Aripo sokuti asingagadzirisiki dambudziko: Navier-Stokes equations, ari Hodge fungidziro, ari Riemann pfungwa. Millennium zvinangwa

Aripo sokuti asingagadzirisiki dambudziko - a 7 anonakidza kwemasvomhu matambudziko. Mumwe nomumwe wavo yave wakatangwa pane imwe nguva yakakurumbira masayendisiti, kazhinji zviri muchimiro hypotheses. Kwemakumi akawanda emakore, kuzvigadzirisa scratching misoro yavo masvomhu yose. Avo vanobudirira, vakamirira mubayiro miriyoni imwe US emadhora inopiwa Institute of Clay.

prehistory

Muna 1900, mukuru yemasvomhu German David Hilbert ngoro, akapa mazita 23 matambudziko.

Research akaita nechinangwa vasarudza, vakaita zvakawanda kwakabatsira nesayenzi remakore rechi20. Panguva iyoyo, vakawanda vavo kare kurega kuva chakavanzika. Pakati unsolved kana zvishoma chakagadziriswa vaiva:

• dambudziko kwemashoko ari axioms ose svomhu;
• mukuru mutemo reciprocity iri nzvimbo ipi Numeric munda;
• kwemasvomhu kudzidza muviri axioms;
• mukudzidza quadratic siyana kuti zvemasanga algebraic nhamba coefficients;
• dambudziko zvakaoma kururamiswa enumerative geometry Fedor Schubert;
• nezvakadaro.

Unexplored vari kuparadzira dambudziko chipi algebraic nharaunda rationality anozivikanwa Kronecker theorem no uye Riemann pfungwa .

Institute of Clay

Pasi zita iri zvinozivikanwa private vasiri haibatsiri sangano, makuru Cambridge, Massachusetts. It rakaumbwa muna 1998 na Harvard yemasvomhu uye muzvinabhizimisi A. Jeffrey L. Clay. Chinangwa Institute riri kusimudzira uye kukudziridza kwemasvomhu ruzivo. Kuti vawane sangano iri rinopa mibayiro kuti masayendisiti uye kutsigira vaizotibata tsvakurudzo.

Mukutanga kwezana remakore rechi21 Clay kwemasvomhu Institute akaita akapa shoma kune vaya huchagadzirisa matambudziko, izvo vanozivikanwa zvikuru kunzwisisa aripo sokuti asingagadzirisiki dambudziko, achidana zvako Millennium Prize Problems. Kubva "List pamusoro Hilbert" chakava chete Riemann pfungwa.

Millennium zvinangwa

Pane zvakarongwa pamusoro Institute of Clay pakutanga zvaisanganisira:

• Hodge fungidziro pamusoro zvinogara;
• ari equations ose quantum dzidziso Yang - Mills;
• Poincaré fungidziro ;
• dambudziko wakanyatsojeka nemakirasi P uye NP;
• Riemann pfungwa;
• Navier-Stokes equations, kuvapo uye kumeso kwayo sarudzo;
• dambudziko Birch - Swinnerton-Dyer.

matambudziko aya rakazaruka kwemasvomhu vari kufarira kukuru nokuti vanogona dzinoshanda implementations zhinji.

Chii akaratidza Grigoriy Perelman

Muna 1900, yakakurumbira musayendisiti uye muzivi Anri Puankare akataura kuti ose nyore chokuita tsindirana 3-siyana pasina muganhu ndiyo homeomorphic kune 3-dimensional bhora. The uchapupu mune vakawanda nyaya dzakaratidzirwa anopfuura zana. Chete muna 2002-2003, ari St. Petersburg yemasvomhu G. Perelman yakabudisa nyaya chete mhinduro dambudziko Poincare. Ivo bombshell. Muna 2010, kuti Poincaré fungidziro yave kunze kubva pamazita "zvisingagadziriswi dambudziko" Clay Institute, uye kuna Perelman akakokwa kuwana rebei remuneration nokuda kwaari, izvo yokupedzisira vakaramba pasina kutsanangura zvikonzero zvayo chisarudzo.

