9u c\u00e1ch c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng h\u00ecnh h\u1ecdc ch\u1ed3ng l\u1ea5p l\u00ean nhau \u2014 trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng (nh\u1eefng h\u00e0ng c\u00e2y) v\u00e0 c\u00e1c \u0111i\u1ec3m (nh\u1eefng c\u00e1i c\u00e2y). V\u01b0\u01a1ng H\u1ed3ng nhanh ch\u00f3ng t\u00ecm ra l\u1eddi gi\u1ea3i: h\u00e3y tr\u1ed3ng b\u1ea3y c\u00e1i c\u00e2y theo h\u00ecnh tam gi\u00e1c \u0111\u1ec1u, v\u1edbi m\u1ed9t c\u00e2y \u1edf m\u1ed7i \u0111\u1ec9nh, m\u1ed9t c\u00e2y \u1edf trung t\u00e2m \u0111i\u1ec3m c\u1ee7a m\u1ed7i c\u1ea1nh v\u00e0 c\u00e2y th\u1ee9 b\u1ea3y \u1edf ch\u00ednh gi\u1eefa tam gi\u00e1c. C\u00e1ch s\u1eafp x\u1ebfp n\u00e0y t\u1ea1o ra s\u00e1u h\u00e0ng, m\u1ed7i h\u00e0ng g\u1ed3m \u0111\u00fang ba c\u00e2y: ba h\u00e0ng theo ba c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 ba h\u00e0ng \u0111i qua t\u00e2m. C\u00f4 \u0111\u00e3 t\u00ecm ra \u0111\u00e1p \u00e1n c\u00f2n nhanh h\u01a1n c\u1ea3 cha m\u00ecnh, v\u1ed1n l\u00e0 m\u1ed9t gi\u00e1o vi\u00ean d\u1ea1y to\u00e1n. Khi \u0111\u00f3, V\u01b0\u01a1ng H\u1ed3ng m\u1edbi 6 tu\u1ed5i.<\/p>\n

    V\u01b0\u01a1ng H\u1ed3ng d\u1ea7n y\u00eau th\u00edch to\u00e1n h\u1ecdc v\u00ec t\u00ednh b\u1ea5t bi\u1ebfn c\u1ee7a n\u00f3. L\u1ecbch s\u1eed lu\u00f4n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c vi\u1ebft l\u1ea1i; c\u00f2n vi\u1ec7c h\u1ecdc ti\u1ebfng Anh khi\u1ebfn c\u00f4 n\u1ea3n l\u00f2ng v\u00ec trong ng\u00f4n ng\u1eef n\u00e0y d\u01b0\u1eddng c\u00e1c ngo\u1ea1i l\u1ec7 c\u0169ng nhi\u1ec1u kh\u00f4ng k\u00e9m g\u00ec c\u00e1c quy t\u1eafc. Ch\u1ec9 c\u00f3 c\u00e1c \u0111\u1ecbnh l\u00fd to\u00e1n h\u1ecdc t\u1ecf ra \u0111\u00e1ng tin c\u1eady. “Ch\u1eb3ng ai c\u00f3 th\u1ec3 \u0111\u1ebfn v\u00e0 n\u00f3i: ‘\u1ed2, th\u1ef1c ra \u0111i\u1ec1u n\u00e0y kh\u00f4ng \u0111\u00fang \u0111\u00e2u'” c\u00f4 n\u00f3i.<\/p>\n

    “T\u00f4i \u0111\u00e3 g\u1eedi email cho c\u00f4 \u1ea5y v\u00e0 ch\u1ec9 vi\u1ebft: ‘Wow.'” (<\/strong><\/span>Jonathan Hickman)<\/strong><\/p>\n

    V\u01b0\u01a1ng H\u1ed3ng k\u1ec3 r\u1eb1ng c\u1ea3 cha l\u1eabn m\u1eb9 \u0111\u1ec1u mong c\u00f4 c\u00f3 m\u1ed9t cu\u1ed9c s\u1ed1ng b\u00ecnh th\u01b0\u1eddng nh\u1ea5t c\u00f3 th\u1ec3. Nh\u01b0ng b\u1ea3n th\u00e2n c\u00f4 ch\u1ec9 mu\u1ed1n h\u1ecdc<\/em> \u0111\u01b0\u1ee3c c\u00e0ng nhi\u1ec1u c\u00e0ng t\u1ed1t, v\u00ec th\u1ebf c\u00f4 \u0111\u00e3 h\u1ecdc nh\u1ea3y v\u00e0i l\u1edbp.<\/p>\n

    \u0110\u1ebfn cu\u1ed1i c\u1ea5p hai, \u0111i\u1ec3m s\u1ed1 b\u1eaft \u0111\u1ea7u tr\u1edf th\u00e0nh y\u1ebfu t\u1ed1 quy\u1ebft \u0111\u1ecbnh \u0111\u1ec3 \u0111\u01b0\u1ee3c nh\u1eadn v\u00e0o m\u1ed9t tr\u01b0\u1eddng trung h\u1ecdc t\u1ed1t \u1edf Qu\u1ebf L\u00e2m. V\u01b0\u01a1ng H\u1ed3ng \u0111\u1eb7t m\u1ee5c ti\u00eau theo h\u1ecdc ng\u00e0nh To\u00e1n t\u1ea1i \u0110\u1ea1i h\u1ecdc B\u1eafc Kinh (B\u1eafc \u0110\u1ea1i), m\u1ed9t trong nh\u1eefng tr\u01b0\u1eddng \u0111\u1ea1i h\u1ecdc danh gi\u00e1 nh\u1ea5t Trung Qu\u1ed1c. Theo c\u00f4, v\u00e0o n\u0103m 2007, khoa To\u00e1n c\u1ee7a B\u1eafc \u0110\u1ea1i ch\u1ec9 d\u00e0nh m\u1ed9t ch\u1ec9 ti\u00eau tuy\u1ec3n sinh duy nh\u1ea5t cho h\u1ecdc sinh \u0111\u1ebfn t\u1eeb t\u1ec9nh c\u1ee7a c\u00f4, d\u1ef1a tr\u00ean k\u1ebft qu\u1ea3 c\u1ee7a m\u1ed9t k\u1ef3 thi chu\u1ea9n h\u00f3a. \u0110\u00e1ng ti\u1ebfc l\u00e0 V\u01b0\u01a1ng H\u1ed3ng kh\u00f4ng ph\u1ea3i l\u00e0 ng\u01b0\u1eddi \u0111\u1ea1t \u0111i\u1ec3m cao nh\u1ea5t.<\/p>\n

    Tuy nhi\u00ean, c\u00f4 v\u1eabn \u0111\u1ea1t k\u1ebft qu\u1ea3 \u0111\u1ee7 t\u1ed1t \u0111\u1ec3 tr\u00fang tuy\u1ec3n v\u00e0o chuy\u00ean ng\u00e0nh Khoa h\u1ecdc Tr\u00e1i \u0110\u1ea5t c\u1ee7a Tr\u01b0\u1eddng v\u00e0 c\u00f4 hy v\u1ecdng c\u00f3 th\u1ec3 chuy\u1ec3n sang ng\u00e0nh To\u00e1n sau khi nh\u1eadp h\u1ecdc. Gi\u00e1o s\u01b0 \u0111\u1ecba v\u1eadt l\u00fd c\u1ee7a c\u00f4 \u0111\u00e3 \u0111\u1ed9ng vi\u00ean c\u00f4, kh\u1eb3ng \u0111\u1ecbnh t\u1ea7m quan tr\u1ecdng c\u1ee7a to\u00e1n h\u1ecdc \u0111\u1ed1i v\u1edbi khoa h\u1ecdc, ch\u1eb3ng h\u1ea1n nh\u01b0 c\u00e1ch s\u00f3ng \u0111\u1ecba ch\u1ea5n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 l\u1eadp b\u1ea3n \u0111\u1ed3 c\u1ea5u tr\u00fac b\u00ean trong Tr\u00e1i \u0110\u1ea5t (tr\u00ean th\u1ef1c t\u1ebf, \u0111\u00e2y c\u0169ng l\u00e0 th\u1ee9 to\u00e1n h\u1ecdc c\u00f3 li\u00ean quan \u0111\u1ebfn b\u00e0i to\u00e1n Kakeya, m\u1eb7c d\u00f9 l\u00fac \u0111\u00f3 V\u01b0\u01a1ng H\u1ed3ng ch\u01b0a h\u1ec1 hay bi\u1ebft). C\u00f4 \u0111\u00e3 r\u1ea5t n\u1ed7 l\u1ef1c h\u1ecdc t\u1eadp v\u00e0 cu\u1ed1i c\u00f9ng c\u0169ng \u0111\u01b0\u1ee3c ch\u1ea5p thu\u1eadn chuy\u1ec3n ng\u00e0nh. V\u01b0\u01a1ng H\u1ed3ng nh\u1edb l\u1ea1i m\u1ed9t nh\u1eadn x\u00e9t t\u00ecnh c\u1edd c\u1ee7a cha c\u00f4 r\u1eb1ng gi\u1ea3i t\u00edch, ng\u00e0nh nghi\u00ean c\u1ee9u c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng bi\u1ebfn thi\u00ean, gi\u1edbi h\u1ea1n, \u0111\u1ed9 \u0111o v\u00e0 ph\u00e9p x\u1ea5p x\u1ec9, d\u1ec5 h\u01a1n nhi\u1ec1u so v\u1edbi \u0111\u1ea1i s\u1ed1, v\u1ed1n xoay quanh c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh k\u00fd hi\u1ec7u v\u00e0 nh\u1eefng nghi\u1ec7m ch\u00ednh x\u00e1c. V\u01b0\u01a1ng H\u1ed3ng \u0111\u00e3 \u201cn\u1ed5i lo\u1ea1n\u201d b\u1eb1ng c\u00e1ch t\u1eadp trung v\u00e0o \u0111\u1ea1i s\u1ed1.<\/p>\n\"\"\n

