Inkinga Unsolvable: Navier-Stokes zibalo, le Hodge conjecture le Riemann hypothesis. izinjongo Millennium

inkinga Unsolvable - nezinkinga 7 ezithakazelisayo zezibalo. Ngamunye wabo siphakamisiwe ngesikhathi esisodwa ososayensi adumile, ngokuvamile ngesimo imicabango. Amashumi eminyaka, ukuzixazulula ukunwaya amakhanda abo wezibalo emhlabeni wonke. Labo aphumelele, elinde umvuzo esigidini aseMelika ahlinzekwa yi-Institute of Clay.

prehistory

Ngo-1900, i-elikhulu sezibalo German uDavide Hilbert zenqola, owethulwe uhlu lwezinkinga 23.

Ucwaningo eyenziwa ngenjongo isinqumo sabo, baye baba nethonya elikhulu ku-isayensi kwekhulu lama-20. Okwamanje, abaningi kubo okuyizingane ayekile kakade ukuba imfihlakalo. Phakathi ezingaxazululeki noma ingxenye ixazululwe kwakuyilawa:

• inkinga ukungaguquguquki we axioms emkhakheni we-arithmetic;
• umthetho jikelele reciprocity esikhaleni noma iyiphi inkundla ezinombolo;
• cwaningo nezibalo axioms ngokomzimba;
• cwaningo amafomu quadratic ngoba ngokungenasizathu algebraic inombolo okuza;
• inkinga okunzima ukulungisiswa geometry enumerative Fedor Schubert;
• nokunjalo.

Nhlobo chithi inkinga nganoma yisiphi algebraic esifundeni rationality eyaziwa Kronecker theorem futhi Riemann hypothesis .

Ihlangano yokuNgeza Clay

Ngaphansi leli gama yangasese inhlangano engenzi inzuzo, ikomkhulu Cambridge, Massachusetts ezaziwayo. It yasungulwa ngo-1998 ngu-Harvard sezibalo kanye nosomabhizinisi A. Jeffrey L. Clay. Inhloso ye-Institute ukukhuthaza nokuthuthukisa ilwazi leembalo. Ukuze kuzuzwe lokhu inhlangano ibanikeza imiklomelo ososayensi kanye uxhasa ucwaningo ethembisa.

Ekuqaleni kwekhulu lama-21 Clay Mathematical Institute unikezele premium kulabo ngeke ukuxazulula izinkinga, ezaziwa ngokuthi inkinga eyinkimbinkimbi kunazo unsolvable, ukushaya ohlwini lwakho Millennium Izinkinga Prize. Kusukela "Uhlu Hilbert" kwaba kuphela Riemann hypothesis.

izinjongo Millennium

Ohlwini Institute of Clay kuhlanganisiwe ekuqaleni:

• Hodge conjecture ku imijikelezo;
• i-zibalo theory quantum ye Yang - Mills;
• Poincaré conjecture ;
• inkinga kokulingana amakilasi P no NP;
• Riemann hypothesis;
• Navier-Stokes zibalo, khona kanye olubushelelezi izinqumo zayo;
• inkinga Birch - Swinnerton-Dyer.

Lezi zinkinga evulekile zezibalo Sinesithakazelo esikhulu ngoba ungaba implementations eziningi ezingokoqobo.

Yini wazibonakalisa Grigoriy Perelman

Ngo-1900, isazi sesayensi esidumile sefilosofi Anri Puankare wasikisela ukuba zonke nje uxhumeke compact 3-ezininginingi ngaphandle umngcele kuyinto homeomorphic kuya sphere 3-ntathu. Ubufakazi esimweni jikelele akubanga khona eminyakeni eyikhulu edlule. Kuphela 2002-2003, i-St Petersburg sezibalo G. Perelman eshicilelwe ochungechungeni lwezingxenye ikhambi yenkinga Poincaré. Bona sigemegeme. Ngo-2010, Poincaré conjecture ubekwe ngaphandle kusukela uhlu "inkinga kungalungiswanga" Clay Institute, futhi Perelman wamenywa ukuba uthole iholo eside ngenxa kuye, lapho yokugcina wenqaba 'ngaphandle kokuchaza nezizathu zesinqumo salo.

