Iingxaki ezingenakuthenjwa: ukulinganisa kweNavier-Stokes, i-Hodge conjecture, i-hyemhesis yeRiemann. Iinjongo zeMillennium

Imisebenzi engenakukhunjulwa yimiba ye-mathematical 7 enomdla kakhulu. Ngamnye wabo wahlongozwa ngexesha elifanelekileyo kunye nososayensi abaziwayo, ngokuqhelekileyo ngeendlela zokucinga. Kwiminyaka emashumi, ngaphezu kwesigqibo sabo, baye bephula iintloko zeemathematika kuwo wonke umhlaba. Abo baphumelelayo baya kuvuzwa nge-award-million dollar enikezelwa yiClay Institute.

Ngaphambili

Ngomnyaka we-1900, umphathi omkhulu wezeMathematika uJalimane uDavid Gilbert, wabonisa uluhlu lweengxaki ezingama-23.

Izifundo ezenziwe ukuzisombulula ziye zachaphazela kakhulu inzululwazi yekhulu lama-20. Ngeli xesha, abaninzi babo sele beyeke ukuba babe yimigqomo. Phakathi kweengxaki ezingaxilwanga okanye ezinqunyulwe ngokukhawuleza:

• Ukuhambelana kwama-arithmetical axioms;
• Umthetho oqhelekileyo wokulungelelanisa kwisikhundla naliphi na inamba yenkalo;
• Uvavanyo lweMathematika lweexioms ngokomzimba;
• Ukufundwa kweefom ze-quadratic zeenombolo ze-algebraic zeenombolo ezingabonakaliyo;
• Ingxaki yokulungiswa ngokuthe tye kwe-geometry ye-calculus ye-Fedor Schubert;
• Kwaye nabanye.

Oku kulandelayo akunakulindelwa: ingxaki yokwandisa nakweyiphi idilesi ye-algebraic ukuqonda kwe-Kronecker theorem eyaziwayo kunye ne- Riemann hypothesis .

Clay Institute

Ngaphantsi kweli gama liyaziwa inhlangano yabucala yangasese, inkulu layo iCambridge, eMassachusetts. Yayisungulwa ngo-1998 nguHarvard wezibalo zeemathematika A. I-Jeffy kunye nomsebenzi woshishino uL. Clay. Injongo yeSikolo kukukhuthaza nokuphuhlisa ulwazi lweemathematika. Ukufezekisa oku, umbutho unikezela ibhaso kwenzululwazi kunye nabaxhasi abacebisa uphando.

Kwiminyaka yokuqala ye-21, iClay Mathematical Institute yanikezela ibhaso kwabo baxazulula iingxaki ezaziwa ngokuba yingxaki ezinzima kakhulu ezingabonakaliyo, zibiza uluhlu lwabo lweengxaki ze-Millennium Prize. Ukusuka kwi "Uluhlu lweHilbert" kuphela i-hypothesis yeRiann engena kuyo.

Iinjongo zeMillennium

Uludwe lweClay Institute ekuqaleni lwaquka:

• I-hypothesis yemijikelezo yeHodge;
• Ukulingana kwe-quantum Yang-Mill theory;
• I-Poincare conjecture ;
• Ingxaki yokulingana kwamacandelo eP and NP;
• I-hyemhesis yeRiemann;
• U-Navier Stokes ulinganiso, ngokukhokelela kunye nokunyanzeliswa kwezisombululo zayo;
• Ingxaki yeBirch-Swinnerton-Dyer.

Ezi ngxaki zeemathematika ezivulekileyo zinomdla omkhulu, kuba zinokusetyenziswa ezininzi.

Yintoni eye yabonisa uGrigory Perelman

Ngowe-1900, isazi sefilosofi esidumileyo uHenri Poincaré sacebisa ukuba yonke into edibeneyo edibeneyo ye-3-dimensional ngaphandle kwemida i-homeomorphic to 3-dimensional sphere. Ubungqina balo kwiimeko eziqhelekileyo kwakungekho ikhulu leminyaka. Kuphela ngo-2002 ukuya ku-2002 umphathi wezeMathematika wasePetersburg uG. Perelman wapapasha amanqaku amaninzi kunye nesisombululo seNgxaki yePoincaré. Bavelisa umphumo webhobho eqhuma. Ngo-2010, i-hyinchesis yePoincaré yayingabandakanywa kwiluhlu lweengxaki ezingaphendululwayo zeClay Institute, kwaye uPerman ngokwakhe wacelwa ukuba athole umvuzo omkhulu ngenxa yakhe, apho kuye kwaliwa khona, ngaphandle kokuchaza izizathu zesigqibo sakhe.

