Unsolvable matsala: Navier-dana kunamar rura lissafai, da Hodge zato, da Riemann jarrabawa. Millennium manufofin

Unsolvable matsala - mai 7 ban sha'awa ilmin lissafi matsaloli. Kowane daga cikinsu an samarwa a lokaci daya shahara masana kimiyya, yawanci a cikin nau'i na shiriritar. Domin da yawa shekarun da suka gabata, don magance su, yanã tõno kawunansu lissafi a dukan duniya. Waɗanda suka ci, jiran wani sakamako na daya dalar Amurka miliyan miƙa ta Institute of Clay.

prehistory

A shekarar 1900, babban Jamus lissafi David Hilbert wagon, gabatar da wani jerin 23 matsaloli.

Binciken da za'ayi domin manufar su yanke shawara, sun yi wani gagarumin tasiri a kan kimiyya na karni na 20th. A lokacin, mafi yawansu ba su riga ya daina zama asiri. Daga cikin kasa warwaruwa ko partially warware su ne:

• matsalar da daidaito da axioms na ilmin lissafi.
• general dokar juna a cikin sarari na wani Tazarar filin.
• ilmin lissafi nazarin jiki axioms.
• nazarin quadratic siffofin ga sabani algebraic yawan coefficients.
• matsalar tsaurara gaskata enumerative lissafi Fedor Schubert.
• da sauransu.

Unexplored suna yada matsala ga wani algebraic yankin rationality sani Kronecker Theorem da Riemann jarrabawa .

Cibiyar Clay

A karkashin wannan sunan da aka sani mai zaman kansa ba riba kungiyar, hedkwatarsa a Cambridge, Massachusetts. Yana da aka kafa a 1998 ta Harvard lissafi da kasuwa A. Jeffrey L. Clay. Dalilin da Cibiyar shi ne ya gabatar da kuma harkokin ilmin lissafi ilimi. Don cimma wannan kungiyar bada lambobin yabo ga masana kimiyya da kuma gayyar alamar bincike.

A farkon 21st karni Clay Ilmin Lissafi Institute ya miƙa premium wa waɗanda suka yi za su warware matsalolin, wanda aka fi sani da mafi hadaddun unsolvable matsalar, kira your jerin Millennium Prize Matsaloli. Daga cikin "List of Hilbert" ya zama kawai Riemann jarrabawa.

Millennium manufofin

A cikin jerin Cibiyar Clay asali hada da:

• Hodge zato a kan hawan keke.
• da lissafai na jimla ka'idar Yang - Mills.
• Poincaré zato .
• matsalar da daidaici da azuzuwan P da kuma NP.
• Riemann jarrabawa.
• Navier-dana kunamar rura lissafai, kasancewar kuma smoothness al'amarinta.
• matsalar Birch - Swinnerton-Dyer.

Wadannan bude ilmin lissafi matsaloli ne na babban sha'awa saboda su iya samun yawa m implementations.

Abin da ya tabbatar da Grigoriy Perelman

A shekarar 1900, sanannen masanin kimiyya da falsafa Anri Puankare da shawarar cewa kowane kawai da alaka m 3-da yawa ba tare da iyaka ne homeomorphic zuwa 3-girma Sphere. A hujja a general hali bai kasance a kan wata karni. Kawai a 2002-2003, da St. Petersburg lissafi G. Perelman buga jerin articles tare da bayani na Poincare matsala. Su bombshell. A 2010, da Poincaré zato da aka cire daga jerin "warware matsalar matsalar" Clay Institute, kuma zuwa Perelman aka kira su zuwa ga samun wani babba albashin saboda shi, wanda karshen ƙi ba tare da bayyana dalilai ba domin ta yanke shawara.

