Raruraru unsolvable: Navier-Stokes whārite, te whakapae Hodge, te whakapae Rēimāna. whāinga Mileniuma

raruraru unsolvable - he 7 ngā raruraru pāngarau. Kua Ia o ratou kua whakaarohia i tetahi wa kaipūtaiao rongonui, te tikanga i roto i te puka o whakapae. No te tekau tau maha, ki te whakatau ia ratou rakuraku ratou pāngarau upoko te ao. Ko te hunga e angitu, e tatari ana mo te utu o tetahi miriona tāra US tapaea e te Institute o Clay.

prehistory

I roto i 1900, i te nui mathematician Tiamana Rawiri Hilbert pereoo, te aroaro he rārangi o 23 raruraru.

kawea Rangahau i mo te whakaaro o ratou whakatau, kua i te pānga rahi i runga i te pūtaiao o te rau tau 20. I te kau, kua kua mutu te nuinga o ratou ki te hei i te mea ngaro. I roto i te kāore ranei wāhanga faatiti'aifarohia i:

• te raruraru o te ōrite o te axioms o tauhanga;
• te ture whānui o te tauutuutu i te wāhi o tetahi mara tau;
• ako pāngarau o axioms tinana;
• ako o ngā puka pūrua mō te noho tau whakarea tau taurangi;
• raruraru pakari tika āhuahanga enumerative Fedor Schubert;
• a pera atu.

Unexplored e horahia raruraru mo tetahi rationality rohe taurangi mohiotia Kronecker ture tauwehe me Rēimāna whakapae .

Institute o Clay

I raro i tenei ingoa mohiotia te whakahaere pai-kore tūmataiti, hetikuota i Kemureti, Massachusetts. I whakaturia te reira i roto i 1998 e Harvard mathematician me kaipakihi A. Jeffrey L. Clay. Ko te whakaaro o te Institute ko ki te whakatairanga me te whakawhanake i te mōhiotanga pāngarau. Hei whakatutuki i tenei whakahaere homai tohu ki pūtaiao, me te tautoko rangahau whaihua.

I roto i te tīmatanga o te rautau 21, kua patua ana Clay Mathematical Institute he moni ki te hunga e ka whakaoti i te raruraru, e mohiotia ana ko te raruraru unsolvable tino matatini, karanga koutou rārangi o Mileniuma paraihe Problems. Mai i te "Rārangi o Hilbert" ka anake te whakapae Rēimāna.

whāinga Mileniuma

I roto i te rārangi o te Institute o Clay ngā tuatahi:

• Hodge whakapae i runga i huringa;
• nga whārite o ariā aronui o Yang - Mills;
• Poincaré whakapae ;
• te raruraru o te taurite o ngā akomanga P me NP;
• Rēimāna whakapae;
• whārite Navier-Stokes, te oraraa, me te whakapati o ona whakatau;
• raruraru Birch - Swinnerton-Dyer.

Ko o te pānga nui enei raruraru pāngarau tuwhera no te mea e taea e whai ratou maha implementations mahi.

He aha whakamatauria Grigoriy Perelman

I roto i te 1900, te whakaaro te pūtaiao rongonui me te tangata tohe Anri Puankare e nga hono noa kiato 3-maha, kahore rohe he homeomorphic ki te ao-ahu 3. E kore kua te tohu i roto i te take whānui i roto i te i runga i te rau tau. Anake i roto i te 2002-2003, whakaputaina te St Petersburg mathematician G. Perelman te raupapa o ngā tuhinga ki te otinga o te raruraru Poincaré. bombshell ratou. I roto i te 2010, kua araia te tāpae kōrero Poincaré i te rārangi o "raruraru Kāore i" Clay Institute, ka i karangatia ki Perelman ki te tiki i te utu nui e tika ana ki a ia, i kihai te whakamutunga i waho whakamārama i te take mo tona whakatau.

