Unsolvable pilikia: Navier-Stokes nā helu kaulike, i ka Hodge conjecture, ka Riemann kuhiakau. Ka Wā Kaukani Nä Pahuhopu

Unsolvable pilikia - he 7 hoihoi 'makemakika pilikia. Kēlā me kēia no ia i ua manaoia i kekahi manawa kaulanaʻepekema, i hookuu ia ma ke ano o hypotheses. No ka nui makahiki, e hoʻonā i ia scratching i ko lakou poo makemakika nā hualoaʻa a. Ka poe i loaa ia oe, e kali ana no ka uku o ka hoʻokahi miliona US dala mohai aku ma ke Institute o Clay.

prehistory

I ka 1900, o ka nui Kelemānia mathematician David Hilbert hale, a hoike aku i ka papa inoa o 23 pilikia.

Research lawe mai no ka mea o ko lākou mau olelo hooholo, ua loaa i ka weliweli hopena ma luna o 'epekema o ka 20th kenekulia. Ma ka manawa, ka hapanui o ia i oki ia ia i ka mea pohihihi. Mawaena o ka unsolved paha hapa 'ia' Wehewehe i nā hāʻina i:

• ka pilikia o ka hana mau o na axioms o ka makemakika;
• ka luna kānāwai o ka mā lama i loko o ka makahiki o kekahi laulā kahua;
• makemakika like o physical axioms;
• like o quadratic ano no ākeʻakeʻa kumu algebraic helu coefficients;
• pilikia rigorous hoaponoia enumerative anahonua Fedor Schubert;
• a pela aku.

Unexplored i hohola pilikia no kekahi algebraic māhele rationality ike ia Kronecker theorem a me Riemann kuhiakau .

Institute o Clay

Ma lalo o keia inoa, ua ikeia ka paulele i ka hoʻomana 'ole-e pono ai hui, headquartered ma Kamepelika, Hawaii. Mea, ua hookumuia ia ma 1998 ma Harvard mathematician a me ka pāʻoihana A. Jeffrey L. Clay. Ke kumu o ka Institute mea e paipai a me ka hoʻomōhala makemakika ike. E loaʻa ai i kēia hui, oia ke hoʻolilo 'ia' ana i kānakaʻepekema, a Loulou o i olelo mua iaʻi noiʻi.

I ke kakahiaka nui 21st kenekulia Clay makemakika Institute i kaumaha aku i ka uku nui i ka poe e hoʻoponopono i nā pilikia, a i ike ia ka loa luna 'unsolvable pilikia, e kahea ana i kou papa inoa o Ka Wā Kaukani waiwai pio pilikia. Mai ka "Papa Inoa o Hilbert" ka mea, lilo wale ka Riemann kuhiakau.

Ka Wā Kaukani Nä Pahuhopu

Ma ka papa inoa o ka Institute o Clay mua hui pū:

• Hodge conjecture ma luna o ka pōʻaiapuni;
• na nā helu kaulike o quantum pähola 'o Yang - Mills;
• Poincaré conjecture ;
• ka pilikia o ka like o ka papa P a me np;
• Riemann kuhiakau;
• Navier-Stokes nā helu kaulike, i ke ola ana a me ka smoothness o kona olelo hooholo;
• pilikia Birch - Swinnerton-Dyer.

Mau hamama makemakika pilikia i ka nui hoihoi, no ka mea, hiki i na mea he nui mea hiki implementations.

He aha hoao Grigoriy Perelman

I ka 1900, i ke nä känaka 'epekema kaulana a me ka poe akeakamai Anri Puankare? Aaeaaaaony i kela wale pili olelo hoopomaikai 3-nui loa me ka palena mea homeomorphic i ka 3-dimensional poepoe. Ke hooiaio i loko o ka mau hihia i ole i loko no o ka kenekulia. Wale i loko o 2002-2003, o ka St. Petersburg mathematician G. Perelman paʻi i ka moʻo o ka 'atikala a me ka pāʻoihana o ke Poincare pilikia. Ka mea, bombshell. I ka makahiki 2010, i ka Poincaré conjecture i ua hoʻokoe 'ia mai i ka papa inoa o "Unresolved pilikia" Clay Institute, a me Perelman i kono e kiʻi i ka nui uku ku e ia ia, i ka la mahope hoole me ka weheweheʻana i ke kumu no kona hooholo ana.