    Khi du h\u1ecdc t\u1ea1i Ph\u00e1p, V\u01b0\u01a1ng H\u1ed3ng t\u1eebng c\u00f3 m\u1ed9t kho\u1ea3ng th\u1eddi gian ng\u1eafn chuy\u1ec3n sang h\u1ecdc ng\u00e0nh ki\u1ebfn tr\u00fac. Tuy nhi\u00ean, s\u1ee9c h\u1ea5p d\u1eabn c\u1ee7a to\u00e1n h\u1ecdc \u0111\u00e3 k\u00e9o c\u00f4 tr\u1edf l\u1ea1i v\u1edbi gi\u1ea3i t\u00edch.\u00a0\u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    \u0110i\u1ec3m s\u1ed1 c\u1ee7a V\u01b0\u01a1ng H\u1ed3ng kh\u00f4ng n\u1eb1m trong nh\u00f3m cao nh\u1ea5t v\u00e0 c\u00f4 \u0111\u00e3 t\u1eebng ho\u00e0i nghi li\u1ec7u m\u00ecnh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c nh\u1eadn v\u00e0o ch\u01b0\u01a1ng tr\u00ecnh sau \u0111\u1ea1i h\u1ecdc hay kh\u00f4ng. \u0110\u00fang l\u00fac \u0111\u00f3, \u0111\u1ea1i di\u1ec7n c\u1ee7a \u00c9cole Polytechnique, m\u1ed9t trong nh\u1eefng grandes \u00e9coles<\/em> danh gi\u00e1 v\u00e0 tuy\u1ec3n sinh kh\u1eaft khe nh\u1ea5t n\u01b0\u1edbc Ph\u00e1p, \u0111\u00e3 \u0111\u1ebfn B\u1eafc Kinh t\u1ed5 ch\u1ee9c k\u1ef3 thi tuy\u1ec3n sinh cho ch\u01b0\u01a1ng tr\u00ecnh sau c\u1eed nh\u00e2n c\u1ee7a tr\u01b0\u1eddng. N\u0103m 2011, V\u01b0\u01a1ng H\u1ed3ng sang Ph\u00e1p. T\u1ea5t c\u1ea3 c\u00e1c m\u00f4n h\u1ecdc \u0111\u1ec1u \u0111\u01b0\u1ee3c gi\u1ea3ng d\u1ea1y b\u1eb1ng ti\u1ebfng Ph\u00e1p, m\u1ed9t ng\u00f4n ng\u1eef c\u00f4 ho\u00e0n to\u00e0n kh\u00f4ng bi\u1ebft. May m\u1eafn thay, ph\u1ea7n l\u1edbn ki\u1ebfn th\u1ee9c to\u00e1n trong c\u00e1c m\u00f4n h\u1ecdc c\u1ee7a h\u1ecdc k\u1ef3 \u0111\u1ea7u ti\u00ean c\u00f4 \u0111\u1ec1u \u0111\u00e3 n\u1eafm v\u1eefng. Trong c\u00e1c b\u1eefa \u0103n, c\u00f4 ng\u1ed3i c\u00f9ng c\u00e1c b\u1ea1n h\u1ecdc n\u00f3i ti\u1ebfng Ph\u00e1p, l\u1eb7ng l\u1ebd l\u1eafng nghe, l\u1ecbch s\u1ef1 nh\u1edd gi\u1ea3i th\u00edch v\u00e0 d\u1ea7n d\u1ea7n hi\u1ec3u \u0111\u01b0\u1ee3c nhi\u1ec1u h\u01a1n. C\u00f4 theo h\u1ecdc c\u00e1c m\u00f4n gi\u1ea3i t\u00edch v\u00e0 nh\u1eadn ra r\u1eb1ng l\u0129nh v\u1ef1c n\u00e0y \u0111\u1ebfn v\u1edbi m\u00ecnh m\u1ed9t c\u00e1ch t\u1ef1 nhi\u00ean h\u01a1n so v\u1edbi \u0111\u1ea1i s\u1ed1.<\/p>\n

    M\u1eb7c d\u00f9 \u0111\u1ea1t k\u1ebft qu\u1ea3 t\u1ed1t \u1edf c\u00e1c m\u00f4n, V\u01b0\u01a1ng H\u1ed3ng v\u1eabn kh\u00f4ng tin r\u1eb1ng m\u00ecnh \u0111\u1ee7 gi\u1ecfi \u0111\u1ec3 theo \u0111u\u1ed5i nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc. C\u00f3 m\u1ed9t h\u1ecdc k\u1ef3, c\u00f4 chuy\u1ec3n sang h\u1ecdc ki\u1ebfn tr\u00fac v\u00e0 th\u1ef1c t\u1eadp t\u1ea1i m\u1ed9t c\u00f4ng ty \u1edf Paris. “T\u00f4i kh\u00f4ng ph\u1ea3i ch\u1ecbu qu\u00e1 nhi\u1ec1u \u00e1p l\u1ef1c,” c\u00f4 nh\u1edb l\u1ea1i. “Nh\u01b0ng t\u00f4i kh\u00f4ng nh\u00ecn th\u1ea5y m\u1ee5c ti\u00eau c\u1ee7a m\u00ecnh.” Cu\u1ed1i c\u00f9ng, c\u00f4 quy\u1ebft t\u00e2m quay tr\u1edf l\u1ea1i v\u1edbi to\u00e1n h\u1ecdc. “T\u00f4i quy\u1ebft \u0111\u1ecbnh ng\u1eebng lo l\u1eafng li\u1ec7u m\u00ecnh c\u00f3 \u0111\u1ee7 gi\u1ecfi hay kh\u00f4ng, m\u00e0 ch\u1ec9 t\u1eadp trung v\u00e0o vi\u1ec7c th\u1ea5u hi\u1ec3u v\u1ea5n \u0111\u1ec1 t\u1ed1t h\u01a1n.”<\/p>\n

    Nh\u1eefng t\u1eadp h\u1ee3p k\u1ef3 l\u1ea1<\/strong><\/span><\/p>\n

    V\u00e0o n\u0103m 2013, trong th\u1eddi gian th\u1ef1c t\u1eadp nghi\u00ean c\u1ee9u t\u1ea1i Vi\u1ec7n C\u00f4ng ngh\u1ec7 Massachusetts (MIT), V\u01b0\u01a1ng H\u1ed3ng tham d\u1ef1 m\u1ed9t bu\u1ed5i h\u1ed9i th\u1ea3o do nh\u00e0 gi\u1ea3i t\u00edch Larry Guth ch\u1ee7 tr\u00ec. Guth \u0111\u00e3 tr\u00ecnh b\u00e0y v\u1ec1 c\u00f4ng tr\u00ecnh m\u00e0 \u00f4ng v\u1eeba ho\u00e0n th\u00e0nh c\u00f9ng nh\u00e0 to\u00e1n h\u1ecdc Nets Katz, \u0110\u1ea1i h\u1ecdc Rice, xoay quanh b\u00e0i to\u00e1n kho\u1ea3ng c\u00e1ch kh\u00e1c bi\u1ec7t c\u1ee7a Erd\u0151s. B\u00e0i to\u00e1n \u0111\u1eb7t ra c\u00e2u h\u1ecfi: cho m\u1ed9t t\u1eadp h\u1ee3p \u0111i\u1ec3m h\u1eefu h\u1ea1n b\u1ea5t k\u1ef3 tr\u00ean m\u1eb7t ph\u1eb3ng, c\u00f3 bao nhi\u00eau kho\u1ea3ng c\u00e1ch kh\u00e1c nhau gi\u1eefa c\u00e1c c\u1eb7p \u0111i\u1ec3m? C\u00e1ch Guth gi\u1ea3i th\u00edch v\u1ea5n \u0111\u1ec1 c\u0169ng nh\u01b0 l\u1eddi gi\u1ea3i r\u00f5 r\u00e0ng \u0111\u1ebfn m\u1ee9c V\u01b0\u01a1ng H\u1ed3ng c\u1ea3m th\u1ea5y m\u00ecnh c\u00f3 th\u1ec3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c m\u1ed9t ph\u1ea7n b\u1ea3n ch\u1ee9ng minh, v\u00e0 \u0111i\u1ec1u \u0111\u00f3 \u0111\u00e3 ti\u1ebfp th\u00eam cho c\u00f4 ngu\u1ed3n \u0111\u1ed9ng l\u1ef1c m\u1ea1nh m\u1ebd. C\u00f4 c\u0169ng nh\u1eadn ra r\u1eb1ng b\u00e0i to\u00e1n n\u00e0y c\u00f3 m\u1ed1i li\u00ean h\u1ec7 m\u1eadt thi\u1ebft v\u1edbi nhi\u1ec1u b\u00e0i to\u00e1n kh\u00e1c c\u00f3 b\u1ea3n ch\u1ea5t t\u01b0\u01a1ng t\u1ef1, v\u1edbi c\u1ed1t l\u00f5i l\u00e0 h\u00ecnh h\u1ecdc li\u00ean thu\u1ed9c (incidence geometry<\/em>). N\u0103m sau, c\u00f4 tr\u00fang tuy\u1ec3n v\u00e0o ch\u01b0\u01a1ng tr\u00ecnh ti\u1ebfn s\u0129 t\u1ea1i MIT v\u00e0 ch\u1ecdn Guth l\u00e0m ng\u01b0\u1eddi h\u01b0\u1edbng d\u1eabn.<\/p>\n\"\"\n

    C\u00e1c b\u00e0i to\u00e1n d\u1ea1ng Kakeya m\u00e0 V\u01b0\u01a1ng H\u1ed3ng theo \u0111u\u1ed5i c\u00f3 m\u1ed1i li\u00ean h\u1ec7 m\u1eadt thi\u1ebft v\u1edbi gi\u1ea3i t\u00edch \u0111i\u1ec1u h\u00f2a, l\u00fd thuy\u1ebft \u0111\u1ed9 \u0111o h\u00ecnh h\u1ecdc, ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ea1o h\u00e0m ri\u00eang, c\u0169ng nh\u01b0 l\u00fd thuy\u1ebft s\u1ed1, t\u1ed5 h\u1ee3p h\u1ecdc v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c. \u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    V\u1ec1 sau, chuy\u00ean m\u00f4n c\u1ee7a c\u00f4 t\u1eadp trung v\u00e0o c\u00e1c b\u00e0i to\u00e1n d\u1ea1ng Kakeya. N\u1ed5i ti\u1ebfng nh\u1ea5t trong nh\u00f3m n\u00e0y, \u0111\u1ed3ng th\u1eddi c\u0169ng l\u00e0 n\u1ec1n t\u1ea3ng m\u00e0 nhi\u1ec1u b\u00e0i to\u00e1n kh\u00e1c ph\u1ee5 thu\u1ed9c v\u00e0o, l\u00e0 gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Kakeya (Kakeya set conjecture<\/em>). \u0110\u00e2y l\u00e0 phi\u00ean b\u1ea3n hi\u1ec7n \u0111\u1ea1i c\u1ee7a m\u1ed9t c\u00e2u h\u1ecfi do nh\u00e0 to\u00e1n h\u1ecdc S\u014dichi Kakeya, \u0110\u1ea1i h\u1ecdc Tohoku n\u00eau ra v\u00e0o n\u0103m 1917. \u00d4ng t\u1ef1 h\u1ecfi: khi xoay m\u1ed9t c\u00e2y kim theo m\u1ecdi h\u01b0\u1edbng tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng, di\u1ec7n t\u00edch nh\u1ecf nh\u1ea5t m\u00e0 c\u00e2y kim qu\u00e9t qua l\u00e0 bao nhi\u00eau? N\u1ebfu ch\u1ec9 xoay c\u00e2y kim quanh trung \u0111i\u1ec3m c\u1ee7a n\u00f3, v\u00f9ng qu\u00e9t \u0111\u01b0\u1ee3c s\u1ebd l\u00e0 m\u1ed9t h\u00ecnh tr\u00f2n. Nh\u01b0ng Kakeya nh\u1eadn ra r\u1eb1ng, n\u1ebfu v\u1eeba xoay v\u1eeba t\u1ecbnh ti\u1ebfn c\u00e2y kim \u2014 gi\u1ed1ng nh\u01b0 m\u1ed9t chi\u1ebfc \u00f4 t\u00f4 th\u1ef1c hi\u1ec7n c\u00fa quay \u0111\u1ea7u ba \u0111i\u1ec3m \u2014 th\u00ec c\u00f3 th\u1ec3 gi\u1eef to\u00e0n b\u1ed9 chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a c\u00e2y kim trong m\u1ed9t v\u00f9ng ch\u1ec9 b\u1eb1ng kho\u1ea3ng m\u1ed9t n\u1eeda di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n, t\u1ea1o th\u00e0nh m\u1ed9t h\u00ecnh g\u1ecdi l\u00e0 deltoid (\u0111\u01b0\u1eddng cong delta ho\u1eb7c tam gi\u00e1c cong Steiner)<\/p>\n

    \nhttps:\/\/rosetta.vn\/nguyenxuanxanh\/wp-content\/uploads\/sites\/6\/2026\/08\/Kakeya-Set-1.mp4<\/a><\/video><\/div>\n