The kupfuura zvinonzwisisika kufananidzira chii aigona kuratidza kuti Russian yemasvomhu, anogona kupiwa, ichipa kuti doughnut (torus), kudhonza rabha Disc, wozoedza kudhonza kumucheto wayo sekamufarenzi pane imwe nguva. Zviri pachena, izvi hazvibviri. Chimwe chinhu ndechokuti, kana tikaita kuedza ichi chete bhora. Muchiitiko chino, unoita-dimensional matatu bhora, tinowana kubva Disc sekamufarenzi akasungirirawo kusvikira tsvagai tambo iri-dimensional matatu mukunzwisisa paavhareji munhu, asi maviri-dimensional tichitaura masvomhu.

Poincare akataura kuti-dimensional matatu bhora ndiye chete "chinhu"-dimensional matatu, pose anogona kondirakiti chete pfungwa, uye Perelman akakwanisa kuzviratidza. Nokudaro, "aripo sokuti asingagadzirisiki dambudziko" pasi zvino ine 6 matambudziko.

Yang-Mills dzidziso

dambudziko iri kwemasvomhu kwave dzataurwa nokuda vanyori muna 1954. Scientific Pfungwa yacho dzidziso iri sezvinotevera: chipi nyore tsindirana geji boka nzvimbo quantum dzidziso akasikwa Yang uye Millsom ariko, uye nokudaro ane razero vakawanda urema.

Kutaura mutauro ndakanzwisisa zvake, nesungano pakati dzinongoitika zvinhu (. Nezvimedu, mitumbi, mafungu, etc.) akakamurwa 4 Marudzi: remagetsi, rinokweva, simba uye simba. Kwemakore akawanda, yefizikisi vari kuedza kuumba wemauto munda dzidziso. Inofanira kuva chishandiso kutsanangura zvose mukukurukurirana izvi. Yang-Mills dzidziso - mutauro kwemasvomhu izvo zvaibvira kurondedzera 3 4 masimba inokosha zvakasikwa. It hairevi negiravhiti. Naizvozvo hatigoni kufungidzira kuti Yang uye Mills akakwanisa kutanga dzidziso musango.

Mukuwedzera, vasiri linearity richaitirwa equations ndinovaita zvakaoma kugadzirisa. vanokwanisa kugadzirisa zvinenge panguva diki coupling constants somunhu perturbation akatevedzana. Zvisinei, hazvina pachena sei kugadzirisa equations izvi nokuda simba akabatanidzwa pamwechete.

Navier-Stokes Equations

With mashoko aya akarondedzera pezvakaitwa akadai mhepo aibuda, Urume chokubuda uye mhirizhonga. Nokuti dzimwe nguva, Analytical zvingaitwa of Navier-Stokes equations akawanikwa, asi itai kuti vanhuwo asi hapana yabudirira. Panguva iyoyowo, nhamba simulation nokuda dzakananga tsika akurumidze, arambe achirema, kumanikidzwa, nguva, uye zvichingodaro rinobvumira kuti vabudirire nemigumisiro yakanaka. Tinogona chete tariro kuti munhu achashandisa Navier-Stokes equations mu negwara, kureva. E. computed vachishandisa parameters dzavo, kana kuti kuratidza kuti nzira hakusi mhinduro.

Basa iri Birch - Swinnerton-Dyer

Muchikwata che "Zvinetso Mutsindo" chinoshanda pfungwa dzataurwa nokuda British masayendisiti kuCambridge University. Kunyange 2300 apfuura, vekare nyanzvi yechiGiriki Euclid akapa rondedzero mhinduro yacho mukana wokuti vanhu vanga x2 + Y2 = Z2 kwakakwana.

Kana chimwe chikuru nhamba kuti ngaaverenge nhamba pfungwa pamusoro munyonga kuti chikwata chake, tinowana isingaperi akagadzirwa integers. Kana kongiri nzira "guruu" kuti 1 kushanda kunzwisisa shanduka, ipapo kuwana Hasse-Weil Zeta mashandiro kuti wechitatu kurongeka munyonga, runotaurwa tsamba L. Rine mashoko pamusoro maitiro ari modulo zvose of times pakarepo.