Ingcaciso ecacileyo kakhulu yento yemathematika yaseRashiya eyakwazi ukubonisa ukuba yenziwa ngokucinga ukuba isangxobo senkunzi yeberber ifakwa kwi-bagel, kwaye ngoko uzama ukutsala iingcambu zesangqa sayo kwindawo enye. Kucacile ukuba oku akunakwenzeka. Enye into, ukuba wenza le nto ibhola. Kule meko, kubonakala ngathi i-three-dimensional sphere efunyenwe kwi-disk, i-circumkerence yayo ifakwe kwinqanaba le-cord hypordination, iya kuba yintathu-ntathu ekuqondeni umntu oqhelekileyo, kodwa i-two-dimensional ngokwemathematika.

I-Poincare iphakanyise ukuba i-dimensional sphere iyona nto kuphela "into" engamatshatsheli, ummandla wayo unokukhangela kwelinye iphuzu, kwaye uPerman wazama ukubonakalisa oku. Ngaloo ndlela, uluhlu lwemisebenzi "engenakususwa" namhlanje linemiba-6.

Imfundiso ye-Yang-Mills

Le ngxaki yeemathematika iphakanyiswe ngababhali bayo ngo-1954. Ukuqulunqwa kwezenzululwazi yenkcazo yile ndlela ilandelayo: kuyo nayiphi na iqela elilula le-compact gauge, i-quantum space theory eyenziwe nguYang ne-Mills ikhoyo kwaye inesiphene esikhulu.

Ukuthetha ngolwimi oluqondakalayo kumntu oqhelekileyo, intsebenziswano phakathi kwezinto zendalo (iinqununu, imizimba, amagagasi, njl.) Zihlulwe ngohlobo lwe-4: i-electromagnetic, i-gravitation, inobuthakathaka kwaye inamandla. Kwiminyaka emininzi i-physicists bezama ukudala i-theory jikelele. Kufuneka sibe sisixhobo sokuchazela zonke ezi zinto. Inkolelo ye-Yang-Mills yilwimi lwezemathematika, ngoncedo apho kuye kwaba lula ukuchaza 3 yezinto ezine ezisisiseko zemvelo. Ayisebenzisi kummandla wendalo. Ngoko ke, akunakucingelwa ukuba i-Yangu kunye neMills bayaphumelela ekudaleni inkolelo yenkalo.

Ukongezelela, ukungaxilwanga kwamanqanaba atyunjweyo kubangela ukuba kunzima kakhulu ukusombulula. Ukuncinciza amancinci amancinci, anokukwazi ukusombulula ngohlobo lwethotho ye-perturbation theory. Nangona kunjalo, akucaci ukuba ezi zilinganiso zingasombulula njani ukudibanisa okunamandla.

Ukulinganisa kweNavier-Stokes

Ngokuncedwa kwezi binzana, iinkqubo ezinjengeengcingo zomoya, ukuhamba kwee-liquids kunye ne-turbulence zichazwe. Kwezinye iimeko ezithile, isisombululo sokuhlalutya se-Navier-Stokes equation sele sitholiwe, kodwa oku akukaze kwenziwe ngokubanzi. Ngexesha elifanayo, ukulinganisa kwamanani kwiimpawu ezithile zesantya, ubuninzi, uxinzelelo, ixesha, njalo njalo kukuvumela ukuba uphumelele kwiziphumo ezigqwesileyo. Kufuneka nethemba lokuba umntu uya kuba nokusebenzisa ukulinganisa kwe-Navier-Stokes kwinqanaba elincinane, oko kukuthi, ukubala iipameters ezisebenzisayo, okanye ukubonisa ukuba akukho sombululo.

Ingxaki yeBirch-Swinnerton-Dyer

Udidi "Iingxaki ezingaxilwanga" ziquka neengcamango ezicetywayo ngabasosayensi beNgesi baseYunivesithi yaseCambridge. Kwiminyaka engama-2300 edlulileyo, isazi-mlando seGrike u-Euclid sanikezela ngengcaciso epheleleyo yezisombululo ze-equation x2 + y2 = z2.

Ukuba sibala inani lamaphuzu kwikota nge-modulus yayo nganye yamanani aphezulu, sithola i-integers ye-integers. Ukuba ngokuqinisekileyo "siwufaka" kumsebenzi wenguqu eguqukileyo, ngoko ke sithola umsebenzi we-Hasse-Weil we-curtain-third-order, echazwe nguL. Iqulethe inkcazelo malunga nokuziphatha kwe-modulo onke amanqaku aphezulu kanye kanye.