Incazelo kuyaqondakala kakhulu ngalokho ongaba sezibalo isiRashiya, inganikelwa, ukuhlinzeka ukuthi Ungalokothi (Torus), donsa disc iraba, bese azame ukudonsa emaphethelweni selilonke yayo ngesinye isikhathi. Ngokusobala, lokhu akunakwenzeka. Enye into, uma senza lokhu linga ngamasu ahlukahlukene ngenhloso ibhola. Kulokhu, ibonakala sphere ngakuthathu, sithola kusukela selilonke disc eyibophele iphuzu intambo yezinto kuyinto ngakuthathu ekuqondeni umuntu ovamile, kodwa mgudumbili ngokuya wezibalo.

Poincaré wasikisela ukuthi sphere ngakuthathu iyona ngakuthathu "into" kuphela, ebusweni okungase izinkontileka iphuzu elilodwa, futhi Perelman wakwazi ukuba kufakazelwe. Ngakho, "inkinga unsolvable" uhlu manje siqukethe izinkinga 6.

Yang-Mills ithiyori

Le nkinga zezibalo siphakamisiwe abalobi ngo-1954. ekwakhiweni Scientific kwemfundiso yokuziphendukela simiswe ngalendlela lelandzelako: nganoma yisiphi compact gauge iqembu isikhala quantum theory elula adalwe Yang futhi Millsom ukhona, futhi ngenxa yalokho elinomthwalo zero isici mass.

Ukukhuluma ulimi olwaluqondwa somuntu ovamile, ukusebenzisana phakathi izinto zemvelo (. Izinhlayiyana, imizimba, amagagasi, njll) zihlukaniswe 4 izinhlobo: kagesi, okudonsa, ababuthakathaka futhi eqinile. Kwaphela iminyaka eminingi, izazi zesayensi uzama ukudala i-jikelele emkhakheni theory. Kumelwe abe ithuluzi ukuchaza konke lokhu kuxhumana. Yang-Mills ithiyori - ulimi zezibalo ngawo kwakunokwenzeka ukuchaza 3 zamabutho 4 eziyisisekelo nemvelo. Ayisebenzi namandla adonsela phansi. Ngakho-ke ngeke sikwazi ucabange ukuthi Yang futhi 'uMills wayeyinceku bakwazi ukuthuthukisa inkolelo-mbono yokuziphendukela emkhakheni.

Ngaphezu kwalokho, okungezona linearity we zibalo ezihlongozwayo kubenza kunzima kakhulu ukuxazulula. abayiphethe ukuxazulula cishe ngesikhathi constants encane elihlangana njengoba uchungechunge perturbation. Nokho, akucaci ngokuthi zingaxazululwa kanjani lezi zibalo for elihlangana eqinile.

Navier-Stokes Izibalo

Nge lezi zinkulumo echazwe izinqubo ezifana komoya, ukugeleza uketshezi omawala. Ukuze Kwezinye izimo ezikhethekile, izixazululo kohlaziyo we Navier-Stokes zibalo eziye zatholakala, kodwa ukukwenza ngenxa ezivamile kodwa asikho esiye saphumelela. Ngesikhathi esifanayo, ukumbumbuluzwa kwamanani for amagugu ethile isivinini, ukuminyana, ingcindezi, isikhathi, njalo njalo evumela ukufeza imiphumela emihle kakhulu. Siyethemba ngokuthi othize uzosebenzisa Navier-Stokes zibalo kolunye uhlangothi, isb. E. ngekhompyutha usebenzisa nemingcele zabo, noma ukufakazela ukuthi indlela akulona ikhambi.

Umsebenzi we-Birch - Swinnerton-Dyer

Isigaba "izinkinga Ezivelele" osebenza ku umbono ezihlongozwayo ososayensi baseBrithani eCambridge University. Ngisho 2300 edlule, isazi yamaGreki asendulo Euclid wanikeza incazelo ephelele izixazululo of the equation X2 + y2 = Z2.

Uma ngamunye izinombolo eziyinhloko ukubala inani lamaphuzu phezu ijika unit yakhe, sithola i isethi okungenamkhawulo integers. Uma indlela aphathekako "glue" yona 1 umsebenzi kwenombolo eziyinkimbinkimbi ke uthole Hasse-Weil Zeta umsebenzi somyalelo ijika lwesithathu, okhonjiswe incwadi L. Liqukethe ulwazi mayelana ukuziphatha modulo zonke primes ngokushesha.

Bryan Birch noPetru Swinnerton-Dyer hypothesized eyisihlobo Curves elliptic. Ngokusho lokhu, isakhiwo kanye nenani isethi yayo izinqumo okunengqondo elihlobene ne ukuziphatha L-umsebenzi iyunithi. Okwamanje hypothesis unproven Birch - Swynnerton-Dyer incike zibalo algebraic echaza 3 degrees kanye kuphela indlela elithe elula jikelele kuhlaziywa elisezingeni Curves elliptic.