     <\/p>\n

    V\u00e0i n\u0103m sau, nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi Nga, sau n\u00e0y l\u00e0m vi\u1ec7c t\u1ea1i Cambridge, Abram Besicovitch \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng k\u1ebft qu\u1ea3 c\u00f2n c\u00f3 th\u1ec3 g\u00e2y kinh ng\u1ea1c h\u01a1n nhi\u1ec1u. Trong m\u1ed9t phi\u00ean b\u1ea3n tr\u1eebu t\u01b0\u1ee3ng c\u1ee7a b\u00e0i to\u00e1n, ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 h\u01b0\u1edbng c\u00e2y kim theo m\u1ecdi h\u01b0\u1edbng m\u00e0 kh\u00f4ng qu\u00e9t qua b\u1ea5t k\u1ef3 di\u1ec7n t\u00edch n\u00e0o.\u00a0\u1ede \u0111\u00e2y kh\u00f4ng c\u00f2n c\u00e2y kim chuy\u1ec3n \u0111\u1ed9ng n\u1eefa, m\u00e0 thay v\u00e0o \u0111\u00f3 l\u00e0 m\u1ed9t t\u1eadp v\u00f4 h\u1ea1n c\u00e1c \u0111o\u1ea1n th\u1eb3ng, m\u1ed7i \u0111o\u1ea1n \u1ee9ng v\u1edbi m\u1ed9t h\u01b0\u1edbng m\u00e0 c\u00e2y kim c\u00f3 th\u1ec3 ch\u1ec9 t\u1edbi tr\u00ean m\u1eb7t ph\u1eb3ng. T\u1eadp h\u1ee3p \u1ea5y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1eadp h\u1ee3p Kakeya (Kakeya set<\/em>).\u00a0N\u1ebfu gi\u1eef nguy\u00ean h\u01b0\u1edbng c\u1ee7a t\u1eebng \u0111o\u1ea1n th\u1eb3ng nh\u01b0ng cho ph\u00e9p t\u1ecbnh ti\u1ebfn ch\u00fang, ta c\u00f3 th\u1ec3 s\u1eafp x\u1ebfp ch\u00fang v\u00e0o m\u1ed9t v\u00f9ng c\u00f3 di\u1ec7n t\u00edch ng\u00e0y c\u00e0ng nh\u1ecf. Besicovitch ch\u1ee9ng minh r\u1eb1ng, tr\u00ean th\u1ef1c t\u1ebf, c\u00e1c \u0111o\u1ea1n th\u1eb3ng \u1ea5y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c n\u00e9n v\u00e0o m\u1ed9t t\u1eadp h\u1ee3p c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng kh\u00f4ng.\u00a0Nh\u01b0ng \u0111i\u1ec1u \u0111\u00f3 \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n nh\u01b0 th\u1ebf n\u00e0o?\u00a0M\u1ed9t tam gi\u00e1c \u0111\u1ec1u c\u0169ng c\u00f3 th\u1ec3 ch\u1ee9a m\u1ed9t t\u1eadp h\u1ee3p Kakeya, t\u01b0\u01a1ng t\u1ef1 nh\u01b0 h\u00ecnh deltoid nh\u01b0ng c\u00f3 di\u1ec7n t\u00edch l\u1edbn h\u01a1n. H\u00e3y h\u00ecnh dung c\u1eaft \u0111\u00f4i tam gi\u00e1c \u1ea5y theo m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua \u0111\u1ec9nh v\u00e0 trung \u0111i\u1ec3m c\u1ea1nh \u0111\u00e1y, r\u1ed3i t\u1ecbnh ti\u1ebfn (kh\u00f4ng xoay) m\u1ed9t n\u1eeda sao cho n\u00f3 ch\u1ed3ng l\u1ea5n l\u00ean n\u1eeda c\u00f2n l\u1ea1i nhi\u1ec1u nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n

    \"\"<\/p>\n

    Ti\u1ebfp theo, l\u1ea1i c\u1eaft \u0111\u00f4i m\u1ed7i n\u1eeda c\u1ee7a tam gi\u00e1c ban \u0111\u1ea7u v\u00e0 ti\u1ebfp t\u1ee5c t\u1ecbnh ti\u1ebfn c\u00e1c ph\u1ea7n v\u1eeba t\u1ea1o ra \u0111\u1ec3 m\u1ee9c \u0111\u1ed9 ch\u1ed3ng l\u1ea5n \u0111\u1ea1t l\u1edbn \u0111\u1ed9 l\u1edbn nh\u1ea5t. B\u1eb1ng c\u00e1ch \u0111\u00f3, c\u00e1c \u0111o\u1ea1n th\u1eb3ng l\u1ea1i \u0111\u01b0\u1ee3c n\u00e9n v\u00e0o m\u1ed9t v\u00f9ng c\u00f3 di\u1ec7n t\u00edch nh\u1ecf h\u01a1n n\u1eefa.<\/p>\n\"\"\n

    L\u1eb7p \u0111i l\u1eb7p l\u1ea1i quy tr\u00ecnh n\u00e0y \u0111\u1ebfn v\u00f4 h\u1ea1n, li\u00ean t\u1ee5c tr\u01b0\u1ee3t c\u00e1c \u0111o\u1ea1n th\u1eb3ng qua l\u1ea1i theo m\u1ed9t k\u1ef9 thu\u1eadt h\u00ecnh h\u1ecdc g\u1ecdi l\u00e0 kh\u1edbp n\u1ed1i P\u00e1l (P\u00e1l joint<\/em>), r\u1ed3i xoay tam gi\u00e1c \u0111\u1ec3 l\u1eb7p l\u1ea1i quy tr\u00ecnh t\u1eeb m\u1ed7i \u0111\u1ec9nh. Gh\u00e9p t\u1ea5t c\u1ea3 c\u00e1c k\u1ebft qu\u1ea3 l\u1ea1i, ta s\u1ebd thu \u0111\u01b0\u1ee3c m\u1ed9t t\u1eadp h\u1ee3p ch\u1ee9a c\u00e1c \u0111o\u1ea1n th\u1eb3ng theo m\u1ecdi h\u01b0\u1edbng, nh\u01b0ng c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng kh\u00f4ng. Besicovitch c\u00f2n ch\u1ec9 ra r\u1eb1ng hi\u1ec7n t\u01b0\u1ee3ng n\u00e0y c\u0169ng \u0111\u00fang trong kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u h\u01a1n. Ch\u1eb3ng h\u1ea1n, m\u1ed9t t\u1eadp h\u1ee3p Kakeya g\u1ed3m c\u00e1c \u0111o\u1ea1n th\u1eb3ng h\u01b0\u1edbng theo m\u1ecdi ph\u01b0\u01a1ng trong kh\u00f4ng gian ba chi\u1ec1u v\u1eabn c\u00f3 th\u1ec3 c\u00f3 th\u1ec3 t\u00edch b\u1eb1ng kh\u00f4ng.<\/p>\n

    \"\"<\/p>\n

    Th\u1ebf nh\u01b0ng, d\u00f9 kh\u00f4ng c\u00f3 di\u1ec7n t\u00edch hay th\u1ec3 t\u00edch, nh\u1eefng t\u1eadp h\u1ee3p k\u1ef3 l\u1ea1 \u0111\u1ea7y nh\u1eefng “gai nh\u1ecdn” n\u00e0y v\u1eabn chi\u1ebfm m\u1ed9t ph\u1ea7n kh\u00f4ng gian. C\u00e1c \u0111o\u1ea1n th\u1eb3ng trong t\u1eadp h\u1ee3p Kakeya kh\u00f4ng h\u1ec1 b\u1ecb \u00e9p l\u1ea1i th\u00e0nh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng m\u1ed9t chi\u1ec1u; ch\u00fang v\u1eabn h\u01b0\u1edbng theo m\u1ecdi h\u01b0\u1edbng. V\u1ea5n \u0111\u1ec1 \u0111\u1eb7t ra l\u00e0: m\u1ed9t t\u1eadp h\u1ee3p Kakeya th\u1ef1c s\u1ef1 chi\u1ebfm bao nhi\u00eau kh\u00f4ng gian? N\u00f3i theo ng\u00f4n ng\u1eef to\u00e1n h\u1ecdc, c\u00e2u h\u1ecfi \u1ea5y l\u00e0: M\u1ed9t t\u1eadp h\u1ee3p Kakeya c\u00f3 bao nhi\u00eau chi\u1ec1u?<\/p>\n

    M\u1ed9t ph\u01b0\u01a1ng ph\u00e1p th\u1ef1c nghi\u1ec7m \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh s\u1ed1 chi\u1ec1u c\u1ee7a m\u1ed9t v\u1eadt th\u1ec3 l\u00e0 t\u01b0\u1edfng t\u01b0\u1ee3ng ph\u1ee7 k\u00edn n\u00f3 b\u1eb1ng nh\u1eefng \u00f4 l\u1eadp ph\u01b0\u01a1ng r\u1ea5t nh\u1ecf c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc, r\u1ed3i \u0111\u1ebfm xem c\u1ea7n bao nhi\u00eau \u00f4. S\u1ed1 l\u01b0\u1ee3ng \u00f4 c\u1ea7n d\u00f9ng ph\u1ee5 thu\u1ed9c v\u00e0o k\u00edch th\u01b0\u1edbc c\u1ee7a ch\u00fang, nh\u01b0ng s\u1ed1 chi\u1ec1u c\u1ee7a \u0111\u1ed1i t\u01b0\u1ee3ng l\u1ea1i \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi c\u00e1ch s\u1ed1 l\u01b0\u1ee3ng \u1ea5y thay \u0111\u1ed5i khi k\u00edch th\u01b0\u1edbc c\u00e1c \u00f4 ng\u00e0y c\u00e0ng nh\u1ecf \u0111i.\u00a0V\u00ed d\u1ee5, \u0111\u1ec3 ph\u1ee7 k\u00edn m\u1ed9t \u0111\u1ed1i t\u01b0\u1ee3ng m\u1ed9t chi\u1ec1u, ch\u1eb3ng h\u1ea1n m\u1ed9t \u0111o\u1ea1n th\u1eb3ng, s\u1ed1 \u00f4 c\u1ea7n d\u00f9ng t\u1ef7 l\u1ec7 v\u1edbi 1\/r<\/em>, trong \u0111\u00f3 r l\u00e0 b\u1ec1 r\u1ed9ng c\u1ee7a m\u1ed7i \u00f4. \u0110\u1ed1i v\u1edbi m\u1ed9t \u0111\u1ed1i t\u01b0\u1ee3ng hai chi\u1ec1u, s\u1ed1 \u00f4 t\u1ef7 l\u1ec7 v\u1edbi 1\/r<\/em>\u00b2. \u0110\u1ed1i v\u1edbi m\u1ed9t \u0111\u1ed1i t\u01b0\u1ee3ng ba chi\u1ec1u, con s\u1ed1 \u1ea5y l\u00e0 1\/r<\/em>\u00b3. V\u00e0 c\u1ee9 ti\u1ebfp t\u1ee5c nh\u01b0 v\u1eady.<\/p>\n