Ko te whakamārama tino mārama o te aha i taea e whakamatau ki te mathematician Russian, e taea te hoatu, te whakarato e te tōnati (Torus), wahia i te kōpae rapa, a ka ngana ki te wahia te mata o tona paenga i kotahi ira. Oia mau, kore tenei e taea. Ko tētahi atu mea, ko te, ki te hanga matou i tenei whakamātau ki te pōro. I roto i tenei take, te mea ki te hei ruri e toru-ahu, whiwhi tatou i te paenga kōpae whitikiria ki te wāhi taura hypothetical ko e toru-ahu i roto i te māramatanga o te tangata toharite, engari he-ahu e rua i roto i ngā o te pāngarau.

fokotu'u Poincaré e te ao e toru-ahu ko te toru-ahu anake "ahanoa", te mata o e taea te kirimana ki te wāhi kotahi, a ka i taea ki te whakamatau i te reira Perelman. Ko te kupu, i teie nei ngā o 6 raruraru te "raruraru unsolvable" rārangi.

Yang-Mills ariā

Kua tēnei raruraru pāngarau kua whakaarohia e te kaituhi i roto i 1954. waihanga Scientific o te ariā, ko e whai ake: vai hoki tetahi rōpū mehua aronui wāhi ariā kiato ohie i hanga e Yang ko Millsom, a ko te kupu kua kore koha papatipu.

A paraparau i te reo i matau e te tangata noa, e wehea te pāhekoheko i waenganui i ngā taiao (matūriki, tinana, ngaru, etc..) Ki 4 momo: hiko, tō, ngoikore, me te kaha. No te tau maha, e tamata i physicists ki te waihanga i tētahi ariā mara whānui. Me riro te reira i te taputapu ki te whakamārama katoa o enei taunekeneke. Yang-Mills ariā - he reo pāngarau ki i ia e taea te ki te whakaahua 3 o te ope taketake 4 o te natura. e kore e tono te reira ki te mahara. Na reira e kore e taea e tatou e amo i taua i taea ki te whakawhanake i te ariā o te parae Yang me Mills.

I tua atu, i te linearity-kore o te whārite e whakaarohia hanga ratou tino uaua ki te whakaoti. te whakahaere ratou ki te whakaoti āhua i taimau hononga iti rite te raupapa perturbation. Heoi, ehara i te mea mārama pehea ki te whakaoti i enei whārite mō te hononga kaha.

Navier-Stokes Equations

Ki enei kīanga fakamatala'i tukanga pērā i rere o te hau, rere inu, me te arepurepuraa. Hoki ētahi wā motuhake, kua kitea nga rongoā tātari o te whārite Navier-Stokes, engari rave i te reira mo te noa ano kua muri kahore tetahi. I te wa ano, whaihanga tau hoki ngā uara motuhake o te tere, kiato, te pēhanga, wa, a kia ki runga ki taea ki te whakatutuki i ngā hua pai. Ka taea e anake tatou tumanako e ka whakamahi te tangata whārite Navier-Stokes i te huarahi i te ritenga, ie. E. computed te whakamahi i ratou tawhā, ki te whakamatau e kore ko te tikanga te otinga ranei.

Ko te mahi o te Birch - Swinnerton-Dyer

Ko te kāwai o "raruraru Kōhure" tano ki te whakapae e whakaarohia ana e te pūtaiao Ingarangi i University Cambridge. Ahakoa 2300 tau ki muri, i hoatu e te aivanaa tawhito Kariki Euclid te whakaahuatanga katoa o nga rongoā o te x2 whārite + y2 = Z2.

Ki te hoki ki ia o nga tau pirimia tātai i te maha o ngā i runga i te ānau o tona wae, whiwhi tatou he huinga mure ore o tau tōpū. Ki te he ara raima ki "kāpia" reira ki 1 mahi o te tāupe matatini, ka tiki i te Zeta mahi Hasse-Weil mo te ānau kia tuatoru, denoted e te pukapuka L. Kei te reira i ngā mōhiohio e pā ana ki te whanonga o te modulo primes katoa tonu.

hypothesized Bryan Birch me Pita Swinnerton-Dyer whanaunga o ngā ānau Ēripitiki. E ai ki tenei, te hanganga, me te maha o ona huinga o whakatau kouma e pā ana ki te whanonga o te wae L-mahi. I tēnei wā whakapae e keri Birch - tei Swynnerton-Dyer i runga i whārite taurangi whakaahua 3 nekehanga, me te he anake tikanga whānui auhia ohie mō te tātai i te ana'iraa o ngā ānau Ēripitiki.

