Abel Prize

Bambalwa abafundi abangasho lutho ngegama elithi Abela. Cha, lokhu akuphathelene nensizwa eneshwa eyabulawa umfowabo uKhayini. Ngibhekise kusazi sezibalo saseNorway u-Niels Henrik Abel (1802–1829) kanye nomklomelo oqanjwe ngaye osanda kukhishwa (ngoMashi 16, 2016) yiNorwegian Academy of Sciences kanye nezincwadi eziya ku-Sir Andrew J. Wiles. Lokhu kunxephezela ongoti bezibalo ngokushiywa ngaphandle ngu-Alfred Nobel esigabeni sokukleliswa komklomelo wesayensi obaluleke kakhulu emhlabeni.

Nakuba izazi zezibalo zikwazisa lokho okuthiwa. Indondo Yezinkundla (ngokusemthethweni ibhekwa njenge-laurel ephakeme kakhulu emkhakheni wayo), ihlotshaniswa nezinkulungwane eziyi-15 kuphela. (hhayi izigidi, izinkulungwane!) zamadola aseCanada kuze kube umnqobi Abel Awards ubeka isheke le-6 million Norwegian kroner (cishe 750 8 euros) ephaketheni lakhe. Abahlomuli beNobel bathola izigidi ezingama-SEK ezingama-865, noma cishe izinkulungwane eziyi-XNUMX. i-euro - abadlali bethenisi abangaphansi kokuwina umqhudelwano omkhulu. Kunezizathu ezimbalwa okungenzeka ukuthi kungani u-Alfred Nobel engabafaki ochwepheshe bezibalo phakathi kwabangase bawine imiklomelo. Itestamente likaNobel lalikhuluma “ngezinto ezisunguliwe kanye nokutholwayo” okuletha inzuzo enkulu esintwini, kodwa mhlawumbe hhayi okusezingqondweni, kodwa okungokoqobo. Izibalo zazingabhekwa njengesayensi engaletha izinzuzo ezingokoqobo esintwini.

Kungani u-Abela

Wayengubani Niels Henrik Abel futhi wayedume ngani? Kumelwe ukuba wayekhaliphile, ngoba nakuba abulawa isifo sofuba eneminyaka engu-27 kuphela, wakwazi ukuphumelela ngokugcwele ezibalweni. Hhayi-ke, vele sisesikoleni samabanga aphakeme esincane basifundisa ukuxazulula izibalo; idigri yokuqala, bese kuba isikwele, futhi ngezinye izikhathi cubic. Kakade eminyakeni engamakhulu amane edlule, ososayensi base-Italy bakwazi ukubhekana nakho i-quartic equationnobonakala engenacala.

nokuthi iyiphi enye yezakhi

Yebo, ososayensi bebengakwenza lokhu ngekhulu lesi-XNUMX. Akunzima ukuqagela ukuthi izilinganiso zamadigri aphezulu zazibhekwa. Futhi lutho. Akekho ophumelele eminyakeni engamakhulu amabili. U-Niels Abel naye wehlulekile. Futhi wabe eseqaphela ukuthi ... mhlawumbe akunakwenzeka nhlobo. Kungafakazelwa ukungenzeki kokuxazulula isibalo esinjalo - noma kunalokho, ukuveza isixazululo ngezindlela ezilula ze-arithmetic.

Kwakungowokuqala kwabangu-2. iminyaka (!) yalolu hlobo lokucabanga: into ayikwazi ukuqinisekiswa, into engeke yenziwe. I-monopoly ebufakazini obunjalo ingeyezibalo - isayensi esebenzayo iphula imigoqo ngokuqhubekayo. Ngo-1888, usihlalo we-US Patent Commission wamemezela ukuthi "kumbalwa okuqanjiwe okufanele kulindeleke esikhathini esizayo, ngoba cishe yonke into isivele yasungulwa." Namuhla kunzima kithina ngisho ukuyihleka le nto... Kodwa ezibalweni, uma sekuqinisekisiwe, kuyalahleka. Ngeke kwenziwe.

