N'ngosathetseka vuto: Navier-Stokes maikwezhoni, ndi Hodge kungolota, ndi Riemann kungoganizira. zolinga Millennium

N'ngosathetseka vuto - 7 chidwi mavuto masamu. Aliyense wa iwo anali akufuna pa nthawi ina asayansi otchuka, kawirikawiri mu mawonekedwe a malingaliro. Kwa zaka zambiri, kuti mulithetse kukanda mitu yawo masamu lonse. Amene bwino, kuyembekezera mphotho ya madola miliyoni US anapereka Institute of Clay.

prehistory

Mu 1900, akulu German masamu David Hilbert ngolo, naperekanso mndandanda wa mavuto 23.

Kafukufuku cholinga cha zochita zawo, akhala akuthandiza kwambiri pa sayansi ya m'ma 20. Pa nthawi, ambiri a iwo kale unasiya kukhala chinsinsi. Pakati pa sanathetsedwe kapena pang'ono anathana anali:

• vuto la kugwirizana kwa axioms a masamu;
• lamulo ambiri reciprocity mu danga la mmunda uliwonse M'ndandanda;
• kuphunzira masamu a axioms thupi;
• kuphunzira mitundu quadratic kwa umasinthasintha koefishienti chiwerengero algebraic;
• vuto okhwima kulungamitsidwa enumerative Masamu Fedor Schubert;
• ndi zina zotero.

Unexplored amafalitsidwa vuto lililonse algebraic dera rationality kudziwika Kronecker Lingaliro Lovomerezeka ndi Riemann kungoganizira .

Institute of Clay

Pansi pa dzina ili amadziwika paokha sanali phindu gulu liku- lu ku Cambridge, Massachusetts. Idamangidwa mu 1998 ndi Harvard masamu ndi wabizinesi A. Jeffrey L. Clay. Cholinga cha Institute ndi kulimbikitsa ndi kukhala odziwa masamu. Pofuna kukwaniritsa bungwe amapereka mphoto kwa asayansi ndi ukulipirira kafukufuku zingamuthandize.

Mu zaka za m'ma 21 Clay masamu Institute ali anapereka umafunika amene adzathetsa mavuto, amene amadziwika ngati vuto zovuta kwambiri n'ngosathetseka, akuitana mndandanda wanu wa Millennium Prize Mavuto. Kuchokera "List of Hilbert" anakhala yekha Riemann kungoganizira.

zolinga Millennium

Mu mndandanda wa Institute of Clay poyamba m'gulu:

• Hodge kungolota pa m'zinthu;
• ndi maikwezhoni wa kwadzidzidzi chiphunzitso cha Yang - Mills;
• Poincaré kungolota ;
• vuto la kuyanjana kwa makalasi P ndi NP;
• Riemann kungoganizira;
• Navier-Stokes maikwezhoni, kukhalapo ndi kusalala kwa zosankha zake;
• vuto Birch - Swinnerton-Dyer.

Izi lotseguka mavuto masamu ndi chidwi kwambiri chifukwa ndi implementations zambiri.

Chomwe chinali Grigoriy Perelman

Mu 1900, wasayansi wotchuka ndi nzeru zapamwamba Anri Puankare adaganiza kuti aliyense chabe chikugwirizana yaying'ono 3-zobwezedwa popanda malire ndi homeomorphic ku dera 3-ooneka enieni. Umboni zinachitikira ambiri sinapite zaka zambiri. Only mu 2002-2003, ndi St. Petersburg masamu G. Perelman lofalitsidwa nkhani ndi yankho la vuto Poincare. Iwo bombshell. Mu 2010, kungolota Poincaré ali itachotsedwa mndandanda wa "osathetsedwa vuto" Institute Clay, ndi Perelman anaitanidwa kupeza Malipilo ndithu chifukwa iye ndi yotsirizira anakana popanda kufotokoza chifukwa chake anasankha ake.