Ka loa maopopo wehewehe o ka mea hiki ke hooiaio i Lūkini mathematician, hiki ke haawiia mai, ka hoʻolako 'ana i ka donut (torus), huki i ka laholio iwi kuamoʻo, a laila, ho'āʻo e huki i ka maka o kona anapuni ma kekahi wahi. ʻae nō hoʻi, i kēia mea ole. ʻO kekahi mea mea, inā mākou e keia ho okolohua me ka poepoe. Ma keia hihia, pono e e ekolu-dimensional poepoe, mai ka iwi kuamoʻo anapuni strapped i ka wahi mea hypotheticalʻaha ua loaa ka ekolu-dimensional i loko o ka naauao o ka awelika kanaka, akā, he mau-dimensional i ka hua'ōlelo o ka makemakika.

Poincare? Aaeaaaaony i ka ekolu-dimensional poepoe o ka wale ekolu-dimensional "e hoopii mai ai", i ka ili o ka i hiki ke ano, i ka hookahi wahi, a me Perelman ua hiki ke hooiaio ia. Ke'ī mai, ka "unsolvable pilikia" papa manawa he o 6 pilikia.

Yang-Mills kumumanaʻo

Kēia makemakika pilikia ua manaoia e ke kākau i ka makahiki 1954. ʻepekema hoʻomanaʻo o ke kumumanaʻo, ua like penei: no ka kekahi poe noonoo ole olelo hoopomaikai moʻokūʻikena pae makahiki quantum kumumanaʻo hana e Yang a me Millsom nei, a pela ua Aʻohe nuipa a kina.

Olelo ana i ka 'ōlelo maopopo ma ke ano o kanaka, ka AaOIeIOUIeXAOAaIN maoli mea (. (Particles), kino, nalu, etc.) e māheleʻia i loko o 4 ke ano: electromagnetic a, gravitational, nāwaliwali a me ka ikaika. No ka nui makahiki, physicists e ho'āʻo ana e hana i kekahi mau kahua kumumanaʻo. Ua pono lilo i kahi mea paahana e wehewehe ana a pau o kēia mau hana kūleʻa. Yang-Mills kumumanaʻo - he makemakika ōlelo me i ka mea i hiki ke wehewehe 3 o ka 4 walaʻauʻana koa o ke ano. Ia aole i pili i ka umekaumaha. No ia mea, ua hiki ole kuhi Yang, a Mills ua hiki ke kūkulu i ka pähola 'ana o ke kula ia.

Eia hou, ke ole-linearity o ka i manaoia nā helu kaulike hana ia paʻakikī loa ia ke hoʻoponopono. ka mea mālama i ka hoʻoponopono i ka hola i ka poe liilii, huina o ia a eia i ka perturbation moʻo. Eia naʻe, ia mea e ike ana i ka hoʻoponopono i kēia mau nā helu kaulike no ka ikaika lua.

Navier-Stokes nā helu kaulike

Me kēia mau, ka 'aoʻao i ho'ākāka' ia keʻano o ka hanaʻana e like me lewa pele, loli pele a me ka turbulence. No kekahi kūikawā hihia, ka mākau pāʻoihana o ke Navier-Stokes nā helu kaulike i ua loaʻa, akā, hana ia no ka mea pono i koe ole kekahi i pomaikai ae la lakou. I ka Ia manawa, laulā hōʻulu no kekahi aiee o ka wikiwiki, nuʻa, puʻe, manawa, a no laila, ma e leie aku e loaʻa ai maikaʻi loa nā hualoaʻa. Mākou hiki wale manaʻolana i kekahi, e hoʻohana Navier-Stokes nā helu kaulike i loko o ka e ku pono kuhikuhi, oa. E. Me ka hoʻohana 'ana i ko lakou mau mea kiko'î, a me ka hooiaio ana i ka iaoia mea i ka pāʻoihana.

I ka hana o ka Birch - Swinnerton-Dyer

Ka waeʻano o "poʻokela pilikia" pili i ke kuhiakau i manaoia e Pelekāneʻepekema ma Kamepelika University. O 2300 makahiki aku nei, i ke kahiko Greek haumāna Euclid i ka piha ano o nā pāʻoihana o ka helu kaulike X2 + y2 = z2.

Inā no kela a me keia o na Kuhina Nui helu, e hoʻomaulia i ka helu o nā kumu ma ka hālawa o kona pa alima, ua loaa he mana loa 'ia paha o nā integers. Inā he pōhaku puna ala e "glue" ia i 1 hana ana i ka luna 'ee iaaanu aey, laila, kiʻi i ka Hasse-Weil zeta hana no ke kolu o ka mea hālawa, denoted ma ka palapala L. It kekahi mau' ike e pili ana i ka hana o ka modulo a pau primes koke.