Umlando uhlukanisa phakathi kokutholakala engikuchazile Niels Abel i Evarista Galois, bobabili ‘njengabakhethiweyo bonkulunkulu’ bafa bengakayihlanganisi iminyaka engamashumi amathathu, bebukelwa phansi abantu besikhathi sabo. U-Niels Abel ungomunye wochwepheshe bezibalo abambalwa baseNorway abadume kakhulu (empeleni ababili, omunye Sophus Lee, 1842-1899 - amagama awazwakali eScandinavia, kodwa bobabili babengabaseNorway bomdabu).

Abantu baseNorwegi abaphikisana nabaseSweden - ngeshwa, lokhu kuvamile kubantu abangomakhelwane. Esinye sezisusa zokusungulwa koMklomelo ka-Abel ngabaseNorway kwakuyisifiso sokukhombisa abantu bakubo u-Alfred Nobel: sicela, asibi kakhulu.

Ukujaha ukufakwa kwemajini okungekho

Nangu u-Niels Henrik Abel wakho. Manje mayelana nowine umklomelo, iNgisi elineminyaka engu-63 (elihlala e-USA). Ukwenza kwakhe ngo-1993 kungafaniswa kuphela nokuqwala i-Everest, ukugibela inyanga, noma into efana naleyo. Ubani mnumzane Andrew Wiles? Uma ubheka uhlu lwezincwadi zakhe kanye nezinkomba ezihlukahlukene zokucaphuna okungenzeka, uzoba usosayensi omuhle - kunezinkulungwane zazo. Nokho, ubhekwa njengesazi sezibalo esikhulu kunazo zonke. Ucwaningo lwakhe luhlobene nethiyori yezinombolo futhi lusebenzisa ubudlelwano i-algebraic geometry Oraz ithiyori yokumelela.

Waduma ngokuxazulula inkinga eyayingenamsebenzi nhlobo ngokombono wezibalo ubufakazi be-Theorem yokugcina kaFermat (Kulabo abangazi ukuthi kuyini - ngikukhumbuza ngezansi). Nokho, ukubaluleka kwangempela kwakungelona ikhambi ngokwalo, kodwa ukwakhiwa kwendlela entsha yocwaningo eyasetshenziswa ukuxazulula ezinye izinkinga eziningi ezibalulekile.

Akunakwenzeka ukuthi ungacabangi ngencazelo yezindaba ezithile, ngezigaba zokuphumelela komuntu. Amakhulu ezinkulungwane zentsha aphupha ngokukhahlela ibhola kangcono kunabanye, amashumi ezinkulungwane afuna ukuzichaya emoyeni wase-Himalaya, agxume enjoloba ebhulohweni, enze imisindo ayibiza ngokuthi ukucula, afake ukudla okungenampilo kwabanye ... isibalo esingadingekile kunoma ubani . Umnqobi wokuqala we-Mount Everest, Sir Edward Hillary, wawuphendula ngokuqondile umbuzo othi kungani eya lapho: “Ngoba ukhona, ngoba u-Everest ukhona!” Umbhali wala mazwi wayeyisazi sezibalo impilo yakhe yonke, kwakuyindlela yami yokuphila. Okuwukuphela kwayo okulungile! Kodwa ake siyiqede le filosofi. Ake sibuyele endleleni enempilo yezibalo. Kungani kunengxabano mayelana neTheorem kaFermat?

Ngicabanga ukuthi sonke siyazazi ukuthi ziyini izinombolo eziyinhloko. Impela wonke umuntu uyaliqonda igama elithi "bola ube yizici eziyinhloko", ikakhulukazi lapho indodana yethu iguqula amawashi abe yizingxenye.