A mafi m bayani daga abin da zai iya tabbatar da zuwa Rasha lissafi, za a iya ba, samar da cewa a Donut (torus), ja da roba Disc, sa'an nan kokarin cire gefen ta karkara a daya batu. Babu shakka, wannan bashi yiwuwa. Wani abu shi ne, idan muka yi wannan gwajin tare da ball. A wannan yanayin, ya zama alama uku-girma Sphere, mun samu daga Disc karkara Shades ga zance tamkar igiyar ne mai hawa uku a fahimtar da talakawan mutum, amma a biyu-girma cikin sharuddan lissafi.

Poincare nuna cewa uku-girma Sphere ne kawai uku-girma "abu", da farfajiya na wanda za a iya ƙulla wani guda batu, kuma Perelman ya iya tabbatar da shi. Saboda haka, "unsolvable matsala" list yanzu kunshi 6 matsaloli.

Yang-Mills ka'idar

Wannan ilmin lissafi matsalar da aka samarwa da mawallafa a 1954. Kimiyya halitta ka'idar ne kamar haka: ga wani sauki m ma'auni kungiyar sarari jimla ka'idar halitta da Yang da kuma Millsom wanzu, kuma ta haka ne yana da sifili taro lahani.

Magana da harshen gane da mutum talakawa, da hulda tsakanin halitta abubuwa (. Gaɓũɓuwa, jikunanmu, tãguwar ruwa, da dai sauransu) ya kasu kashi 4 iri: electromagnetic, gravitational, rauni da karfi. Domin shekaru masu yawa, lissafin kimiyya na kokarin haifar da wani janar filin ka'idar. Yana dole ne ya zama wani kayan aiki don bayyana duk wadannan interactions. Yang-Mills ka'idar - a ilmin lissafi da harshen da wanda shi yiwuwa a bayyana 3 na 4 na asali sojojin na halitta. Bai shafi zuwa nauyi. Saboda haka ba za mu iya ɗauka cewa Yang da kuma Mills ya iya samar da wani ka'idar da filin.

Bugu da kari, wadanda ba linearity na samarwa lissafai sa su musamman wuya a warware. suka gudanar don warware kamar a kananan hada guda biyu constants matsayin perturbation jerin. Duk da haka, shi ne ba a bayyana yadda za a warware wadannan lissafai for karfi hada guda biyu.

Navier-dana kunamar rura lissafai

Tare da wadannan maganganu da aka bayyana matakai kamar iska ya kwarara, ruwa ya kwarara da kuma haukan kogi. Ga wasu lokuta na musamman, da hikimar tantance mafita na Navier-dana kunamar rura lissafai da aka samu, amma aikata shi ga kowa amma ba wanda ya yi nasara. A daidai wannan lokaci, na lamba kwaikwaiyo na musamman dabi'u na gudun, yawa, matsa lamba, lokaci, kuma haka a kan damar cimma kyau kwarai da sakamakon. Za mu iya kawai fatan cewa wani zai yi amfani da Navier-dana kunamar rura lissafai a gaban shugabanci, watau. E. lissafta yin amfani da su sigogi, ko ya tabbatar da cewa Hanyar ba da bayani.

The aiki na Birch - Swinnerton-Dyer

A category na "fice matsaloli" ta shafi jarrabawa samarwa da Birtaniya masana kimiyya a jami'ar Cambridge. Ko 2300 shekaru da suka wuce, da tsoho Greek masanin Euclid ya ba da cikakken bayanin irin mafita daga lissafi x2 + y2 = Z2.

Idan ga kowane daga cikin Firayim lambobi zuwa lissafi da yawan maki a kan kwana na naúrar, mu samu wani iyaka sa na integers. Idan wani kankare hanya zuwa "manne" shi zuwa 1 aiki na wani hadadden m, sa'an nan samun da Hasse-Weil zeta aiki a karo na uku domin kwana, denoted da wasika L. Ya ƙunshi bayani game da hali na modulo duk primes nan da nan.