Bryan Birch a me Peter Swinnerton-Dyer wänana i hoahanau o elliptic curves. E like me keia, me ka 'ole, a me ka helu o kona kau ana i ka naauao hoʻoholo pili i ka hana o ka L-kuleana pili i pa alima. Currently unproven kuhiakau Birch - Swynnerton-Dyer hilinaʻi nui ma algebraic nā helu kaulike hōʻike no 3 degere a me ka mea wale comparatively mea mau hana no ka helu ana o ka huakaʻi o elliptic curves.

No ka maopopo i ka mea hiki nui o keia pilikia, ka mea, ke kala i ka olelo i loko o ke kālā no cryptography ma muli o elliptic curves i ka papa o ka asymmetric nenoai, a me kā lākou palapala noi i ka nānā 'wahi lulu mau hae o ka mīkini inoa.

Like o nā papa pa, a np

Inā i ke koena o ka "Ka Wā Kaukani kū'ē'ē 'ana i" mea hoʻokahi wale nō makemakika, keia ua pili i ka maoli kumumanaʻo o algorithms. hiki e ua kālaiʻia A pilikia me ka like papa pa, a np, iʻikeʻia e like me ka pilikia o ka Cook-Levin 'ōlelo maopopo No like penei. Ina i ka maikaʻi pane ana i ka ninau hiki ke hōʻoia koke lawa, i mea. E. I polynomial manawa (PT). A laila, ina ka hoakaka mea pololei, i ka pane hiki e kokoke koke e huli? O maʻalahi , keia pilikia ua: Ua i ka pāʻoihana anei ka huli ole aku paʻakikī ma mua o ka loaʻa ia? Inā e hoʻokolokolo pono o nā papa pa, a np e loa e ho'āʻo ai i nā mea a pau i ke koho pilikia hiki ke wehe pilikia no PV. I ka manawa, he nui akamai kanalua no ka ike i ka oiaio o keia olelo, akā, hiki i hooiaio ole ia.

Ka Riemann kuhiakau

Up a 1859, aole he hoike o kekahi kānāwai i makemake wehewehe ana, e hāʻawi i ke Kuhina Nui helu i waena o ka mea maoli. Paha ia ua aie i ka mea i ka 'epekema' ole i loko o kekahi mea e. Eia naʻe, ma ka hapalua like-19th kenekulia, ke kahua i loli, a ua lilo kekahi o ka loa ka manaʻo, a hoomaka ae la e hana makemakika mea.

Ke Riemann Ke Kuhiakau, iʻikeʻia i loko o kēia wā - keia mea i ka mea mahuʻi ia he mea i kekahi kumu i loko o ka puunaue ana o primes.

I kēia lā, he nui ke kālā noʻepekema manaoio i ina ka mea, ua maopopo, ka mea e loaʻa, e noonoo na mea he nui o na kumu me nā loina o ke kālā no cryptography, lilo i kumu o kekahi hapa nui o ka e-kalepa maomeka.

E like me ka Riemann kuhiakau, ka ano o ka puunaue ana o Kuhina Nui helu i oko materially, mai mua mai i keia manawa. Ka mea o ia a hiki i keia wa ua ole i ua loaʻa o kekahi'ōnaehana i loko o ka puunaue ana o Kuhina Nui helu. No ka laʻana, aia no he pilikia "kapu", i ka likeʻole ma waena o i mea like me kēia mau 2. nui, he 11 a me 13, 29. Other primes kuahene huhui. O 101, 103, 107 a me kekahi poe e ae.ʻepekema, ua lōʻihi mahuʻi mua ia e like me he mau huhui ola i waena o nui loa Kuhina Nui helu. Inā e loaʻa iā lākou, i ka ia'ku o kēia crypto ki e ia ma lalo o nīnau.

Ke kuhiakau o Hodge pōʻaiapuni

Kēia unsolved pilikia ua nō ua kālaiʻia i loko o 1941. Hodge kuhiakau paipai i ka manawa kūpono o approximating ke ano o kekahi mea ma "tuko i" pu na mea kino nui Ana. Kēia papa hana i uaʻikeʻia, a ua ua hoʻohana ana i ka lōʻihi manawa. Naʻe, ka mea, ua i ike i ka mea i simplification hiki ke i.

Ano, ia oe i mea unsolvable pilikia nei i ka manawa. Ka mea, i ke kumuhana o nā tausani o nā kānakaʻepekema a puni ka honua. Ua Ua manaolana i ka mea e koke e hoʻonā 'ia, a me kā lākou e pili ana, e kōkua manaʻo kanaka hiki i ka hou a oʻanoʻenehana? Acaeoey.