    Tuy nhi\u00ean, s\u1ed1 m\u0169 \u0111\u00f3 kh\u00f4ng ph\u1ea3i l\u00fac n\u00e0o c\u0169ng tr\u00f9ng v\u1edbi s\u1ed1 chi\u1ec1u quen thu\u1ed9c c\u1ee7a kh\u00f4ng gian m\u00e0 v\u1eadt th\u1ec3 t\u1ed3n t\u1ea1i trong \u0111\u00f3. H\u00e3y l\u1ea5y h\u00ecnh ph\u00e2n d\u1ea1ng (fractals<\/em>) l\u00e0m v\u00ed d\u1ee5 \u2014 nh\u1eefng \u0111\u1ed1i t\u01b0\u1ee3ng ng\u00e0y c\u00e0ng b\u1ed9c l\u1ed9 nhi\u1ec1u chi ti\u1ebft h\u01a1n khi ta ph\u00f3ng to, ch\u1eb3ng h\u1ea1n \u0111\u01b0\u1eddng cong Koch hay b\u00f4ng tuy\u1ebft Koch.\u00a0Trong nh\u1eefng tr\u01b0\u1eddng h\u1ee3p n\u00e0y, c\u00e1c \u00f4 c\u00e0ng nh\u1ecf th\u00ec c\u00e0ng c\u00f3 nhi\u1ec1u c\u1ea5u tr\u00fac \u0111\u1ec3 ch\u00fang x\u1ebfp d\u1ecdc theo, do \u0111\u00f3 ch\u00fang tu\u00e2n theo quy lu\u1eadt t\u1ef7 l\u1ec7 kh\u00e1c bi\u1ec7t. S\u1ed1 m\u0169 c\u1ee7a r<\/em> tr\u1edf th\u00e0nh m\u1ed9t ph\u00e2n s\u1ed1, ph\u1ea3n \u00e1nh l\u01b0\u1ee3ng c\u1ea5u tr\u00fac m\u1edbi xu\u1ea5t hi\u1ec7n khi ta ph\u00f3ng to h\u00ecnh \u1ea3nh. Do \u0111\u00f3, c\u00e1c fractal nh\u01b0 \u0111\u01b0\u1eddng cong Koch hay b\u00f4ng tuy\u1ebft Koch, v\u1edbi ph\u1ea7n r\u00eca c\u00f3 \u0111\u1ed9 chi ti\u1ebft v\u00f4 h\u1ea1n, n\u1eb1m \u1edf \u0111\u00e2u \u0111\u00f3 gi\u1eefa c\u00e1c s\u1ed1 chi\u1ec1u nguy\u00ean.<\/p>\n

    \"\"<\/p>\n

    C\u1ed1t l\u00f5i c\u1ee7a gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Kakeya l\u00e0 c\u00e2u h\u1ecfi li\u1ec7u nh\u1eefng t\u1eadp h\u1ee3p n\u00e0y c\u00f3 th\u1ef1c s\u1ef1 chi\u1ebfm tr\u1ecdn s\u1ed1 chi\u1ec1u c\u1ee7a kh\u00f4ng gian m\u00e0 c\u00e1c \u0111o\u1ea1n th\u1eb3ng trong \u0111\u00f3 h\u01b0\u1edbng t\u1edbi m\u1ecdi ph\u01b0\u01a1ng hay kh\u00f4ng. N\u00f3i c\u00e1ch kh\u00e1c, li\u1ec7u m\u1ed9t t\u1eadp h\u1ee3p Kakeya g\u1ed3m c\u00e1c \u0111o\u1ea1n th\u1eb3ng h\u01b0\u1edbng theo m\u1ecdi ph\u01b0\u01a1ng tr\u00ean m\u1eb7t ph\u1eb3ng c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t v\u1eadt th\u1ec3 2D, c\u00f2n m\u1ed9t t\u1eadp h\u1ee3p Kakeya g\u1ed3m c\u00e1c \u0111o\u1ea1n th\u1eb3ng h\u01b0\u1edbng theo m\u1ecdi ph\u01b0\u01a1ng trong kh\u00f4ng gian c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t v\u1eadt th\u1ec3 3D, v\u00e0 t\u01b0\u01a1ng t\u1ef1 nh\u01b0 v\u1eady \u0111\u1ed1i v\u1edbi c\u00e1c s\u1ed1 chi\u1ec1u cao h\u01a1n.<\/p>\n

    Theo ngh\u0129a n\u00e0y, c\u00e1c t\u1eadp h\u1ee3p Kakeya c\u00f3 h\u00e0nh x\u1eed gi\u1ed1ng nh\u01b0 nh\u1eefng v\u1eadt th\u1ec3 \u0111\u1eb7c, m\u1eb7c d\u00f9 Besicovitch \u0111\u00e3 ch\u1ec9 ra r\u1eb1ng ch\u00fang ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 kh\u00f4ng c\u00f3 di\u1ec7n t\u00edch ho\u1eb7c th\u1ec3 t\u00edch.\u00a0Kh\u00f4ng ai bi\u1ebft ch\u00ednh x\u00e1c gi\u1ea3 thuy\u1ebft n\u00e0y \u0111\u01b0\u1ee3c ai n\u00eau ra \u0111\u1ea7u ti\u00ean ho\u1eb7c xu\u1ea5t hi\u1ec7n t\u1eeb khi n\u00e0o. Tuy nhi\u00ean, v\u00e0o n\u0103m 1971, nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi Anh Roy Davies \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng gi\u1ea3 thuy\u1ebft \u0111\u00fang trong tr\u01b0\u1eddng h\u1ee3p 2D. Phi\u00ean b\u1ea3n t\u01b0\u01a1ng \u1ee9ng trong kh\u00f4ng gian ba chi\u1ec1u v\u1ec1 sau \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ebfn v\u1edbi t\u00ean g\u1ecdi gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Kakeya ba chi\u1ec1u (3D Kakeya set conjecture<\/em>).\u00a0N\u1ebfu gi\u1ea3 thuy\u1ebft n\u00e0y b\u1ecb b\u00e1c b\u1ecf, \u0111i\u1ec1u \u0111\u00f3 s\u1ebd c\u00f3 ngh\u0129a r\u1eb1ng c\u00e1c \u0111o\u1ea1n th\u1eb3ng trong m\u1ed9t t\u1eadp h\u1ee3p Kakeya, d\u00f9 v\u1eabn h\u01b0\u1edbng theo m\u1ecdi ph\u01b0\u01a1ng, v\u1eabn c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp kh\u00e9o l\u00e9o \u0111\u1ebfn m\u1ee9c t\u1eadp h\u1ee3p \u1ea5y h\u00e0nh x\u1eed gi\u1ed1ng m\u1ed9t fractal h\u01a1n l\u00e0 m\u1ed9t v\u1eadt th\u1ec3 \u0111\u1eb7c \u2014 ngh\u0129a l\u00e0 n\u00f3 c\u00f3 s\u1ed1 chi\u1ec1u nh\u1ecf h\u01a1n s\u1ed1 chi\u1ec1u c\u1ee7a ch\u00ednh kh\u00f4ng gian m\u00e0 n\u00f3 t\u1ed3n t\u1ea1i trong \u0111\u00f3.<\/p>\n

    Do t\u1eadp h\u1ee3p Kakeya \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh t\u1eeb c\u00e1c \u0111o\u1ea1n th\u1eb3ng, c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 h\u00ecnh dung nh\u1eefng “chi\u1ebfc h\u1ed9p” d\u00f9ng \u0111\u1ec3 \u0111o s\u1ed1 chi\u1ec1u nh\u01b0 \u0111\u01b0\u1ee3c k\u00e9o d\u00e0i v\u00e0 gh\u00e9p l\u1ea1i th\u00e0nh nh\u1eefng \u1ed1ng d\u00e0i, m\u1ea3nh (long, thin tubes<\/em>).\u00a0Khi \u0111\u00f3, c\u00e2u h\u1ecfi tr\u1edf th\u00e0nh: s\u1ed1 l\u01b0\u1ee3ng c\u00e1c \u1ed1ng c\u1ea7n \u0111\u1ec3 ph\u1ee7 k\u00edn m\u1ed9t t\u1eadp h\u1ee3p Kakeya s\u1ebd thay \u0111\u1ed5i nh\u01b0 th\u1ebf n\u00e0o khi \u0111\u1ed9 d\u00e0y c\u1ee7a c\u00e1c \u1ed1ng ng\u00e0y c\u00e0ng nh\u1ecf \u0111i? Gi\u1ea3 thuy\u1ebft v\u1ec1 t\u1eadp h\u1ee3p Kakeya kh\u1eb3ng \u0111\u1ecbnh r\u1eb1ng quy lu\u1eadt thay \u0111\u1ed5i \u1ea5y gi\u1ed1ng h\u1ec7t nh\u01b0 \u0111\u1ed1i v\u1edbi b\u1ea5t k\u1ef3 v\u1eadt th\u1ec3 ba chi\u1ec1u th\u00f4ng th\u01b0\u1eddng n\u00e0o.\u00a0Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu c\u00e1c t\u1eadp h\u1ee3p Kakeya ch\u1ec9 chi\u1ebfm m\u1ed9t ph\u1ea7n s\u1ed1 chi\u1ec1u \u0111\u1ea7y \u0111\u1ee7 c\u1ee7a kh\u00f4ng gian, th\u00ec \u1edf nh\u1eefng thang \u0111o ng\u00e0y c\u00e0ng nh\u1ecf, ng\u01b0\u1eddi ta s\u1ebd ph\u00e1t hi\u1ec7n ng\u00e0y c\u00e0ng nhi\u1ec1u c\u1ea5u tr\u00fac tinh vi h\u01a1n \u2014 t\u1ee9c ng\u00e0y c\u00e0ng c\u00f3 nhi\u1ec1u \u0111o\u1ea1n th\u1eb3ng t\u1eadp trung d\u00e0y \u0111\u1eb7c trong nh\u1eefng v\u00f9ng r\u1ea5t nh\u1ecf.<\/p>\n\"\"\n

    V\u01b0\u01a1ng H\u1ed3ng tr\u00f2 chuy\u1ec7n c\u00f9ng nh\u00e0 to\u00e1n h\u1ecdc Frank Merle trong l\u00fac d\u00f9ng tr\u00e0. Tr\u01b0\u1edbc khi ch\u1ee9ng minh \u0111\u01b0\u1ee3c gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Kakeya trong kh\u00f4ng gian ba chi\u1ec1u, t\u00ean tu\u1ed5i c\u1ee7a c\u00f4 ng\u00e0y c\u00e0ng \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ebfn qua m\u1ed9t chu\u1ed7i c\u00e1c c\u00f4ng tr\u00ecnh h\u1ee3p t\u00e1c mang l\u1ea1i nh\u1eefng k\u1ebft qu\u1ea3 t\u1ea1o ti\u1ebfng vang l\u1edbn.\u00a0\u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/em><\/p>\n