UBrian Birch noPeter Swinnerton-Dyer baqhubela phambili ingcamango malunga neengqungquthela ze-elliptic. Ngokutsho kwalo, isakhiwo kunye nenani lezisombululo zayo ezinengqiqo zihlobene nokuziphatha komsebenzi we-L kwiyunithi. Inkolelo yeBirch-Swinnerton-Dyer, engakabonakalwanga, ixhomekeke kwinkcazo ye-algebraic equations yesigaba sesithathu kwaye yindlela elula nje yokubala ireyiti yee-elliptic curves.

Ukuze uqonde ukubaluleka okubalulekileyo kwalo msebenzi, kunelungelo lokuthetha ukuba kwi-cryptography yanamhlanje kwii-elliptical curve iiklasi ezipheleleyo zeenkqubo ezizimeleyo zisekelwe, kwaye kwisicelo sazo sasekhaya sokusayinwa kwesigxina sisekelwe kwisicelo sazo.

Ukulingana kweeklasi p ne np

Ukuba i-"Millennium Challenges" eseleyo yodwa imathematika, ngoko oku kuhambelana nomgaqo-nkqubo we-algorithms. Ingxaki malunga nokulingana kweeklasi p ne np, eyaziwa nangokuthi ingxaki yeCook-Levin, ingaqulunqwa ngolwimi olucacileyo ngendlela elandelayo. Cinga ukuba impendulo enombuzo kumbuzo othize inokutshekishwa ngokukhawuleza, oko kukuthi, ngexesha le-polynomial (PV). Ngaba ke ingxelo echanekileyo ukuba impendulo yalo ingatholakala ngokukhawuleza? Kulula kakhulu, le ngxaki izandile kanje: ngaba kunokwenzeka ukuba uhlole isicombululo sengxaki ngokulula kunokukufumana? Ukuba ukulingana kweeklasi p ne-np kubonakele, ke zonke iingxaki zokukhetha zixazululwa kwi-PV. Okwangoku, iingcali ezininzi zingathandabuzeki inyaniso yale nkcazo, nangona iyakwazi ukubonakalisa okuchaseneyo.

IRiemann hypothesis

Kuze kube ngu-1859, akuzange kubonakaliswe nawuphi na umzekelo onokuthi uchaze ukuba amanani ambalwa asasazwa phakathi kwamanani emvelo. Mhlawumbi oku bekubangelwa kukuba inzululwazi yayibandakanyeka kwezinye iimeko. Nangona kunjalo, phakathi kwekhulu le-19 leminyaka imeko yatshintshile, kwaye yaba yinto yezona zinto zichaphazelekayo, ezithe zaqala ukuhlangabezana nemathematika.

Iingcamango zeRiemann ezavela kweli xesha liqikelela ukuba kukho ukuhlaziya ngokuthe ngqo kwi-primes.

Namhlanje, izazinzulu ezininzi zanamhlanje zikholelwa ukuba ukuba zibonakalisiwe, imigaqo emininzi yemigaqo yokubhala i-cryptography yamanje, eyakha isiseko senxalenye ebalulekileyo yeendlela zorhwebo lwekhompyutha, iya kuhlaziywa.

Ngokutsho kukaRiemann, indlela yokuhanjiswa kweenombolo eziphambili ingahluka ngokuthe ngqo kwizinto ezifunekayo ngoku. Inyaniso kukuba kude kubekho inkqubo efunyenwe ekusasazeni kwamanani aphezulu. Ngokomzekelo, kukho ingxaki ye "mawele," umahluko phakathi kokulingana no-2. La manani anama-11 no-13, 29. Amanye amaqela e-primes. Le 101, 103, 107, njl. Nzululwazi sele ikhunjulwe ukuba amaqela anjalo aphakathi kwamanani amakhulu kakhulu. Ukuba zifunyenwe, ukuzinza kwezikhiye ze-crypto zangoku kuza kubakho.

I-hypothesis malunga nemijikelezo yeHodge

Le ngxaki ingaphendulwanga yenziwe ngowe-1941. I-Hodge hypothesis ibonisa ukuba kungenzeka ukulingana nomfanekiso wento nayiphi "ngokuqoqa kunye" nemizimba elula yomlinganiselo. Le ndlela yaziwa kwaye yasetyenziswa ngempumelelo ngexesha elide. Nangona kunjalo, awaziwa ukuba yeyiphi indlela yokwenza lula ukulula.

Ngoku uyazi ukuba zeziphi iingxaki ezingenakulinganiswa nazo zikhoyo ngexesha. Ziyintloko yophando ngeenkulungwane zeengcali kwihlabathi jikelele. Kuhlala kuthathelwa ukuba ikusasa elikufutshane liza kusombululwa, kunye nesicelo sabo esiza kubancedisa uluntu ukungena kwinqanaba elitsha lophuhliso lobuchwepheshe.