Pierre de Fermat (1601-1665) wayengummeli waseToulouse, kodwa futhi wabhekana nezibalo njengemfundamakhwela, futhi waba nemiphumela emihle kakhulu, ngoba wangena emlandweni wezibalo njengombhali wemibono eminingi yethiyori yezinombolo nokuhlaziya. Wayenomkhuba wokufaka amazwi akhe kanye nokuphawula kwakhe emaphethelweni ezincwadi ayezifunda. Futhi kunjalo - cishe ngo-1660 wabhala kwelinye lamaphethelo:

Nangu u-Pierre de Fermat wakho. Kusukela ngesikhathi sakhe (futhi ake ngikukhumbuze ukuthi uGascon umhlonishwa d'Artagnan onesibindi wayehlala eFrance ngaleso sikhathi, futhi u-Andrzej Kmitsich walwa noBoguslav Radziwill ePoland), amakhulu, futhi mhlawumbe nezinkulungwane zezibalo ezinkulu nezincane zazama ukuvuselela kabusha ukulahlekelwa ukucabanga komuntu oyimfundamakhwela okhaliphile . Nakuba namuhla siqinisekile ukuthi ubufakazi bukaFermat abunakuba yiqiniso, kwakucasula ukuthi umbuzo olula wokuthi ngabe isibalo xⁿ +yⁿ = gⁿ, n> 2 inezixazululo ezinombolweni ezingokwemvelo? kungaba nzima kangako.

Izazi zezibalo eziningi ezafika zizosebenza ngoJuni 23, 1993, zathola ku-imeyili yazo (ngaleso sikhathi eyayiyinguqulo entsha, eyayisafudumele) umyalezo omfushane owawufundeka kanje: “Amahemuhemu avela eBrithani: Wiles proves Fermat.” Ngakusasa, abezindaba nsuku zonke babhala ngakho, futhi uchungechunge lokugcina lwezinkulumo zikaWiles lwaqoqa abezindaba, ithelevishini kanye nabathwebuli bezithombe - njengasengqungqutheleni yomdlali webhola odumile.

Noma ubani ofunda "uSathane kusukela ebangeni lesikhombisa" nguKornel Makuszyński ngokuqinisekile ukhumbula lokho uMnu Iwo Gąsowski, umfowabo kaprofesa womlando ohlelo lwakhe lokubuza abafundi abatholwa ngu-Adaś Cisowski, benza. U-Iwo Gąsowski wayesanda kuxazulula isibalo sikaFermat, emosha isikhathi, impahla futhi enganakekeli ikhaya lakhe:

Ekugcineni, uMnu Iwo waqonda ukuthi wayengeke aqinisekise injabulo yomndeni ngezibalo zamandla futhi wayeka. UMakuszyński wayengayithandi isayensi, kodwa wayeqinisile ngoMnu. Gąsowski. U-Iwo Gąsowski wenze iphutha elilodwa elibalulekile. Wayengazami ukuba uchwepheshe ngokweqiniso, wayezenza umuntu ofundayo. U-Andrew Wiles ungumbungazi ovelele.

Indaba yokulwa ne-Theorem yokugcina kaFermat iyathandeka. Kungabonakala kalula nje ukuthi kwanele ukuzixazulula kuma-exponents okuyizinombolo eziyinhloko. Ku-n = 3 isisombululo sanikezwa ngo-1770. Leonhard Euler, kwe-n = 5 - Peter Gustav Lejeune Dirichlet (1828) kanye U-Adrien Marie Legendre ngo-1830, futhi ku-n = 7 - UGabriel Lama ngo-1840. Ngekhulu lesi-XNUMX, isazi sezibalo saseJalimane sasebenzisa amandla akhe amaningi enkingeni kaFermat U-Ernst Eduard Kummer (1810-1893). Nakuba engazange aphumelele ekugcineni, wafakazela amacala amaningi akhethekile futhi wathola izici eziningi ezibalulekile zezinombolo eziyinhloko. Iningi le-algebra yesimanje, i-arithmetic yetiyori, kanye nethiyori yezinombolo ze-algebra isuka emsebenzini ka-Kummer wethiyori kaFermat.