    S\u1ef1 quan t\u00e2m \u0111\u1ed1i v\u1edbi gi\u1ea3 thuy\u1ebft Kakeya ba chi\u1ec1u b\u00f9ng n\u1ed5 v\u00e0o th\u1eadp ni\u00ean 1970, khi nh\u00e0 to\u00e1n h\u1ecdc Charles Fefferman t\u1eeb \u0110\u1ea1i h\u1ecdc Princeton ch\u1ee9ng minh \u0111\u01b0\u1ee3c r\u1eb1ng n\u00f3 c\u00f3 m\u1ed1i li\u00ean h\u1ec7 m\u1eadt thi\u1ebft v\u1edbi m\u1ed9t hi\u1ec7n t\u01b0\u1ee3ng to\u00e1n h\u1ecdc m\u1ea1nh m\u1ebd mang t\u00ean ph\u00e9p bi\u1ebfn \u0111\u1ed5i Fourier (Fourier transformation<\/em>). Th\u00f4ng qua ph\u00e9p bi\u1ebfn \u0111\u1ed5i n\u00e0y, b\u1ea5t k\u1ef3 t\u00edn hi\u1ec7u hay h\u00e0m s\u1ed1 n\u00e0o c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n t\u00edch th\u00e0nh c\u00e1c s\u00f3ng h\u00ecnh sin v\u1edbi \u0111\u1ee7 lo\u1ea1i t\u1ea7n s\u1ed1 v\u00e0 ph\u01b0\u01a1ng h\u01b0\u1edbng kh\u00e1c nhau. M\u1ed9t trong nh\u1eefng b\u00e0i to\u00e1n l\u1edbn ch\u01b0a c\u00f3 l\u1eddi gi\u1ea3i c\u1ee7a gi\u1ea3i t\u00edch Fourier (hay c\u00f2n g\u1ecdi l\u00e0 gi\u1ea3i t\u00edch \u0111i\u1ec1u h\u00f2a) ch\u00ednh l\u00e0: \u0111i\u1ec1u g\u00ec s\u1ebd x\u1ea3y ra khi c\u00e1c s\u00f3ng n\u00e0y \u0111\u1ec1u c\u00f3 chung b\u01b0\u1edbc s\u00f3ng nh\u01b0ng l\u1ea1i lan truy\u1ec1n theo nh\u1eefng ph\u01b0\u01a1ng kh\u00e1c nhau? Chuy\u1ec7n g\u00ec s\u1ebd x\u1ea3y ra v\u1edbi t\u00edn hi\u1ec7u t\u1ed5ng h\u1ee3p t\u1ea1i v\u00f9ng ch\u00fang t\u01b0\u01a1ng t\u00e1c? Gi\u1ea3 thuy\u1ebft gi\u1edbi h\u1ea1n Fourier (restriction conjecture) ph\u1ecfng \u0111o\u00e1n r\u1eb1ng trong tr\u01b0\u1eddng h\u1ee3p \u0111\u00f3, t\u00edn hi\u1ec7u t\u1ed5ng h\u1ee3p ph\u1ea3i lan t\u1ecfa r\u1ea5t r\u1ed9ng trong kh\u00f4ng gian v\u00e0 c\u00f3 \u0111\u1ed9 khu\u1ebfch t\u00e1n cao. \u00a0Do c\u00e1c t\u1ea7n s\u1ed1 th\u00e0nh ph\u1ea7n \u0111\u1ec1u di chuy\u1ec3n theo nh\u1eefng h\u01b0\u1edbng l\u1ec7ch \u0111i \u0111\u00f4i ch\u00fat, ch\u00fang kh\u00f4ng th\u1ec3 ch\u1ed3ng l\u1ea5n v\u00e0 giao thoa t\u0103ng c\u01b0\u1eddng v\u1edbi nhau \u0111\u1ee7 m\u1ea1nh \u0111\u1ec3 t\u1ea1o n\u00ean m\u1ed9t s\u00f3ng hay t\u00edn hi\u1ec7u t\u1eadp trung cao \u0111\u1ed9. \u0110\u00e2y l\u00e0 m\u1ed9t v\u1ea5n \u0111\u1ec1 c\u00f3 \u00fd ngh\u0129a quan tr\u1ecdng trong k\u1ef9 thu\u1eadt x\u1eed l\u00fd t\u00edn hi\u1ec7u v\u00e0 t\u1ea1o \u1ea3nh.<\/p>\n

    “C\u00f3 th\u1ec3 h\u00ecnh dung r\u1eb1ng m\u1ed7i s\u00f3ng n\u1eb1m trong m\u1ed9t \u1ed1ng d\u00e0i v\u00e0 m\u1ea3nh,” V\u01b0\u01a1ng H\u1ed3ng gi\u1ea3i th\u00edch. C\u00e2u h\u1ecfi l\u00e0: Li\u1ec7u ch\u00fang c\u00f3 ch\u1ed3ng l\u1ea5n l\u00ean nhau nhi\u1ec1u, l\u00e0m t\u1eadp trung t\u00edn hi\u1ec7u, hay kh\u00f4ng?<\/p>\n

    M\u1ed9t t\u00ecnh th\u1ebf l\u1eafc l\u00e9o (sticky situation, sticky m\u01b0\u1ee3n t\u1eeb to\u00e1n h\u1ecdc Kakeya c\u00f3 ngh\u0129a \u2018d\u00ednh\u201d, sticky set, ch\u01a1i ch\u1eef)<\/strong><\/span><\/p>\n

    V\u00e0i n\u0103m sau khi \u0111\u1ebfn MIT, V\u01b0\u01a1ng H\u1ed3ng b\u1eaft \u0111\u1ea7u t\u1eebng b\u01b0\u1edbc chinh ph\u1ee5c nh\u1eefng b\u00e0i to\u00e1n c\u00f3 h\u1ecd h\u00e0ng v\u1edbi b\u00e0i to\u00e1n Kakeya, c\u00f9ng v\u1edbi Larry Guth v\u00e0 c\u00e1c c\u1ed9ng s\u1ef1 kh\u00e1c. Ch\u1ec9 trong v\u00f2ng m\u1ed9t n\u0103m, h\u1ecd \u0111\u00e3 gi\u1ea3i \u0111\u01b0\u1ee3c m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a b\u00e0i to\u00e1n kho\u1ea3ng c\u00e1ch Falconer, m\u1ed9t bi\u1ebfn th\u1ec3 h\u00f3c b\u00faa h\u01a1n c\u1ee7a b\u00e0i to\u00e1n kho\u1ea3ng c\u00e1ch m\u00e0 Guth t\u1eebng gi\u1ea3i v\u1edbi Nets Katz. V\u01b0\u01a1ng H\u1ed3ng c\u0169ng \u0111\u1ea1t \u0111\u01b0\u1ee3c nh\u1eefng b\u01b0\u1edbc ti\u1ebfn quan tr\u1ecdng \u0111\u1ed1i v\u1edbi gi\u1ea3 thuy\u1ebft gi\u1edbi h\u1ea1n Fourier b\u1eb1ng c\u00e1ch \u0111\u1ecbnh h\u00ecnh l\u1ea1i n\u00f3 b\u1eb1ng ng\u00f4n ng\u1eef h\u00ecnh h\u1ecdc li\u00ean thu\u1ed9c. Jonathan Hickman, nh\u00e0 to\u00e1n h\u1ecdc t\u1ea1i \u0110\u1ea1i h\u1ecdc Edinburgh, nh\u1eadn x\u00e9t: “R\u1ea5t hi\u1ebfm khi c\u00f3 ai \u0111\u01b0a ra \u0111\u01b0\u1ee3c \u0111i\u1ec1u g\u00ec m\u1edbi m\u1ebb v\u1ec1 b\u00e0i to\u00e1n n\u00e0y, b\u1edfi n\u00f3 qu\u00e1 kh\u00f3. V\u00ec v\u1eady, vi\u1ec7c m\u1ed9t nghi\u00ean c\u1ee9u sinh ti\u1ebfn s\u0129 l\u1ea1i l\u00e0m \u0111\u01b0\u1ee3c \u0111i\u1ec1u \u0111\u00f3 qu\u1ea3 th\u1eadt r\u1ea5t \u0111\u00e1ng kinh ng\u1ea1c.”<\/p>\n

    “T\u00f4i \u0111\u00e3 g\u1eedi email cho c\u00f4 \u1ea5y v\u00e0 ch\u1ec9 vi\u1ebft m\u1ed9t t\u1eeb: ‘Wow.'”<\/p>\n\"\"\n

    “T\u00f4i quy\u1ebft \u0111\u1ecbnh kh\u00f4ng c\u00f2n b\u1eadn t\u00e2m li\u1ec7u m\u00ecnh c\u00f3 \u0111\u1ee7 gi\u1ecfi hay kh\u00f4ng, m\u00e0 ch\u1ec9 t\u1eadp trung v\u00e0o vi\u1ec7c hi\u1ec3u v\u1ea5n \u0111\u1ec1 ng\u00e0y m\u1ed9t s\u00e2u h\u01a1n,” V\u01b0\u01a1ng H\u1ed3ng chia s\u1ebb.\u00a0\u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    Pablo Shmerkin, nh\u00e0 to\u00e1n h\u1ecdc t\u1eeb \u0110\u1ea1i h\u1ecdc British Columbia, ng\u01b0\u1eddi c\u0169ng \u0111\u00e3 t\u1eebng nghi\u00ean c\u1ee9u v\u1ec1 b\u00e0i to\u00e1n kho\u1ea3ng c\u00e1ch Falconer, \u0111\u00e3 ph\u00e1t hi\u1ec7n ra t\u00e0i n\u0103ng c\u1ee7a V\u01b0\u01a1ng H\u1ed3ng trong m\u1ed9t l\u1ea7n \u0111\u1ebfn th\u0103m Larry Guth t\u1ea1i MIT. Trong m\u1eaft \u00f4ng, c\u00f4 l\u00e0 m\u1ed9t ng\u01b0\u1eddi gi\u00e0u \u00f3c s\u00e1ng t\u1ea1o v\u00e0 c\u00f3 kh\u1ea3 n\u0103ng ti\u1ebfp thu nh\u1eefng k\u1ef9 thu\u1eadt m\u1ed9t c\u00e1ch nhanh ch\u00f3ng. D\u00f9 ch\u1ec9 m\u1edbi chuy\u1ec3n sang nghi\u00ean c\u1ee9u h\u00ecnh h\u1ecdc li\u00ean thu\u1ed9c ch\u01b0a l\u00e2u, c\u00f4 d\u01b0\u1eddng nh\u01b0 \u0111\u00e3 am hi\u1ec3u l\u0129nh v\u1ef1c n\u00e0y m\u1ed9t c\u00e1ch s\u00e2u s\u1eafc.<\/p>\n

    L\u0129nh v\u1ef1c nghi\u00ean c\u1ee9u n\u00e0y v\u1ed1n \u0111\u00e3 s\u1edf h\u1eefu m\u1ed9t kho c\u00f4ng c\u1ee5 phong ph\u00fa v\u00e0 ch\u1eb3ng l\u00e2u sau, V\u01b0\u01a1ng H\u1ed3ng c\u00f2n \u0111\u01b0a th\u00eam v\u00e0o \u0111\u00f3 nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p m\u1edbi t\u1eeb l\u00fd thuy\u1ebft \u0111\u1ed9 \u0111o h\u00ecnh h\u1ecdc, nh\u1eefng k\u1ef9 thu\u1eadt c\u00f4 ti\u1ebfp thu \u0111\u01b0\u1ee3c trong qu\u00e1 tr\u00ecnh h\u1ee3p t\u00e1c v\u1edbi Shmerkin v\u1ec1 b\u00e0i to\u00e1n t\u1eadp h\u1ee3p kho\u1ea3ng c\u00e1ch Falconer. C\u00f4 \u0111\u1eb7c bi\u1ec7t \u0111\u01b0\u1ee3c truy\u1ec1n c\u1ea3m h\u1ee9ng t\u1eeb ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch \u0111a thang (multiscale analysis<\/em>) c\u1ee7a Shmerkin, m\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn so s\u00e1nh hi\u1ec7n t\u01b0\u1ee3ng \u1edf nh\u1eefng thang \u0111o kh\u00e1c nhau \u0111\u1ec3 t\u1eeb \u0111\u00f3 t\u00ecm ra nh\u1eefng m\u00e2u thu\u1eabn. Shmerkin n\u00f3i: “C\u00f4 \u1ea5y lu\u00f4n r\u1ea5t t\u1eed t\u1ebf v\u00e0 ghi nh\u1eadn r\u1eb1ng m\u1ed9t s\u1ed1 \u00fd t\u01b0\u1edfng b\u1eaft ngu\u1ed3n t\u1eeb c\u00f4ng tr\u00ecnh c\u1ee7a t\u00f4i, nh\u01b0ng c\u00f4 \u1ea5y c\u00f3 th\u1ec3 v\u1eadn d\u1ee5ng ch\u00fang theo nh\u1eefng c\u00e1ch tuy\u1ec7t v\u1eddi \u0111\u1ebfn m\u1ee9c ch\u00ednh t\u00f4i c\u0169ng ch\u01b0a t\u1eebng h\u00ecnh dung ra.”<\/p>\n