Mafotokozedwe kwambiri zomveka zimene akanakhoza kutsimikizira kuti masamu Russian, angaperekedwe, popereka ndi donati (torus), kukoka chimbale labala, ndiyeno yeserani kuwakoka m'mphepete mwa circumference ake pa nthawi ina. Mwachionekere, zimenezi n'zosatheka. Chinthu china ndi tikakhala kuyesera ndi mpira. Pankhaniyi, zikuoneka kuti atatu azithunzi omwe tikunena dera timapeza kuchokera circumference ndi chimbale m'chiuno mpaka Wonenedwa chingwe ndi atatu azithunzi omwe tikunena kumvetsetsa munthu wamba, koma ziwiri ooneka enieni mu mawu a masamu.

Poincare adati dera atatu azithunzi omwe tikunena ndi atatu okha-azithunzi omwe tikunena "chinthu", pamwamba amene angatengedwe kuti mfundo imodzi, Perelman anatha kutsimikizira izo. Choncho, "n'ngosathetseka vuto" mndandanda tsopano tichipeza mavuto 6.

chiphunzitso Yang-Mills

Vutoli masamu wakhala akufuna ndi olemba mu 1954. chiphunzitso Scientific chiphunzitso ndi motere: kwa aliyense yosavuta yaying'ono n'zotsimikizira gulu danga kwadzidzidzi chiphunzitso analengedwa ndi Yang ndi Millsom alipo, chotero ali ziro misa chilema.

Kulankhula chilankhulo adazindikira mwa munthu wamba, zimene zimachitika pakati pa zinthu zachilengedwe (. Tinthu, matupi, mafunde, etc.) anawagawa mitundu 4: atomu, yokoka, ofooka ndi amphamvu. Kwa zaka zambiri, asayansi akuyesetsa kuti akonze chiphunzitso ambiri kumunda. Izo ziyenera kukhala chida kufotokoza zonse ankachita izi. Yang-Mills chiphunzitso - chinenero masamu ndi zomwe zinali zotheka kufotokoza 3 4 mphamvu yaikulu ya chikhalidwe. Zilibe ntchito kwa yokoka. Choncho Sitinganene kuti Yang ndi Mills anakhoza kukhala chiphunzitso cha m'munda.

Komanso, sanali linearity wa maikwezhoni akufuna zimawachititsa povuta kuti athetse. amatha kuthetsa pafupifupi pa zokhazikika yaing'ono lumikiza motsatizanatsatizana perturbation. Komabe, si bwino mmene angathetsere maikwezhoni izi lumikiza amphamvu.

Navier-Stokes maikwezhoni

Ndi mawu amenewa njira monga otaya mpweya, otaya madzimadzi ndi kugwedezekagwedezeka. Pakuti zina zapadera, njira mawunikidwe a Navier-Stokes maikwezhoni apezeka, koma izo kwa wamba koma palibe munthu amene wakwanitsa. Pa nthawi yomweyo, n'zosangalatsa kumva kayeseleledwe kwa mfundo yeniyeni liwiro, kachulukidwe, kuthamanga, nthawi, ndi zina zotero walola kuti tikwaniritse zotsatira zabwino. Ife chokha chimene munthu ntchito Navier-Stokes maikwezhoni zosiyana, mwachitsanzo. E. yopangidwa ntchito magawo awo, kapena kutsimikizira kuti njira si njira yothetsera vutolo.

Ntchito ya Birch - Swinnerton-Dyer

Gulu la "Mavuto Apadera" amatanthauza kungoganizira akufuna ndi asayansi a ku Britain pa University Cambridge. Ngakhale 2300 zapitazo, wakale Greek katswiri Euclid linafotokoza wathunthu njira ya aone kuti pali x2 + y2 = z2.

Ngati aliyense wa nambala yaikulu kuti awerengere nambala ya mfundo pa pamapindikira a pachikhalidwe wake, ife wodziwitsidwa amaika malire a integers. Ngati njira yowona kuti "guluwu" kwa 1 ntchito ya variable zovuta, ndiye kutenga Hasse-Weil zeta ntchito kwa dongosolo wachitatu limaoneka lokongola, amaimira kalata L. Lili zokhudza khalidwe la modulo onse primes yomweyo.