Ukuze siqonde ukubaluleka esisebenzayo yale nkinga, lwanele ukusho ukuthi indlela yokubhala efihla incazelo yesimanje esekelwe Curves elliptic ikilasi amasistimu quin, futhi isicelo zabo zisekelwe ezindinganisweni ezifuywayo isignisha yezinombolo.

Ukulingana amakilasi p futhi np

Uma lonke "Izinselelo Millennium" kumane zezibalo, lokhu kuhlobene imfundiso yokuziphendukela langempela algorithm. Inkinga nge ukulingana amakilasi p futhi np, eyaziwa nangokuthi inkinga Cook-Levin ulimi kuyaqondakala ingakleliswa kanje. Ake sithi impendulo omuhle ukuba umbuzo angaqinisekiswa ngokushesha ngokwanele, okungukuthi. E. Ngokuhamba kwesikhathi polynomial (PT). Khona-ke, uma kuyiqiniso, ukuthi impendulo kungaba ngokushesha impela ukuthola? Ngisho kulula , le nkinga is: Ingabe ikhambi ngempela ukuhlola akukho nzima ngaphezu ukuyithola? Uma nokulingana amakilasi p futhi np eliyophinde yafakazela ukuthi izinkinga Ukukhetha zingaxazululwa for PV. Okwamanje, izazi eziningi bakungabaza ukuba yiqiniso kwala mazwi, kodwa awukwazi ziwubufakazi balokho.

I Riemann hypothesis

Kuze kube 1859 babungekho ubufakazi noma iyiphi imithetho ukuthi kungaba ukuchaza ukuthi ungasabalalisa izinombolo prime phakathi zemvelo. Mhlawumbe lokhu kungenxa yokuthi isayensi abenza ezinye izinto. Nokho, phakathi nekhulu leminyaka le-19, isimo sesishintshile futhi ziye zaba enye eziphuthuma kakhulu, okuyinto waqala ukuqhuba izibalo.

I Riemann Hypothesis ezavela lesi sikhathi - lena ngoba kucatshangwa ukuthi kukhona indlela ethile yokuma ekusakazeni primes.

Namuhla, ososayensi abaningi banamuhla bakholelwa ukuthi uma kungase kutholakale ukuthi kuyodingeka ukuba aphinde acabange izimiso eziningi eziyisisekelo zabantu indlela yokubhala efihla incazelo yesimanje, yakha isisekelo bakha ingxenye enkulu yabamemezeli e-commerce izindlela.

Ngokwe Riemann hypothesis, ubunjalo ukusatshalaliswa izinombolo eziyinhloko kungahluka izinto ezibonakalayo Kulindeleke ngalesi sikhathi. Iqiniso liwukuthi kuze kube manje ingakamiswa ezitholakele engasekelwe ohlelweni ekusakazeni izinombolo eziyinhloko. Ngokwesibonelo, kunenkinga "amawele", umehluko phakathi okuyinto ilingana 2. Lezi zinombolo 11 no-13, 29. Okunye primes yakha amaqoqo. Kuyinto 101, 103, 107 kanye nabanye. Sekuyisikhathi eside ososayensi okusolakala ukuthi amaqoqo ezinjalo phakathi siningi eyinhloko. Uma uthola kubo, ukungawi mfihlo ukhiye yesimanje kuyoba ngaphansi mbuzo.

Umbono ka Hodge imijikelezo

Le nkinga ezingaxazululeki namanje zavela ngo-1941. Hodge hypothesis kusikisela ukuthi kungenzeka approximating ifomu banoma iyiphi into nge "gluing" Izidumbu ndawonye elula ubukhulu emikhulu. Le ndlela iye eyaziwa futhi iye yasetshenziswa ngempumelelo isikhathi eside. Nokho, akwaziwa ukuthi yokuncishiswa ngokwezinga zingenziwa.

Manje ngoba sewuyazi ukuthi iziphi izinkinga unsolvable ezikhona okwamanje. Ziyakwazi isihloko ezinkulungwane ososayensi emhlabeni wonke. Kunethemba lokuthi maduze ukuxazululwa, futhi isicelo kwabo okuwusizo kuyosiza esintwini ukufinyelela round esisha nakwezobuchwepheshe.