    Danh ti\u1ebfng c\u1ee7a V\u01b0\u01a1ng H\u1ed3ng ti\u1ebfp t\u1ee5c vang xa khi v\u00e0o n\u0103m 2019, c\u00f4 c\u00f9ng Larry Guth v\u00e0 Ruixiang Zhang t\u1eeb \u0110\u1ea1i h\u1ecdc California, Berkeley ch\u1ee9ng minh \u0111\u01b0\u1ee3c tr\u01b0\u1eddng h\u1ee3p hai chi\u1ec1u c\u1ee7a gi\u1ea3 thuy\u1ebft l\u00e0m m\u1ecbn c\u1ee5c b\u1ed9 (local smoothing conjecture<\/em>), m\u1ed9t trong nh\u1eefng “Ch\u00e9n Th\u00e1nh” c\u1ee7a gi\u1ea3i t\u00edch \u0111i\u1ec1u h\u00f2a. Gi\u1ea3 thuy\u1ebft n\u00e0y ph\u00e1t bi\u1ec3u r\u1eb1ng nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh s\u00f3ng kh\u00f4ng th\u1ec3 t\u1eadp trung n\u0103ng l\u01b0\u1ee3ng trong m\u1ed9t v\u00f9ng kh\u00f4ng gian nh\u1ecf trong m\u1ed9t kho\u1ea3ng th\u1eddi gian d\u00e0i. C\u0169ng trong n\u0103m \u0111\u00f3, sau khi ho\u00e0n th\u00e0nh ch\u01b0\u01a1ng tr\u00ecnh ti\u1ebfn s\u0129, V\u01b0\u01a1ng H\u1ed3ng chuy\u1ec3n \u0111\u1ebfn th\u00e0nh ph\u1ed1 Princeton, bang New Jersey, \u0111\u1ec3 l\u00e0m nghi\u00ean c\u1ee9u sau ti\u1ebfn s\u0129 t\u1ea1i Vi\u1ec7n Nghi\u00ean c\u1ee9u Cao c\u1ea5p (Institute for Advanced Study<\/em>). Ban \u0111\u1ea7u, c\u00f4 lo r\u1eb1ng m\u00ecnh s\u1ebd kh\u00f4ng th\u1ec3 ti\u1ebfp t\u1ee5c th\u00e0nh c\u00f4ng n\u1ebfu thi\u1ebfu s\u1ef1 \u0111\u1ed3ng h\u00e0nh c\u1ee7a Larry Guth. Th\u1ebf nh\u01b0ng, t\u1eebng b\u01b0\u1edbc m\u1ed9t, c\u00f4 b\u1eaft \u0111\u1ea7u x\u00e2y d\u1ef1ng nh\u1eefng m\u1ed1i h\u1ee3p t\u00e1c nghi\u00ean c\u1ee9u m\u1edbi v\u00e0 ti\u1ebfp t\u1ee5c \u0111\u1ea1t \u0111\u01b0\u1ee3c nhi\u1ec1u b\u01b0\u1edbc ti\u1ebfn trong c\u00e1c b\u00e0i to\u00e1n d\u1ea1ng Kakeya. C\u00e1c h\u1ed9i \u0111\u1ed3ng tuy\u1ec3n d\u1ee5ng \u0111\u00e3 \u0111\u1ec3 m\u1eaft \u0111\u1ebfn c\u00f4. N\u0103m 2021, c\u00f4 \u0111\u01b0\u1ee3c b\u1ed5 nhi\u1ec7m l\u00e0m gi\u1ea3ng vi\u00ean t\u1ea1i \u0110\u1ea1i h\u1ecdc California, Los Angeles (UCLA) v\u00e0 v\u00e0o n\u0103m 2023, c\u00f4 tr\u1edf th\u00e0nh ph\u00f3 gi\u00e1o s\u01b0 t\u1ea1i \u0110\u1ea1i h\u1ecdc New York (NYU).<\/p>\n

    Ch\u1ec9 m\u1ed9t th\u00e1ng sau khi chuy\u1ec3n \u0111\u1ebfn NYU, V\u01b0\u01a1ng H\u1ed3ng l\u1ea1i t\u1ea1o n\u00ean m\u1ed9t k\u1ebft qu\u1ea3 g\u00e2y ti\u1ebfng vang l\u1edbn. C\u00f9ng v\u1edbi Kevin Ren, c\u00f4 \u0111\u00e3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Furstenberg hai chi\u1ec1u (2D Furstenberg set conjecture<\/em>), gi\u1ea3 thuy\u1ebft \u01b0\u1edbc l\u01b0\u1ee3ng s\u1ed1 chi\u1ec1u c\u1ee7a m\u1ed9t t\u1eadp h\u1ee3p \u0111i\u1ec3m tr\u00ean m\u1eb7t ph\u1eb3ng ch\u1ee9a m\u1ed9t t\u1eadp con c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng h\u01b0\u1edbng v\u1ec1 m\u1ecdi ph\u00eda.<\/p>\n

    M\u1eb7c d\u00f9 \u0111\u1ea1t \u0111\u01b0\u1ee3c nh\u1eefng th\u00e0nh c\u00f4ng n\u00e0y, V\u01b0\u01a1ng H\u1ed3ng v\u1eabn c\u1ea3m th\u1ea5y m\u00ecnh nh\u01b0 m\u1ed9t \u201ck\u1ebb chi\u1ebfu d\u01b0\u1edbi\u201d. \u201cM\u1ed7i l\u1ea7n th\u00e0nh c\u00f4ng, t\u00f4i \u0111\u1ec1u c\u1ea3m th\u1ea5y gi\u1ed1ng nh\u01b0 nh\u1edd v\u00e0o may m\u1eafn,\u201d c\u00f4 chia s\u1ebb v\u1ec1 c\u00e1c ch\u1ee9ng minh c\u1ee7a m\u00ecnh. Ch\u00ednh t\u1ea1i Vi\u1ec7n Nghi\u00ean c\u1ee9u Cao c\u1ea5p trong th\u1eddi gian di\u1ec5n ra \u0111\u1ea1i d\u1ecbch, V\u01b0\u01a1ng H\u1ed3ng \u0111\u00e3 quy\u1ebft \u0111\u1ecbnh chuy\u1ec3n h\u01b0\u1edbng sang gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Kakeya ba chi\u1ec1u. B\u00e0i to\u00e1n n\u00e0y \u0111\u00e3 th\u00e1ch th\u1ee9c bi\u1ebft bao nh\u00e0 to\u00e1n h\u1ecdc su\u1ed1t nhi\u1ec1u th\u1eadp k\u1ef7; nhi\u1ec1u b\u1ea3n ch\u1ee9ng minh th\u1eadm ch\u00ed t\u1eebng \u0111\u01b0\u1ee3c c\u00f4ng b\u1ed1 r\u1ed3i sau \u0111\u00f3 b\u1ecb ch\u1ec9 ra l\u00e0 sai l\u1ea7m. \u201cT\u00f4i ch\u01b0a bao gi\u1edd gi\u1ea3i \u0111\u01b0\u1ee3c gi\u1ea3 thuy\u1ebft Kakeya, nh\u01b0ng c\u00f3 b\u1ed1n hay n\u0103m l\u1ea7n t\u00f4i t\u1eebng t\u01b0\u1edfng l\u00e0 m\u00ecnh \u0111\u00e3 l\u00e0m \u0111\u01b0\u1ee3c,\u201d Guth chia s\u1ebb. L\u1ea7n n\u00e0o c\u0169ng v\u1eady, \u00f4ng \u0111\u1ec1u k\u1ecbp ph\u00e1t hi\u1ec7n ra l\u1ed7i sai c\u1ee7a m\u00ecnh tr\u01b0\u1edbc khi c\u00f4ng b\u1ed1 c\u00f4ng tr\u00ecnh.<\/p>\n

    V\u01b0\u01a1ng H\u1ed3ng \u0111\u00e3 \u0111\u1ecdc m\u1ed9t b\u00e0i vi\u1ebft n\u0103m 2014 tr\u00ean blog c\u1ee7a nh\u00e0 to\u00e1n h\u1ecdc Terence Tao (\u0110\u00e0o Tri\u1ebft Hi\u00ean) t\u1eeb \u0110\u1ea1i h\u1ecdc California, Los Angeles (UCLA). B\u00e0i vi\u1ebft ph\u00e1c th\u1ea3o m\u1ed9t chi\u1ebfn l\u01b0\u1ee3c ch\u1ee9ng minh m\u00e0 Tao v\u00e0 Katz t\u1eebng ph\u00e1t tri\u1ec3n nh\u01b0ng ch\u01b0a t\u1eebng theo \u0111u\u1ed5i \u0111\u1ebfn c\u00f9ng. Nh\u1eadn th\u1ea5y c\u00e1ch ti\u1ebfp c\u1eadn n\u00e0y r\u1ea5t ti\u1ec1m n\u0103ng, c\u00f4 \u0111\u00e3 li\u00ean h\u1ec7 v\u1edbi Joshua Zahl, m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc t\u1eebng nghi\u00ean c\u1ee9u c\u00e1c kh\u00eda c\u1ea1nh c\u1ee7a b\u00e0i to\u00e1n Kakeya trong lu\u1eadn v\u0103n c\u1ee7a m\u00ecnh, khi \u0111\u00f3 \u0111ang l\u00e0m vi\u1ec7c t\u1ea1i \u0110\u1ea1i h\u1ecdc British Columbia. H\u1ecd quy\u1ebft \u0111\u1ecbnh c\u00f9ng nhau kh\u00e1m ph\u00e1 nh\u1eefng g\u00ec Tao v\u00e0 Katz \u0111\u00e3 m\u00f4 t\u1ea3.<\/p>\n

    Chi\u1ebfn l\u01b0\u1ee3c n\u00e0y \u2014 v\u1ed1n \u0111\u00f2i h\u1ecfi m\u1ed9t “kho t\u00e0ng” k\u1ef9 thu\u1eadt kh\u1ed5ng l\u1ed3 \u2014 l\u00e0 ch\u1ee9ng minh r\u1eb1ng b\u1ea5t k\u1ef3 ph\u1ea3n v\u00ed d\u1ee5 gi\u1ea3 \u0111\u1ecbnh n\u00e0o cho gi\u1ea3 thuy\u1ebft (t\u1ee9c m\u1ed9t c\u00e1ch ti\u1ec1m n\u0103ng \u0111\u1ec3 n\u00e9n c\u00e1c \u0111o\u1ea1n th\u1eb3ng h\u01b0\u1edbng v\u1ec1 m\u1ecdi ph\u00eda trong kh\u00f4ng gian 3D v\u00e0o s\u1ed1 chi\u1ec1u \u00edt h\u01a1n 3) – \u0111\u1ec1u ph\u1ea3i s\u1edf h\u1eefu m\u1ed9t c\u1ea5u tr\u00fac ch\u1eb7t ch\u1ebd v\u00e0 t\u1ed1i \u01b0u t\u1edbi m\u1ee9c n\u00f3 s\u1ebd m\u00e2u thu\u1eabn v\u1edbi c\u00e1c \u0111\u1ecbnh l\u00fd chi ph\u1ed1i s\u1ef1 t\u01b0\u01a1ng t\u00e1c gi\u1eefa ph\u00e9p c\u1ed9ng v\u00e0 ph\u00e9p nh\u00e2n. Ph\u01b0\u01a1ng ph\u00e1p ti\u1ebfp c\u1eadn t\u1ed5ng qu\u00e1t n\u00e0y \u2014 \u0111\u01b0a ra m\u1ed9t ph\u1ea3n v\u00ed d\u1ee5 nh\u1eb1m b\u00e1c b\u1ecf gi\u1ea3 thuy\u1ebft (mu\u1ed1n \u0111\u01b0\u1ee3c ch\u1ee9ng minh), r\u1ed3i d\u1eabn n\u00f3 v\u00e0o nh\u1eefng m\u1ed1i b\u1ebf t\u1eafc logic cho \u0111\u1ebfn khi b\u1ea1n k\u1ebft lu\u1eadn r\u1eb1ng n\u00f3 kh\u00f4ng th\u1ec3 t\u1ed3n t\u1ea1i (ngh\u0129a l\u00e0 gi\u1ea3 thuy\u1ebft l\u00e0 l\u1ef1a ch\u1ecdn duy nh\u1ea5t \u0111\u00fang) \u2014 v\u1ed1n l\u00e0 m\u1ed9t chi\u1ebfn l\u01b0\u1ee3c ch\u1ee9ng minh r\u1ea5t ph\u1ed5 bi\u1ebfn.<\/p>\n\"\"\n