Bryan Birch da Bitrus Swinnerton-Dyer hypothesized dangi na elliptic masu lankwasa. A cewar wannan, tsarin da yawan ta sa na m yanke shawara hade da hali na L-aiki naúrar. A halin yanzu unproven jarrabawa Birch - Swynnerton-Dyer ya dogara algebraic lissafai kwatanta 3 darajõji, kuma shi ne kawai comparatively sauki janar Hanyar for kirga daraja na elliptic masu lankwasa.

Don gane da m muhimmancin wannan matsala, shi isa a ce a zamani cryptography dangane elliptic masu lankwasa ne a aji na asymmetric tsarin, da kuma su aikace-aikace ne tushen m ma'aunansa na dijital sa hannu.

Daidaitan azuzuwan p kuma NP

Idan da sauran "Millennium fuskanci kalubale" ne zalla ilmin lissafi, wannan yana alaka da ainihin ka'idar lissafi mai tsauri. Wata matsala da daidaici azuzuwan p kuma NP, kuma aka sani da matsala na Cook-Levin m harshe iya tsara kamar haka. Yi tsammani cewa wani tabbatacce amsar wata tambaya da za a iya tabbatar da sauri isa, cewa shi ne. E. A polynomial lokaci (PT). Sa'an nan kuma, idan da sanarwa daidai ne, cewa amsar iya zama quite da sauri samu? Ko da sauki , wannan matsala ne: Shin da gaske bayani duba ba wuya fiye da samun da shi? Idan daidaici da azuzuwan p kuma NP zai taba a tabbatar da cewa duk zabin matsaloli za a iya warware for PV. A lokacin, kwararru da yawa shakka da gaskiyar wannan sanarwa, amma ba zai iya tabbatar da in ba haka ba.

A Riemann jarrabawa

Up har 1859 babu wata shaida ta kowace dokokin da zai bayyana yadda za a raba Firayim lambobi daga cikin halitta. Wata kila wannan shi ne saboda cewa da kimiyya da hannu a wasu al'amura. Duk da haka, da tsakiyar karni na 19th, halin da ake ciki ya canza kuma sun zama daya daga cikin mafi gaggawa, wanda ya fara gudanar da aiki ilimin lissafi.

A Riemann jarrabawa, abin da ya bayyana a cikin wannan lokaci - wannan shi ne zato cewa akwai wani juna a rarraba primes.

Yau, da yawa zamani masana kimiyya yi imani da cewa idan an tabbatar, shi zai yi don sake da yawa daga cikin muhimman hakkokin ka'idodinta zamani cryptography, samar da tushen babban ɓangare na e-kasuwanci sunadaran.

Bisa ga Riemann jarrabawa, da yanayi na rarraba Firayim lambobin iya bambanta materially daga tsammani a wannan lokaci. Gaskiyar ita ce, har yanzu ya ba tukuna aka samu daga wani tsarin a rarraba Firayim lambobi. Alal misali, akwai wani matsala "tagwaye", bambanci tsakanin wanda shi ne daidai 2. Wadannan lambobi ne 11 da kuma 13, 29. Sauran primes nunawa gungu. Yana 101, 103, 107 da sauransu. Masana kimiyya sun jima suna zargin cewa irin wannan gungu zama tsakanin manya-manyan Firayim lambobi. Idan ka same su ba, da juriya na zamani Hikimar key zai zama a karkashin tambaya.

A cikin jarrabawa na Hodge hawan keke

Wannan kasa warwaruwa matsala ne har yanzu tsara a 1941. Hodge jarrabawa da shawara da yiwuwar approximating nau'i na wani abu da "gluing" tare sauki jikinsu ya fi girma girma. Wannan hanya da aka sani, kuma an yi amfani da nasarar na dogon lokaci. Duk da haka, shi ne ba su sani ba abin da har simplification za a iya sanya.

Yanzu da ka san abin da unsolvable matsaloli zama a wannan lokacin. Su ne batu na dubban masana kimiyya a duniya. Ana fatan cewa za su nan da nan za a warware, kuma su m aikace-aikace zai taimaka bil'adama isa wani sabon zagaye na fasaha ci gaba.