Lapho kuxazululwa inkinga ka-Fermat ngezindlela zethiyori yenombolo yakudala, zahlukaniswa zaba izimo ezimbili ezihlukene eziyinkimbinkimbi: eyokuqala, lapho sithatha ngokuthi umkhiqizo u-xyz une-exponent n, kanti eyesibili, lapho inombolo ethi z ihlukaniswa ngokulinganayo i-exponent. Esimweni sesibili, kwaziwa ukuthi azikho izixazululo ezifika ku-n = 150, futhi esimweni sokuqala, kuze kufike ku-n = 000 (Lehmer, 6). Lokhu kwakusho ukuthi i-counterexample okungenzeka ingenzeki kunoma isiphi isimo: izodinga izikweletu zezigidigidi zamadijithi ukuze isithole.

Nansi indaba endala yakho. Ekuqaleni kuka-1988, kwakwaziwa emhlabeni wezibalo ukuthi Yoichi Miyaoka ifakazele ukungalingani okuthile, okwalandela kuyo okulandelayo: uma kuphela i-eksponenti n inkulu ngokwanele, khona-ke isibalo sikaFermat asinazo izixazululo. Uma kuqhathaniswa nomphumela wangaphambili kancane wamaJalimane Gerd Faltings (1983) Umphumela kaMiyaoka wawusho ukuthi uma kukhona izixazululo, kusho ukuthi (ngokuhambisana nokulingana) kukhona isibalo esilinganiselwe sazo. Ngakho-ke, isixazululo senkinga ye-Fermat sincishiselwa ekubhaleni isiphetho samacala amaningi. Ngeshwa, bangaki kubo ababengaziwa: izindlela ezisetshenziswa uMiyaoka azizange zivumele ukulinganisa ukuthi zingaki ezazivele "zihlelekile".

Kuyaphawuleka lapha ukuthi iminyaka eminingi ukufundwa kwethiyori kaFermat akwenziwanga ngaphakathi kohlaka lwethiyori yenombolo emsulwa, kodwa ngaphakathi kohlaka lwe-algebraic geometry, isiyalo sezibalo esithathwe ku-algebra kanye nokunwetshwa kwe-Cartesian analytic geometry, futhi manje. ukusabalala cishe yonke indawo: kusukela ezisekelweni zezibalo (theory topoi in logic), ngokuhlaziywa kwezibalo (izindlela ze-cohomological, izithungu ezisebenzayo), i-classical geometry, kuya ku-theoretical physics (i-vector bundles, i-twistor spaces, i-solitons).

Lapho ukuhlonishwa akusho lutho

Kunzima futhi ukungadabuki ngesiphetho sesazi sezibalo, esinegalelo elikhulu ekuxazululeni inkinga kaFermat. Ngikhuluma ngo-ArakielU-Suren Yurevich Arakelov, Isazi sezibalo sase-Ukraine esinezimpande zase-Armenia), owathi ekuqaleni kwawo-80, lapho eseneminyaka yakhe yesine, wadala okuthiwa. i-intersection theory ezinhlobonhlobo ze-arithmetic. Izindawo ezinjalo zigcwele izimbobo nokungapheleli, futhi amajika aphezu kwazo angashabalala ngokuzumayo, njengokungathi, bese aphinde avele. Ithiyori ye-Intersection ichaza indlela yokubala izinga lokuhlangana kwamajika anjalo. Kwakuyithuluzi eliyinhloko elalisetshenziswa uFaltings noMiyaoka emsebenzini wabo ngenkinga kaFermat.

Ngesinye isikhathi u-Arakelov wamenywa ukuba ethule imiphumela yakhe engqungqutheleni enkulu yezibalo. Nokho, ngenxa yokuthi wayegxeka isimiso samaSoviet, wenqatshelwa ukuba ahambe. Ngokushesha wabuthelwa ebuthweni lezempi. Wabonisa ngendelelo ukuthi wayemelene nenkonzo yezempi ngokuvamile ngenxa yezizathu zokungaphumeleli. Njengoba ngithole emithonjeni engabaza, kusolakala ukuthi wathunyelwa esibhedlela sabagula ngengqondo, lapho ahlala khona isikhathi esingangonyaka. Njengoba wazi, ngokusobala ngezinhloso zezombangazwe, odokotela bengqondo baseSoviet bakhetha uhlobo olukhethekile lwe-schizophrenia (ngesiNgisi kusukela, okusho ukuthi "ukuvilapha", ngesiRashiya. i-schizophrenia evilaphayo).