Bryan Birch uye Peter Swinnerton-Dyer hypothesized hama rakaita denderedzwa chairo makakombama. Maererano neizvi, nemamiriro uye uwandu yayo yakatarwa kufunga zvisarudzo chokuita kwemaitiro L-shanda chikwata. Pari unproven pfungwa Birch - Swynnerton-Dyer zvinoenderana algebraic equations achirondedzera 3 madhigirii uye vanganzi nyore vakawanda nzira bedzi pakuverenga chinzvimbo rakaita denderedzwa chairo makakombama.

Kuti tinzwisise inoshanda kukosha dambudziko iri, zvakatikwanira kutaura kuti cryptography ano kwakavakirwa rakaita denderedzwa chairo makakombama vari boka asymmetric hurongwa, uye kushandisa kwavo kunobva mudzimba tsika digitaalinen siginicha.

Kuenzana nemakirasi s uye NP

Kana vamwe "Zvinetso Millennium" vari pachokwadi akarongeka, uyu yakabatana chaiko dzidziso algorithms. A dambudziko vakaenzana makirasi S. uye madikena, anozivikanwawo sokuti dambudziko Cook-Levin mutauro zvinonzwisisika anogona akagadzira sezvinotevera. Ngatitii mhinduro akanaka kune mubvunzo unogona achasimbiswa nokukurumidza zvakakwana, kuti ndiyo. E. In polynomial nguva (PT). Zvadaro, kana mashoko rakarurama, kuti mhinduro inogona kukurumidza zvikuru kuwana? Kunyange nyore , dambudziko iri riri: Ko mushonga here tione hapana kuoma pane kuti ariwana? Kana kuenzana nemakirasi S. uye madikena ichazofa kwakaratidza kuti zvose kusarudzwa zvinetso zvinogona kugadziriswa kuti PV. Panguva iyoyo, nyanzvi dzakawanda nechokwadi chokwadi aya, asi haagoni kuratidza zvimwe.

The Riemann pfungwa

Up kusvikira 1859 pakanga pasina uchapupu chero mitemo zvaizoitika kutsanangura sei kuparadzira mukuru nhamba pakati zvepanyama. Zvichida izvi zvakakonzerwa ndechokuti nesayenzi munyaya dzimwe nyaya. Zvisinei, nokuda pezana remakore rechi19, mamiriro ezvinhu akachinja uye vava chimwe chezvinhu rokukurumidzira, iro rakatanga kuita masvomhu.

The Riemann pfungwa, yakabuda iyi - ndiro kubvuma kuti pane mumwe muenzaniso ari kuparadzirwa of times.

Nhasi, masayendisiti akawanda ano vanodavira kuti kana vakaedzwa, zvichataurirana afungezve vakawanda chinokosha zvinodiwa cryptography ano, zvinoumba hwaro chikamu chikuru e-zvokutengeserana zvigadziriswe.

Maererano Riemann pfungwa, hunhu kuparadzira wehurumende nhamba zvingasiyana zvinhu kubva taitarisira panguva ino. Chokwadi ndechokuti kusvikira zvino haina asi kuwanikwa chero wemuTesitamende kuparadzirwa inonyanya nhamba. Somuenzaniso, pane dambudziko "mapatya", musiyano pakati izvo zvakaenzana 2. nhamba idzi 11 uye 13, 29. Other of times anoumba zvemichindwe. Ndicho 101, 103, 107, uye vamwe. Masayendisiti refu vanofungidzirwa kuti zvisumbu vakadaro iripo pakati yakakura chaizvo chikuru nhamba. Kana ukaona navo, kurwisa hwemazuva crypto kiyi achava pasi mubvunzo.

Pfungwa pamusoro Hodge zvinogara

dambudziko iri unsolved ichiri akagadzira muna 1941. Hodge pfungwa rinoratidza mukana approximating chimiro chipi chinhu ne "gluing" pamwe chete nyore miviri hombe divi. Nzira iyi yave kuzivikanwa uye yave kushandiswa zvinobudirira kwenguva yakareba. Zvisinei, hazvina kuzivikanwa kuti zvakadini anoitwa zvinogona kuitwa.

Zvino kuti munoziva matambudziko aripo sokuti asingagadzirisiki iripo panguva. Ndivo nyaya zviuru masayendisiti munyika yose. Tinovimba kuti achakurumidza kugadziriswa, uye kushanda kwavo kuchabatsira vanhu kusvika mutsva ose muzvigadzirwa kukura.