Unsolvable teeb meem: Navier-Stokes sib npaug, lub Hodge conjecture, lub Riemann hypothesis. Xyoo txhiab hom phiaj

Unsolvable teeb meem - ib tug 7 nthuav zauv teeb meem. Txhua yam ntawm lawv twb tau npaj siab ntawm ib lub sij hawm nto moo zaum, feem ntau yog nyob rau hauv daim ntawv ntawm hypotheses. Rau ntau xyoo lawm, kom daws tau lawv khawb lawv lub taub hau lej thoob ntiaj teb. Cov neeg uas kawm tau ntawv zoo, tos ib tug nqi zog ntawm ib lab US dollars muaj los ntawm lub koom haum ntawm av nplaum.

prehistory

Nyob rau hauv 1900, tus poj German mathematician David Hilbert wagon, hais ib daim ntawv teev 23 teeb meem.

Kev tshawb fawb nqa tawm rau lub hom phiaj ntawm lawv kev txiav txim siab, tau muaj ib tug zoo kawg li tej yam nyob rau hauv science ntawm lub xyoo pua 20th. Thaum lub caij, feem ntau ntawm lawv twb ceased mus yuav ib tug paub tsis meej. Ntawm cov unsolved los yog solved yog:

• qhov teeb meem ntawm lub taub hau ntawm lub axioms ntawm xam;
• cov kev cai lij choj ntawm them pauj nyob rau hauv lub qhov chaw ntawm txhua numeric teb;
• mathematical txoj kev tshawb no ntawm lub cev axioms;
• txoj kev tshawb no ntawm quadratic ntaub ntawv rau arbitrary algebraic tooj coefficients;
• teeb meem kev kawm ua neeg ncajncees enumerative geometry Fedor Schubert;
• thiab li ntawd.

Unexplored kis teeb meem rau tej algebraic cheeb tsam rationality paub Kronecker theorem thiab Riemann hypothesis .

Lub koom haum ntawm av nplaum

Nyob rau hauv no lub npe yog lub npe hu private non-profit organization, headquartered nyob rau hauv Cambridge, Massachusetts. Nws twb nrhiav tau nyob rau hauv 1998 los ntawm Harvard mathematician thiab businessman A. Jeffrey L. Clay. Lub hom phiaj ntawm lub koom haum yog los txhawb thiab tsim zauv paub. Mus cuag lub koom haum no muab khoom plig rau zaum thiab txhawb nqa pheej tshawb fawb.

Nyob rau hauv thaum ntxov 21st century Clay lej koom haum tau muaj ib tug nqi rau cov neeg uas yuav daws tau qhov teeb meem, uas yog hu ua tus tshaj txoj unsolvable teeb meem, hu rau koj daim ntawv teev cov xyoo txhiab nqi zog teeb meem. Los ntawm cov "Daim ntawv teev cov Hilbert" nws tau los ua xwb lub Riemann hypothesis.

Xyoo txhiab hom phiaj

Nyob rau hauv daim ntawv teev cov koom haum ntawm av nplaum Ameslikas muaj:

• Hodge conjecture rau mus;
• qhov sib npaug ntawm quantum kev tshawb xav ntawm Yang - Mills;
• Poincaré conjecture ;
• qhov teeb meem ntawm koob pheej ntawm lawv cov chav kawm ntawv P thiab NP;
• Riemann hypothesis;
• Navier-Stokes sib npaug, lub hav zoov thiab smoothness ntawm nws cov kev txiav txim siab;
• teeb meem Birch - Swinnerton-Dyer.

Cov qhib zauv teeb meem yog zoo txaus siab vim hais tias lawv muaj peev xwm muaj ntau yam tswv yim implementations.

Yuav ua li cas muaj pov thawj Grigoriy Perelman

Nyob rau hauv 1900, tus naas ej tus paub txog thiab philosopher Anri Puankare pom hais tias txhua txhua tsuas kev cob cog rua compact 3-manifold tsis muaj ciam yog homeomorphic rau lub 3-dimensional kheej. Lub pov thawj nyob rau hauv lub dav dav ntaub ntawv tsis tau nyob rau hauv dhau ib tiam. Tsuas yog nyob rau hauv 2002-2003, lub St. Petersburg mathematician G. Perelman luam tawm ib tug series ntawm cov khoom nrog cov tshuaj ntawm lub Poincare teeb meem. Lawv bombshell. Nyob rau hauv 2010, lub Poincaré conjecture tau cais los ntawm daim ntawv teev cov "teeb meem qhov teeb meem" Av nplaum koom haum, thiab rau Perelman raug caw mus tau ib tug txiav txim remuneration vim nws, uas rau tom kawg tsis kam tsis muaj dab yog vim li cas rau nws cov kev txiav txim siab.