    B\u1ea3n ch\u1ee9ng minh n\u1ed5i ti\u1ebfng cho gi\u1ea3 thuy\u1ebft t\u1eadp h\u1ee3p Kakeya 3D, h\u1ee3p t\u00e1c c\u00f9ng Joshua Zahl, d\u00e0i t\u1edbi 127 trang v\u00e0 \u0111\u00f2i h\u1ecfi m\u1ed9t lo\u1ea1t c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng c\u1ef1c k\u1ef3 tinh t\u1ebf. “B\u1ea1n c\u00f3 th\u1ec3 c\u1ea3m th\u1ea5y ho\u00e0i nghi,” Wang n\u00f3i, “nh\u01b0ng \u0111\u1ed3ng th\u1eddi, l\u1eadp lu\u1eadn \u0111\u00f3 l\u1ea1i mang \u0111\u1ebfn c\u1ea3m gi\u00e1c r\u1ea5t t\u1ef1 nhi\u00ean.”\u00a0\u2014 \u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, V\u01b0\u01a1ng H\u1ed3ng v\u00e0 Zahl t\u1eadp trung v\u00e0o c\u00e1i g\u1ecdi l\u00e0 c\u00e1c t\u1eadp Kakeya \u201cd\u00ednh\u201d (sticky Kakeya sets<\/em>), b\u1edfi c\u00e1c \u0111o\u1ea1n th\u1eb3ng trong c\u00e1c t\u1eadp h\u1ee3p n\u00e0y v\u1edbi \u0111\u1ecbnh h\u01b0\u1edbng t\u01b0\u01a1ng t\u1ef1 nhau th\u00ec c\u00f3 xu h\u01b0\u1edbng “d\u00ednh” l\u1ea1i v\u1edbi nhau trong kh\u00f4ng gian. Nh\u1eefng \u0111o\u1ea1n th\u1eb3ng n\u00e0y b\u00f3 s\u00e1t v\u00e0o nhau \u0111\u1ee7 ch\u1eb7t \u0111\u1ec3 c\u00e1c \u1ed1ng d\u00e0y h\u01a1n c\u00f3 th\u1ec3 ch\u1ee9a ch\u00fang m\u1ed9t c\u00e1ch t\u1ed1i \u01b0u, khi\u1ebfn to\u00e0n b\u1ed9 t\u1eadp h\u1ee3p c\u00f3 ti\u1ec1m n\u0103ng th\u1ec3 hi\u1ec7n t\u00ednh ch\u1ea5t t\u1ef1 \u0111\u1ed3ng d\u1ea1ng ph\u00e2n h\u00ecnh (fractal scaling), thay v\u00ec v\u1eadn h\u00e0nh nh\u01b0 m\u1ed9t v\u1eadt th\u1ec3 3D. \u0110\u1ea7u ti\u00ean, h\u1ecd \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng c\u00e1c t\u1eadp h\u1ee3p d\u00ednh kh\u00f4ng ph\u1ea3i l\u00e0 nh\u1eefng ph\u1ea3n v\u00ed d\u1ee5; ch\u00fang r\u1ed1t cu\u1ed9c v\u1eabn l\u00e0 v\u1eadt th\u1ec3 3D.<\/p>\n

    Nh\u01b0ng v\u1eabn c\u00f2n nhi\u1ec1u vi\u1ec7c ph\u1ea3i l\u00e0m. \u201cM\u1ecdi ng\u01b0\u1eddi l\u00fac \u0111\u00f3 kh\u00f4ng r\u00f5 li\u1ec7u tr\u01b0\u1eddng h\u1ee3p ‘d\u00ednh’ c\u00f3 th\u1ef1c s\u1ef1 l\u00e0 ‘k\u1ebb th\u00f9 ch\u00ednh’ hay kh\u00f4ng,\u201d Zahl \u2014 ng\u01b0\u1eddi s\u1edf h\u1eefu di\u1ec7n m\u1ea1o ch\u1ec9nh chu v\u00e0 phong th\u00e1i c\u1ee7a m\u1ed9t phi c\u00f4ng chi\u1ebfn \u0111\u1ea5u \u2014 cho bi\u1ebft. V\u00ec v\u1eady, ti\u1ebfp theo h\u1ecd gi\u1ea3 \u0111\u1ecbnh m\u1ed9t ph\u1ea3n v\u00ed d\u1ee5 t\u1ed5ng qu\u00e1t h\u01a1n: m\u1ed9t t\u1eadp h\u1ee3p Kakeya c\u00f3 s\u1ed1 chi\u1ec1u nh\u1ecf h\u01a1n 3 (ch\u1eb3ng h\u1ea1n l\u00e0 3\u2013x<\/em>). B\u1eb1ng c\u00e1ch ph\u00e2n t\u00edch s\u1ed1 l\u01b0\u1ee3ng c\u00e1c \u1ed1ng c\u1eaft qua m\u1ed9t v\u00f9ng h\u00ecnh c\u1ea7u k\u00edch th\u01b0\u1edbc trung b\u00ecnh trong t\u1eadp h\u1ee3p \u0111\u00f3, h\u1ecd c\u00f3 th\u1ec3 ch\u1ec9 ra r\u1eb1ng n\u00f3 ho\u1eb7c ph\u1ea3i \u1edf d\u1ea1ng “d\u00ednh” (v\u1ed1n \u0111\u00e3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh l\u00e0 3D), ho\u1eb7c kh\u00f4ng “d\u00ednh” \u2014 m\u00e0 tr\u01b0\u1eddng h\u1ee3p kh\u00f4ng d\u00ednh, theo ch\u1ee9ng minh c\u1ee7a h\u1ecd, \u0111\u1ed3ng ngh\u0129a v\u1edbi vi\u1ec7c n\u00f3 ph\u1ea3i c\u00f3 s\u1ed1 chi\u1ec1u l\u1edbn h\u01a1n m\u1ee9c \u0111\u00e3 gi\u1ea3 \u0111\u1ecbnh l\u00e0 3-x<\/em>. \u201cV\u1eady th\u00ec \u0111\u1eb1ng n\u00e0o ch\u00fang t\u00f4i c\u0169ng th\u1eafng,\u201d V\u01b0\u01a1ng H\u1ed3ng n\u00f3i. H\u1ecd c\u00f3 th\u1ec3 l\u1eb7p l\u1ea1i l\u1eadp lu\u1eadn n\u00e0y cho c\u00e1c gi\u00e1 tr\u1ecb \u00a0ng\u00e0y c\u00e0ng nh\u1ecf d\u1ea7n, cho \u0111\u1ebfn khi \u0111i \u0111\u1ebfn k\u1ebft lu\u1eadn cu\u1ed1i c\u00f9ng r\u1eb1ng m\u1ecdi t\u1eadp h\u1ee3p Kakeya b\u1eaft bu\u1ed9c ph\u1ea3i c\u00f3 3 chi\u1ec1u.<\/p>\n

    \u0110\u1ea7u n\u0103m 2024, t\u1ee9c b\u1ed1n n\u0103m sau khi b\u1eaft \u0111\u1ea7u n\u1ed7 l\u1ef1c c\u1ee7a m\u00ecnh, h\u1ec7 th\u1ed1ng logic quy n\u1ea1p ph\u1ee9c t\u1ea1p c\u1ee7a b\u1ea3n ch\u1ee9ng minh d\u01b0\u1eddng nh\u01b0 \u0111ang \u0111i \u0111\u00fang h\u01b0\u1edbng, m\u1eb7c d\u00f9 c\u1ea3 V\u01b0\u01a1ng H\u1ed3ng l\u1eabn Zahl \u0111\u1ec1u ch\u01b0a d\u00e1m kh\u1eb3ng \u0111\u1ecbnh \u0111i\u1ec1u n\u00e0y. \u201c\u0110\u00e2y l\u00e0 m\u1ed9t b\u00e0i to\u00e1n kh\u00f3, v\u00e0 t\u00f4i l\u00e0 ai m\u00e0 \u0111\u00f2i gi\u1ea3i \u0111\u01b0\u1ee3c n\u00f3 c\u01a1 ch\u1ee9?\u201d V\u01b0\u01a1ng H\u1ed3ng chia s\u1ebb. \u201cB\u1ea1n s\u1ebd lu\u00f4n c\u00f3 nh\u1eefng ho\u00e0i nghi. Nh\u01b0ng \u0111\u1ed3ng th\u1eddi, l\u1eadp lu\u1eadn \u0111\u00f3 c\u0169ng mang l\u1ea1i m\u1ed9t c\u1ea3m gi\u00e1c r\u1ea5t t\u1ef1 nhi\u00ean.\u201d C\u00f4 c\u00f3 th\u1ec3 h\u00ecnh dung r\u00f5 r\u00e0ng ti\u1ebfn tr\u00ecnh logic \u1ea5y trong t\u00e2m tr\u00ed: c\u00e1c h\u00ecnh tr\u1ee5 \u1edf m\u1ed9t t\u1ef7 l\u1ec7 nh\u1ea5t \u0111\u1ecbnh bi\u1ebfn th\u00e0nh c\u00e1c t\u1ea5m v\u00e1n \u1edf c\u00e1c t\u1ef7 l\u1ec7 l\u1edbn h\u01a1n, r\u1ed3i ti\u1ebfp t\u1ee5c m\u1edf r\u1ed9ng th\u00e0nh c\u00e1c kh\u1ed1i d\u00e0y l\u1ea5p \u0111\u1ea7y to\u00e0n b\u1ed9 th\u1ec3 t\u00edch. C\u00e1ch c\u00e1c h\u00ecnh kh\u1ed1i chuy\u1ec3n h\u00f3a l\u1eabn nhau \u0111\u00e3 cho c\u00f4 th\u1ea5y r\u1eb1ng c\u00e1c t\u1eadp h\u1ee3p Kakeya ch\u1eafc ch\u1eafn ph\u1ea3i l\u00e0 kh\u00f4ng gian ba chi\u1ec1u. D\u00f9 v\u1eady, ph\u1ea3i m\u1ea5t th\u00eam m\u1ed9t n\u0103m n\u1eefa V\u01b0\u01a1ng H\u1ed3ng v\u00e0 Zahl m\u1edbi ch\u00ednh th\u1ee9c c\u00f4ng b\u1ed1 b\u1ea3n ch\u1ee9ng minh c\u1ee7a m\u00ecnh ra c\u00f4ng ch\u00fang.<\/p>\n

     <\/p>\n

    T\u00ecm ki\u1ebfm s\u1ef1 c\u00e2n b\u1eb1ng<\/strong><\/span><\/p>\n

    \"\"<\/p>\n

    “T\u00f4i lu\u00f4n \u01b0\u1edbc m\u00ecnh c\u00f3 th\u1ec3 quay tr\u1edf l\u1ea1i qu\u00e3ng th\u1eddi gian tr\u01b0\u1edbc \u0111\u00e2y, khi m\u00e0 t\u00f4i c\u1ea3m th\u1ea5y m\u00ecnh c\u00f3 v\u00f4 t\u1eadn th\u1eddi gian \u0111\u1ec3 \u0111\u1ecdc. T\u00f4i ngh\u0129 kho\u1ea3ng th\u1eddi gian \u0111\u00f3 th\u1ef1c s\u1ef1 r\u1ea5t tuy\u1ec7t.” <\/em><\/span><\/p>\n

