Okubiziweyo iingxaki zemileniyam, Zizonke iingxaki zezibalo ezisixhenxe. Ewe kunjalo, kule meko, isisombululo sayo asikafunyanwa. Ngaphezu, ukuba uphumelele, uya kunikwa isigidi seedola nganye nganye. Ke, wonke umcimbi wokuzama, ukuba ucinga ukuba ungayenza.
Kufuneka kuthiwe ngo-2006, enye yeengxaki zemillennium ezisixhenxe isonjululwe. Ke, sisizathu esihle sokukhuthaza abanye ukuba baphele bekwachazwa. Ngaba uyafuna ukwazi ukuba zintoni?
Zithini iingxaki zemileniyam?
Njengoko sele sihambile ngaphambili, xa sithetha ngeengxaki zemileniyam, kufuneka sithethe nge uthotho lweengqikelelo okanye iingxelo zemathematika. Zonke zinobungqina bokuba ziyinyani ngokupheleleyo. Kodwa ubungqina obuhambelanayo bemathematika abukaziwa. Nangona sele sisazi ukuba omnye wabo uphumelele lo mboniso kwaye siza kubona ngoku. Njengokuba kubalulekile, kufuneka kuthiwe kukho ezininzi iingxaki ezingasonjululwanga. Kuba azikho kuphela iingxaki zemileniyam, kodwa iingxaki zeHilbert azisombululeki ngokupheleleyo. Okwangoku, siza kuhlala nabokuqala.
Ukuqikelela kwePoincaré
Yiyo kuphela ingxaki esonjululweyo, ukuza kuthi ga ngoku. Le yinto ebizwa ngokuba yiPoincaré Conjecture. Ingcali yezibalo uGrigori Perelmán wayisombulula. Emva kwesisombululo sayo yaba ithiyori malunga nomba-ntathu. Uqhubeka athi inqanaba lesine-kuphela kukuphela kwendidi edibeneyo apho isangqa ngasinye esivaliweyo sinokuthi siguqulwe sibe yindawo. Ngaphezulu kwenkulungwane ibiyenye yeengxaki ezinkulu ezingasonjululwanga. Nangona uPerelmán wabhengeza ukuba uyisombulule ngo-2002, kwakungekho ngo-2006 apho afumana iMedical Medal, awayikhabayo.
P ngokuchasene neNP
Ngokucacileyo, imathematics esiyaziyo namhlanje ayinasakhono sokwahlula P kunye nohlobo lweNP iingxaki. Kungenxa yokuba oku, ii-algorithms ezinzima kuya kufuneka ziphuhlisiwe. Kungenxa yoko le nto ukusombulula le ngxaki kungafuneka uthathe isigqibo sokuba ukubandakanywa phakathi kweeklasi ezinobunzima (Oko kukuthi, iseti yeengxaki zesigqibo sobunzima obuhambelana) P kunye ne-NP kungqongqo ngenene.
Ukuqikelela kukaHodge
Enye yeengxaki zezibalo yingqikelelo yeHodge. Kule meko, usixelela ukuba ngokubonakalayo kwe-algebraic manifolds, i imijikelezo yehodge Yindibaniselwano yomgama kunye nengqiqo yemijikelo yealgebra. Kungenxa yoko le nto kunokuthiwa yingxaki yejiometri yealgebra. Kuyo, i-algebraic topology yesakhiwo esintsonkothileyo, esingesosinye sinxulumene, kunye ne-submanifolds. Kodwa ikwakhona ukuba le nto yokuqiqa yongeza ukuba amanye amaqela I-cohomology kaDe Rham zii-algebra. Ke ezi zizibalo ezibini zePoincaré. Ngoku kufuneka ubonakalise!
Ingcinga kaRiemann
Le hypothesis isixelela ukuba zonke ii-zeros ezingenamsebenzi kwi-Riemann Zeta function zinenxalenye yokwenyani ye-½. Ngaba eyaqala ukwenziwa ngo-1859 ngu-Bernhard Riemann. Ngombulelo kubudlelwane babo nokuhanjiswa kwamanani aphambili kuseti lwamanani endalo, benza le hypothesis yenye yeengxaki zeminyaka eliwaka. Nangona uninzi lukholelwa ukuba ingqikelelo ichanekile, kubonakala ngathi kukho iingcali zezibalo ezahlukileyo kolu luvo. Ngelo xesha kwakusithiwa isonjululwe, kodwa iClay Institute iyaphika.
Ubukho beYang-Mills kunye nokutsiba kobunzima
Ukuba siqala ebaleni IYang-Mills Kufuneka kuthiwe yintsimi ebonakalayo esetyenziswa kwithiyori yentsimi ye-quantum. Le ithiyori yayisetyenziselwa ukuchaza i-chromodynamics ye-quantum, echaza ubume beeproton kunye nee-neutron. Ngokufanayo, kwinqanaba lokuzinza kwenucleus yeatom. Ubunzima buza xa kufuneka uchaze ukuba imeko ebophelelayo ibonakala ifumene ubunzima.
Amanani alingana noNavier-Stokes
Ukuhamba kolwelo kunye neegesi kuchazwa yinto ebizwa ngokuba yiNavier-Stokes equation. Ziye zaqulunqwa ngenkulungwane ye-XNUMX kwaye nanamhlanje, zonke iimpembelelo zazo azaziwa. Oku kubangelwe kukungalingani komlinganiso wabo kunye namagama adibeneyo. Kuya kufuneka uze nethiyori malunga ne-fluid dynamics. Kuya kufuneka ukubonisa ukuba ngaba kukho iimeko ezithile zokuqala ulwelo lwe-laminar, isisombululo sokuhamba naso sine-laminar, kuzo zonke iimeko zexesha.
Ingqikelelo yeBirch neSwinnerton-Dyer
Kule meko, ingqokelela yeBirch kunye neSwinnerton-Dyer ijongene nohlobo lwe-equation. Inoxanduva lokuchaza iirliptical curves kwii-rational ones. Kubonakala ngathi ingqikelelo iyasixelela ukuba ikhona indlela yokwazi ukuba ezi zibalo zinokungenasiphelo okanye mhlawumbi inani elingenasiphelo lezisombululo ezinengqiqo. Yabhengezwa ngo-1965 ngoochwephesha ababini baseNgilane: uBryan Birch noPeter Swinnerton-Dyer. Isiteyitimenti sengqikelelo sinika idatha ye-arithmetic enxulunyaniswa ne-arithmetic curve E ngaphezulu kwenani lenkundla, elinokuba ngu-K.
Nguye Iziko lodongwe elijolise ekwandiseni ulwazi lwemathematics, kunye nokusasazeka kwayo okukhulu. Ukongeza kwimisebenzi eyahlukeneyo kunye neeprojekthi, baye baduma ngokuxhasa iingxaki zemillennium okanye ezi ngxaki zemathematika azilula kwaphela. Eminye imiceli mngeni ngeenjongo eziphindwe kabini: Kwelinye icala, isigqibo sokugqibela sabo nakwelinye, ibhaso lezoqoqosho elinencasa elinikezela.