Qhov tseem to taub piav qhia seb yuav ua pov thawj rau Lavxias teb sab mathematician, yuav muab, muab hais tias ib tug donut (torus), rub cov roj hmab disc, thiab ces sim mus rub cov ntug ntawm nws ib ncig ntawm ib tug taw tes. Obviously, qhov no yog tsis yooj yim sua. Ib qho ntxiv uas yog, yog hais tias peb ua no xyaum ua tej yam nrog rau lub npas. Nyob rau hauv cov ntaub ntawv no, nkawd mus ua tau peb-dimensional kheej, peb muab tau los ntawm cov disc ncig strapped rau lub point hypothetical qaum yog peb-dimensional nyob rau hauv qhov kev nkag siab ntawm qhov nruab nrab neeg, tab sis ib tug ob-seem nyob rau hauv cov nqe lus ntawm kev kawm txog zauv.

Poincare pom hais tias peb cov-dimensional kheej yog tus tsuas yog peb-dimensional "kwv", lub qhov chaw uas muaj peev xwm yuav cog lus rau ib tug taw tes, thiab Perelman muaj peev xwm los ua pov thawj nws. Yog li, lub "unsolvable teeb meem" daim ntawv teev tam sim no muaj 6 teeb meem.

Yang-Mills kev tshawb xav

Qhov no xyuam xim teeb meem no twb tau npaj los ntawm tus sau phau ntawv nyob rau hauv 1954. Kev formulation ntawm txoj kev tshawb xav yog raws li nram no: rau tej yam yooj yim compact koob qhia hais tias pab pawg neeg qhov chaw quantum kev tshawb xav tsim los ntawm Yang thiab Millsom tshwm sim, thiab yog li muaj pes tsawg loj kho raws.

Hais lus cov lus to taub los ntawm qhov dog dig, tus neeg sib raug zoo ntawm tej yam ntuj tso khoom (. Hais, lub cev, tsis, etc.) yog muab faib ua 4 hom: electromagnetic, gravitational, tsis muaj zog thiab muaj zog. Rau ntau xyoo, physicists tseem tabtom ua ib tug general teb ziag no. Nws yuav tsum tau ua ib lub cuab tam rau piav qhia txog tag nrho cov kev sib tshuam. Yang-Mills kev tshawb xav - ib tug zauv lus uas nws twb tau mus piav qhia txog 3 lub 4 yooj yim rog ntawm qhov. Nws tsis siv rau lub ntiajteb txawj nqus. Yog li ntawd peb yuav tsis xav hais tias Yang thiab Mills muaj peev xwm los tsim ib tug kev tshawb xav ntawm lub teb.

Nyob rau hauv tas li ntawd, qhov uas tsis yog-linearity ntawm lub tswv yim sib npaug ua rau lawv tsis tshua muaj neeg yooj yim mus daws kom tau. lawv tswj kom daws tau kwv yees li ntawm me me coupling constants raws li ib tug perturbation series. Txawm li cas los, nws tsis yog tseeb yuav ua li cas los daws kom tau cov equations rau muaj zog coupling.

Navier-Stokes sib npaug

Nrog rau cov kab zauv piav dab xws li huab cua khiav, cov kua txaus thiab kiv. Rau ib txhia tshwj xeeb no, lub analytical kev daws teeb meem ntawm lub Navier-Stokes sib npaug tau pom, tab sis ua rau cov tseem tsis muaj ib tug tau ua tau zoo. Nyob rau tib lub sij hawm, hais txog zauv simulation rau tej qhov tseem ceeb ntawm kev ceev, ceev, siab, lub sij hawm, thiab thiaj li nyob tso cai mus cuag tau zoo heev. Peb yuav tsuas vam tias ib tug neeg yuav siv Navier-Stokes sib npaug nyob rau hauv kev coj rov qab, piv txwv li. E. xoo siv lawv tsis, los yog ua pov thawj tias tus qauv yog tsis cov tshuaj.

Cov neeg ua hauj lwm ntawm lub Birch - Swinnerton-Dyer

Cov qeb ntawm "Koj teeb meem" siv rau lub hypothesis npaj los ntawm British zaum ntawm Cambridge University. Txawm 2300 xyoo dhau los, ancient Greek kawm Euclid muab ib tug ua tiav kev piav qhia txog lub ntsiab ntawm kab zauv x2 + y2 = Z2.

Yog hais tias rau txhua txhua tus lub prime xov tooj rau xam tus naj npawb ntawm cov ntsiab lus nyob rau hauv qhov nkhaus ntawm nws tsev, peb tau txais ib txhis txheej zauv. Yog hais tias ib tug qhob txoj kev uas yuav "cov kua nplaum" nws mus rau 1 nuj nqi ntawm ib tug complex nce mus nce los, ces tau lub Hasse-Weil zeta muaj nuj nqi rau ib tug thib peb kev txiav txim nkhaus, denoted los ntawm tsab ntawv L. Nws muaj cov lus qhia txog tus cwj pwm ntawm cov modulo tag nrho cov primes tam sim ntawd.