    \u2014V\u01b0\u01a1ng H\u1ed3ng<\/span><\/p>\n

    Khi b\u1ea3n ch\u1ee9ng minh \u0111\u01b0\u1ee3c xem x\u00e9t, nghi\u00ean c\u1ee9u v\u00e0 x\u00e1c nh\u1eadn, n\u00f3 \u0111\u00e3 l\u00e0m thay \u0111\u1ed5i c\u1ee5c di\u1ec7n trong m\u1ea3ng to\u00e1n h\u1ecdc m\u00e0 V\u01b0\u01a1ng H\u1ed3ng theo \u0111u\u1ed5i. Shmerkin n\u00f3i: “C\u1ea3m gi\u00e1c trong c\u1ed9ng \u0111\u1ed3ng to\u00e1n h\u1ecdc l\u00fac n\u00e0y c\u00f3 ch\u00fat k\u1ef3 l\u1ea1, b\u1edfi v\u00ec theo m\u1ed9t ngh\u0129a n\u00e0o \u0111\u00f3, ‘Ch\u00e9n Th\u00e1nh’ \u0111\u00e3 \u0111\u01b0\u1ee3c t\u00ecm ra.” \u00d4ng gi\u1ea3i th\u00edch: “B\u00e0i to\u00e1n Kakeya v\u1eabn ch\u01b0a \u0111\u01b0\u1ee3c gi\u1ea3i \u1edf m\u1ecdi s\u1ed1 chi\u1ec1u, nh\u01b0ng m\u1ed9t ph\u1ea7n r\u1ea5t l\u1edbn c\u1ee7a ‘Ch\u00e9n Th\u00e1nh’ \u0111\u00e3 \u0111\u01b0\u1ee3c chinh ph\u1ee5c. V\u00ec v\u1eady t\u1ea5t c\u1ea3 ch\u00fang t\u00f4i \u0111\u1ec1u t\u1ef1 h\u1ecfi: ti\u1ebfp theo ch\u00fang ta s\u1ebd l\u00e0m g\u00ec? V\u00e0 d\u0129 nhi\u00ean, to\u00e0n b\u1ed9 nh\u1eefng k\u1ef9 thu\u1eadt n\u00e0y \u0111\u00e3 m\u1edf \u0111\u01b0\u1eddng \u0111\u1ec3 gi\u1ea3i quy\u1ebft r\u1ea5t nhi\u1ec1u b\u00e0i to\u00e1n th\u00fa v\u1ecb kh\u00e1c.”<\/p>\n\"\"\n

    Ngay c\u1ea3 tr\u01b0\u1edbc khi gi\u00e0nh \u0111\u01b0\u1ee3c Fields Medal, V\u01b0\u01a1ng H\u1ed3ng \u0111\u00e3 \u0111\u01b0\u1ee3c nhi\u1ec1u ng\u01b0\u1eddi nh\u1eadn ra tr\u00ean \u0111\u01b0\u1eddng ph\u1ed1 \u1edf Trung Qu\u1ed1c. Gi\u1ea3i th\u01b0\u1edfng n\u00e0y \u0111\u1ed3ng ngh\u0129a v\u1edbi vi\u1ec7c danh ti\u1ebfng c\u1ee7a c\u00f4 \u2013 c\u0169ng nh\u01b0 nh\u1eefng chuy\u1ebfn c\u00f4ng t\u00e1c v\u00e0 nh\u1eefng s\u1ef1 ngh\u1ec9 ng\u01a1i \u0111i k\u00e8m \u2013 s\u1ebd c\u00f2n t\u0103ng l\u00ean. \u1ea2nh: Julien Pebrel\/M.Y.O.P.<\/p>\n

    Nh\u1eefng phi\u00ean b\u1ea3n ba chi\u1ec1u c\u1ee7a c\u00e1c b\u00e0i to\u00e1n kh\u00e1c, th\u1eadm ch\u00ed c\u00f2n kh\u00f3 h\u01a1n, v\u1eabn ch\u01b0a c\u00f3 l\u1eddi gi\u1ea3i, ch\u1eb3ng h\u1ea1n nh\u01b0 gi\u1ea3 thuy\u1ebft h\u1ea1n ch\u1ebf ba chi\u1ec1u (3D restriction conjecture) v\u00e0 gi\u1ea3 thuy\u1ebft l\u00e0m m\u1ecbn c\u1ee5c b\u1ed9 (local smoothing conjecture). M\u1ed9t m\u1ee5c ti\u00eau hi\u1ec3n nhi\u00ean kh\u00e1c \u0111\u1ed1i v\u1edbi V\u01b0\u01a1ng H\u1ed3ng v\u00e0 c\u1ed9ng \u0111\u1ed3ng nghi\u00ean c\u1ee9u c\u1ee7a c\u00f4 l\u00e0 gi\u1ea3 thuy\u1ebft Kakeya trong kh\u00f4ng gian b\u1ed1n chi\u1ec1u (4D Kakeya conjecture), ho\u1eb7c xa h\u01a1n n\u1eefa l\u00e0 m\u1ed9t ch\u1ee9ng minh t\u1ed5ng qu\u00e1t cho m\u1ecdi s\u1ed1 chi\u1ec1u, d\u00f9 cho \u0111\u1ebfn nay v\u1eabn ch\u01b0a ai h\u00ecnh dung \u0111\u01b0\u1ee3c di\u1ec7n m\u1ea1o c\u1ee7a n\u00f3 s\u1ebd ra sao.<\/p>\n

    V\u01b0\u01a1ng H\u1ed3ng cho bi\u1ebft hi\u1ec7n t\u1ea1i c\u00f4 kh\u00f4ng mu\u1ed1n d\u1ed3n qu\u00e1 nhi\u1ec1u t\u00e2m tr\u00ed v\u00e0o vi\u1ec7c gi\u1ea3i quy\u1ebft b\u1ea5t k\u1ef3 b\u00e0i to\u00e1n c\u1ee5 th\u1ec3 n\u00e0o. T\u00ean tu\u1ed5i c\u1ee7a c\u00f4 t\u1ea1i Trung Qu\u1ed1c \u0111\u00e3 n\u1ed5i l\u00ean nhanh ch\u00f3ng \u0111\u1ebfn m\u1ee9c gi\u1edd \u0111\u00e2y m\u1ed7i khi xu\u1ea5t hi\u1ec7n \u1edf n\u01a1i c\u00f4ng c\u1ed9ng, ng\u01b0\u1eddi ta \u0111\u1ec1u nh\u1eadn ra c\u00f4. Huy ch\u01b0\u01a1ng Fields s\u1ebd khi\u1ebfn c\u00f4 tr\u1edf th\u00e0nh m\u1ed9t nh\u00e2n v\u1eadt c\u00f3 v\u1ecb th\u1ebf n\u1ed5i b\u1eadt t\u1ea1i \u0111\u00e2y c\u0169ng nh\u01b0 trong to\u00e0n b\u1ed9 c\u1ed9ng \u0111\u1ed3ng to\u00e1n h\u1ecdc qu\u1ed1c t\u1ebf. D\u00f9 v\u1eady, V\u01b0\u01a1ng H\u1ed3ng v\u1eabn lu\u00f4n lo s\u1ee3 b\u1ecb t\u1ee5t l\u1ea1i ph\u00eda sau v\u00e0 v\u1eabn tin r\u1eb1ng m\u00ecnh c\u1ea7n n\u1ed7 l\u1ef1c nhi\u1ec1u gi\u1edd h\u01a1n c\u00e1c \u0111\u1ed3ng nghi\u1ec7p th\u00ec m\u1edbi c\u00f3 th\u1ec3 gi\u1ecfi b\u1eb1ng h\u1ecd. Khi nghe ng\u01b0\u1eddi kh\u00e1c ph\u1ea3n b\u00e1c l\u1ea1i \u0111i\u1ec1u n\u00e0y – v\u00ec trong m\u1eaft m\u1ecdi ng\u01b0\u1eddi, c\u00f4 l\u00e0 m\u1ed9t t\u00e0i n\u0103ng xu\u1ea5t ch\u00fang – V\u01b0\u01a1ng H\u1ed3ng \u0111\u00e3 t\u1ecf ra v\u00f4 c\u00f9ng ng\u1ea1c nhi\u00ean v\u00e0 vui m\u1eebng.<\/p>\n

    Tr\u01b0\u1edbc m\u1eaft v\u1eabn c\u00f2n nhi\u1ec1u b\u00e0i to\u00e1n d\u1ea1ng Kakeya c\u1ea7n chinh ph\u1ee5c, v\u00e0 V\u01b0\u01a1ng H\u1ed3ng h\u00e0o h\u1ee9ng v\u1edbi nh\u1eefng \u0111i\u1ec1u \u0111ang \u0111\u00f3n ch\u1edd ph\u00eda tr\u01b0\u1edbc. Th\u1ebf nh\u01b0ng, v\u1eabn c\u00f2n m\u1ed9t b\u00e0i to\u00e1n kh\u00f3 kh\u00e1c, \u0111\u01b0\u1ee3c \u0111\u1ec3 d\u00e0nh cho t\u01b0\u01a1ng lai: l\u00e0m sao \u0111\u1ec3 v\u1eeba v\u1eefng tin v\u00e0o b\u1ea3n th\u00e2n v\u1edbi t\u01b0 c\u00e1ch m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc, v\u1eeba gi\u1eef l\u1ea1i cho m\u00ecnh nh\u1eefng kho\u1ea3ng tr\u1eddi kh\u00f4ng xoay quanh to\u00e1n h\u1ecdc. V\u01b0\u01a1ng H\u1ed3ng c\u1ea3m th\u1ea5y \u0111\u01b0\u1ee3c truy\u1ec1n c\u1ea3m h\u1ee9ng khi ng\u01b0\u1eddi h\u01b0\u1edbng d\u1eabn c\u1ee7a m\u00ecnh, Larry Guth, v\u1eabn s\u1eafp x\u1ebfp \u0111\u01b0\u1ee3c th\u1eddi gian \u0111\u1ec3 \u0111\u1ecdc s\u00e1ch gi\u1ea3i tr\u00ed. C\u00f4 chia s\u1ebb: “T\u00f4i lu\u00f4n \u01b0\u1edbc m\u00ecnh c\u00f3 th\u1ec3 quay tr\u1edf l\u1ea1i qu\u00e3ng th\u1eddi gian tr\u01b0\u1edbc \u0111\u00e2y, khi m\u00e0 t\u00f4i c\u1ea3m th\u1ea5y m\u00ecnh c\u00f3 v\u00f4 t\u1eadn th\u1eddi gian \u0111\u1ec3 \u0111\u1ecdc. T\u00f4i ngh\u0129 kho\u1ea3ng th\u1eddi gian \u0111\u00f3 th\u1ef1c s\u1ef1 r\u1ea5t tuy\u1ec7t.”<\/p>\n

    \u2013H\u1ebft\u2013<\/strong><\/span><\/p>\n

    B\u1ea1n \u0111\u1ecdc c\u00f3 th\u1ec3 tham kh\u1ea3o b\u1ea3n g\u1ed1c ti\u1ebfng Anh \u1edf \u0111\u00e2y: https:\/\/www.quantamagazine.org\/hong-wang-wins-2026-fields-medal-the-third-woman-ever-20260723\/<\/p>\n

    Nh\u1eefng b\u00e0i vi\u1ebft g\u1ea7n \u0111\u00e2y:<\/p>\n