Hei mahino te faufaa mahi o tenei raruraru, tatu ki te mea e i roto i tuhiwhakamuna hou e hāngai ana i runga i ngā ānau Ēripitiki ko te piha o ngā pūnaha hangarite, me o ratou tono e hāngai paerewa kāinga o te waitohu mamati.

Takatāpui o ngā akomanga p me np

Ki te mea ko pono pāngarau te toenga o te "titauraa Mileniuma", e pā ana tenei e ki te ariā tūturu o hātepe. He raruraru ki te akomanga taurite p me np, hoki e mohiotia ana te raruraru o te reo mahinongofua Cook-Levin kia whakatakoto ai e whai ake. Tera pea e te whakahoki pai ki te pātai e taea te mana aianei hohoro nui, e ko. E. I roto i te wā pūrau (PT). Na, ki te mea he tika te tauākī, e te whakahoki taea e rawa hohoro ki te kitea? Ahakoa māmā , tenei raruraru kua: He te otinga tino tirohia kore uaua ake atu ki te kitea e te reira? Ki te ake ka mohiotia ōritetanga o ngā akomanga p me np e taea te whakatika i nga raruraru katoa kōwhiringa mō te PV. I te kau, he maha tohunga ruarua te pono o tenei tauākī, engari e kore e taea te whakamatau te kore.

Ko te whakapae Rēimāna

Up tae noa ki 1859 i reira ko kahore he taunakitanga o tetahi ture e pai whakaahua e founga ki te tuwha i te tau pirimia i roto i te taiao. Mahalo ko tenei e tika ana ki te meka i whai wāhi te pūtaiao i roto i te tahi atu mea. Heoi, i te rau tau waenganui-19, kua puta ke te āhuatanga, me te kua meinga e ratou tetahi o te kōhukihuki tino, i timata ki te mahi pāngarau.

Te Rēimāna whakapae, i puta i roto i tenei wā - ko te whakaaro i reira ko tetahi tauira i roto i te tohanga o primes tenei.

I teie mahana, e whakapono maha kaipūtaiao hou e ki te kï reira, ka whai i te reira ki te tokomaha o nga parau tumu faufaa o te tuhiwhakamuna hou whakaaro, i whai ahua ai te pūtake o te wahi nui o tikanga e-tauhokohoko.

E ai ki te whakapae Rēimāna, kia rerekē materia te āhua o te tohatoha o ngā tau pirimia i tūmanako i tenei wa. Ko te meka Ko e kore kua ano i kitea noa nei o tetahi pūnaha i te tohatoha o ngā tau pirimia. Hei tauira, i reira te mea he raruraru "mahanga", te rerekētanga i waenganui i te mea e rite ana ki te 2. enei tau e 11 me te 13, 29. Ētahi primes hanga tautau. Ko te 101, 103, 107 me etahi atu. Kua roa whakapae Scientists e tīari taua tautau i roto i tau tino nui pirimia. Ki te kitea e koe a ratou, ka waiho i te ātete o te kī crypto hou i raro i te pātai.

Ko te whakapae o Hodge huringa

Kei te whakatakoto tonu tenei raruraru kāore i te 1941. fokotu'u Hodge whakapae te taea o whakatau tata i te puka o tetahi ahanoa e "te pia" tinana tahi ohie ahu nui. Kua tēnei tikanga kua mohiotia, me te kua whakamahia pai mo te wa roa. Heoi, e kore e mohiotia ai ki te mea i whānuitanga whakangāwaritanga taea te hanga.

Na e matau ana koutou ki ta raruraru unsolvable te tīariari i te kau. Ko ratou te kaupapa o nga mano o pūtaiao huri noa te ao. Kei te tumanako te reira e hohoro ka kia whakatau ratou, a ka tauturu i to ratou tono mahi te tangata tae te a tawhio hou o te whanaketanga hangarau.