Bryan Birch ndi Peter Swinnerton-Dyer hypothesized wachibale wa zokhotakhota dzira. Malinga ndi izi, dongosolo ndi chiwerengero cha akonzedwa ake a zochita zomveka kugwirizana ndi khalidwe la L-ntchito unit. Panopa unproven kungoganizira Birch - Swynnerton-Dyer zimadalira maikwezhoni algebraic kufotokoza madigiri 3 ndipo ali yekha n'zochepa yosavuta ambiri njira kuwerengetsa udindo wa zokhotakhota dzira.

Kuti timvetse kufunika yeniyeni ya vutoli, suffices kunena kuti cryptography amakono potengera zokhotakhota dzira ndi gulu la machitidwe asymmetric ndi ntchito zawo n'zochokera mfundo zoweta digito siginecha.

Kuyanjana pakathi pa makalasi tsa ndi NP

Ngati ena a "Mavuto Millennium" ndi chosankha masamu, izi zokhudzana ndi chiphunzitso chenicheni cha ma aligorivimu. vuto ndi makalasi kufanana tsa ndi NP, yemwenso amadziwika kuti vuto la Cook-Levin chinenero zomveka akhoza anakonza motere. Tiyerekeze kuti yankho zabwino funso akhoza kutsimikizika msanga zokwanira, kuti ali. E. Pa nthawi polenomiyo (PT). Ndiye, ngati mawu a zolondola, yankho kungakhale mofulumira ndithu kupeza? Ngakhale mosavuta , vuto ili liri: Kodi njira kwenikweni onani palibe zovuta kuposa awapeze? Ngati Kuyanjana pakathi pa makalasi tsa ndi NP adzakhala konse anasonyeza kuti mavuto onse kusankha angathe kuthetsedwa chifukwa PV. Pa nthawi, akatswiri ambiri kukayikira choonadi cha mawu amenewa, koma palibe umboni ayi.

The Riemann kungoganizira

Mpaka 1859 panalibe umboni wa malamulo alionse akhoza kufotokoza momwe mukufuna kugawira manambala yaikulu pakati zachilengedwe. Mwina zimenezi zinachitika chifukwa chakuti sayansi kuchita zinthu zina. Komabe, ndi za m'ma 19, zinthu zasintha ndi iwo akhala mmodzi wa onena, amene anayamba kuchita masamu.

The Riemann kungoganizira, amene anaonekera mu nthawi ino - ichi ndi maganizo oti pali chitsanzo ena mu kufalitsa primes.

Masiku ano, asayansi ambiri masiku ano amakhulupirira kuti ngati kutsimikiziridwa, izo ndi kusintha zambiri za mfundo zofunika za cryptography ano, kupanga maziko a mbali yaikulu ya e-malonda njira.

Malinga ndi Riemann kungoganizira, chikhalidwe cha kufalitsidwa kwa manambala yaikulu zingasiyane chuma mwachidwi, pa nthawi iyi. mfundo ndi yakuti mpaka tsopano silinakwaniritsidwe anapeza zilipo mu kufalitsa manambala yaikulu. Mwachitsanzo, pali vuto "mapasa", kusiyana umene uli wofanana 2. manambala awa 11 ndi 13, 29. primes Other kupanga masango. Ndi 101, 103, 107 ndi ena. Asayansi yaitali amaganiziridwa kuti masango amenewa kukhalapo pakati ambirimbiri kwambiri yaikulu. Mukaona iwo, kulimbikira kwa makono crypto kiyi adzakhala pansi pa funso.

The amanena za Hodge m'zinthu

Vutoli sanathetsedwe akadali anakonza mu 1941. Hodge kungoganizira zikusonyeza kuthekera approximating mawonekedwe a chinthu chilichonse mwa "gluing" matupi pamodzi losavuta gawo zikuluzikulu. njira imeneyi kudziwika ndi lakhala likugwiritsidwa ntchito bwinobwino kwa nthawi yaitali. Komabe, Sizikudziwika kuti zimene mmene zosabvuta zikhoza kupangidwa.

Tsopano inu mukudziwa zomwe mavuto n'ngosathetseka alipo pa nthawiyo. Iwo nkhani ya zikwi asayansi padziko lonse. Tikukhulupirira kuti posachedwapa kuthetsedwa ndi ntchito zawo zothandiza chingathandize anthu kufika wozungulira latsopano la zaumisiri.