Bryan Birch thiab Peter Swinnerton-Dyer hypothesized txheeb ze ntawm elliptic curves. Raws li qhov no, tus qauv thiab tus naj npawb ntawm nws txheej rational kev txiav txim siab txuam nrog tus cwj pwm ntawm L-muaj nuj nqi xauj tsev. Tam sim no meej hypothesis Birch - Swynnerton-Dyer nyob ntawm algebraic equations piav txog 3 degrees thiab tsuas yog comparatively yooj yim general txoj kev xam xyuas nyob qib elliptic curves.

Yuav kom nkag siab txog cov tswv yim tseem ceeb ntawm qhov teeb meem no, nws suffices hais tias nyob rau hauv niaj hnub cryptography raws li elliptic curves yog ib tug hauv chav kawm ntawv ntawm asymmetric systems, thiab lawv daim ntawv thov yog raws li domestic cov qauv ntawm cov kos npe.

Koob pheej ntawm lawv cov chav kawm ntawv p thiab np

Yog hais tias tus so ntawm lub "Millennium Txoj kev sib tw" yog purely zauv, qhov no yog muaj feem xyuam rau lub sij hom phiaj ntawm algorithms. Ib tug teeb meem nrog koob pheej ntawm lawv cov chav kawm p thiab np, kuj hu ua tus teeb meem ntawm lub noj-Levin to taub cov lus tej zaum yuav formulated raws li nram no. Piv txwv hais tias ib tug zoo lus teb rau ib lo lus nug yuav muaj tseeb sai sai txaus, uas yog. E. Nyob rau hauv polynomial lub sij hawm (PT). Ces, yog hais tias tus ntawv no yog muaj tseeb, tias cov lus teb yuav ua tau sai heev mus nrhiav? Txawm yooj yim , qhov teeb meem no yog: Yog cov tshuaj tiag tiag saib tsis muaj ntau nyuaj tshaj mus nrhiav nws? Yog hais tias koob pheej ntawm lawv cov chav kawm ntawv p thiab np yuav puas tau muaj pov thawj tias tag nrho cov xaiv teeb meem yuav tau daws rau PV. Thaum lub caij, ntau cov kws txawj tsis ntseeg qhov tseeb ntawm nqe lus no, tab sis yuav tsis muaj tseeb.

Lub Riemann hypothesis

Txog thaum 1859 muaj tsis muaj pov thawj txog tej kev cai lij choj uas yuav piav li cas mus faib lub prime xov tooj ntawm cov natural. Tej zaum qhov no yog vim lub fact tias cov science muab kev koom tes nyob rau hauv lwm yam teeb meem. Txawm li cas los, los ntawm nruab nrab-xyoo pua puv 19, qhov teeb meem no tau hloov thiab lawv tau ua ib tug ntawm cov tseem ceeb, uas pib xyaum ua lej.

Lub Riemann hypothesis, uas nyob rau hauv lub sij hawm no - qhov no yog qhov assumption tias muaj yog ib cov qauv nyob rau hauv lub tsev ntawm primes.

Niaj hnub no, muaj ntau yam niaj hnub zaum ntseeg tias yog hais tias nws yog pov thawj, nws yuav muaj mus rau reconsider ntau ntawm hauv paus ntsiab cai uas niaj hnub cryptography, lub hauv paus ntawm ib tug loj ib feem ntawm e-commerce mechanisms.

Raws li cov Riemann hypothesis, qhov ntawm lub tsev ntawm prime numbers tej zaum yuav txawv siv khoom los ntawm xav ntawm lub sij hawm no. Qhov tseeb yog tias kom txog rau thaum tam sim no twb tseem tsis tau tau pom tej yam uas system nyob rau hauv lub tsev ntawm prime xov tooj. Piv txwv li, yog ib tug teeb meem "ntxaib", qhov txawv ntawm uas yog sib npaug zos rau 2. Cov lej no yog 11 thiab 13, 29. Lwm yam primes tsim pawg ua ke. Nws yog 101, 103, 107 thiab lwm tus. Cov kws tshawb fawb tau ntev xav tias hais tias xws li pawg nyob ua ib ke nrog loj heev prime xov tooj. Yog hais tias koj nrhiav tau lawv, tus kuj niaj hnub crypto tseem ceeb yuav tsum tau nyob rau hauv nqe lus nug.

Cov hypothesis ntawm Hodge mus

Qhov no unsolved teeb meem yog tseem formulated nyob rau hauv 1941. Hodge hypothesis qhia tau approximating rau hauv daim ntawv ntawm ib yam khoom los ntawm "gluing" ua ke yooj yim lub cev loj dimension. Qhov no txoj kev tau paub thiab twb tau muab siv ntse rau ib ntev lub sij hawm. Txawm li cas los, nws tsis paub yuav ua li cas raws li simplification yuav ua.

Tam sim no uas koj paub tias dab tsi unsolvable teeb meem muaj nyob rau lub caij. Lawv yog cov kawm ntawm txhiab ntawm zaum nyob ib ncig ntawm lub ntiaj teb no. Nws yog vam hais tias lawv yuav sai sai no yuav tau daws, thiab lawv ua daim ntawv thov yuav pab tau tib neeg mus txog ib tug tshiab puag ncig ntawm kev siv technology tshiab txoj kev loj hlob.