Kunzima ukusho amaphesenti ayikhulu ukuthi bekunjani ngempela, ngoba imithombo yami yolwazi ayithembekile kakhulu. Ngokusobala, ngemva kokuphuma esibhedlela, u-Arakelov wachitha izinyanga ezimbalwa endlini yezindela eZagorsk. Njengamanje uhlala eMoscow nomkakhe nezingane ezintathu. Akazenzi izibalo. U-Andrew Wiles ugcwele ukuhlonishwa nemali.

Ngokombono womphakathi waseYurophu owondlekile kahle, lesi sinyathelo asiqondakali UGrigory Perelman, okwathi ngo-2002 kwaxazulula inkinga yesimo sezulu edume kakhulu ekhulwini lama-XNUMX,”Poinari ukucabangaFuthi-ke wenqaba yonke imiklomelo engenzeka. Okokuqala i-Fields Medal, okukhulunywe ngayo ekuqaleni, izazi zezibalo eziyibheka njengelingana noMklomelo KaNobel, bese kuba umklomelo wamadola ayisigidi wokuxazulula enye yezinkinga zezibalo eziyisikhombisa ezibalulekile ezisele kusukela ekhulwini lama-XNUMX. "Abanye bebengcono, anginandaba nokuhlonishwa, ngoba izibalo yinto engizilibazisa ngayo, nginokudla nogwayi," utshele izwe elimangele.

Impumelelo ngemva kweminyaka engaphezu kuka-300

Ithiyori Yokugcina kaFermat ngokuqinisekile yayiyinkinga edume kakhulu futhi emangalisayo kwizibalo. Yayivuliwe iminyaka engaphezu kwamakhulu amathathu, yakhiwe ngendlela ecacile nefundekayo futhi kwakucatshangwa ukuthi kungenzeka ukuthi ihlaselwe yinoma ubani, futhi ngesikhathi sokuthandwa kwamakhompyutha, kwakulula ukuzama ukuphula elinye irekhodi lokulinganisa izixazululo ezingase zibe khona. Emlandweni wezibalo, lolu daba, ngendima yalo ekhuthazayo, ludlale indima ebaluleke kakhulu "yokwakha amasiko", okunomthelela ekuveleni kwayo yonke imikhakha yezibalo. Kuyamangaza ngoba inkinga ngokwayo incane futhi ulwazi nje mayelana nokuntuleka kwezimpande ze-equation kaFermat aluzange lube nomthelela omkhulu kumgcinimafa jikelele wolwazi lwezibalo.

Ngo-1847, uGabriel Lamet (1795-1870) wanikeza inkulumo e-French Academy of Sciences ememezela isisombululo senkinga kaFermat. Nokho, iphutha elicashile ekucabangeni laqashelwa ngokushesha. Isekelwe ekusetshenzisweni okungagunyaziwe kwe-theoem yokubola eyingqayizivele. Siyakhumbula kusukela esikoleni ukuthi inombolo ngayinye inokuhlukaniswa okuyingqayizivele ibe yizici eziyinhloko, isibonelo, 2012 = 2 ∙ 2 ∙ 503. Inombolo 503 ayinazo abahlukanisi (ngaphandle kuka-1 no-503 uqobo), ngakho ayikwazi ukunwetshwa ngokuqhubekayo.

Impahla yokuhluka kokusabalalisa inamanani aphelele, kodwa phakathi kwamanye amasethi ezinombolo akudingekile ukuthi abe njalo. Ngokwesibonelo, izinombolo zabalingiswa

sina 36 = 2²⋅2³ ,kodwa futhi

Ngokuhlaziya ubufakazi bukaLame, uKummer wakwazi ukufakazela ubuqiniso bokucatshangelwa kukaFermat kwabanye abachazi be-p. Wababiza ngokuthi ama-primes ajwayelekile. Lesi kwakuyisinyathelo sokuqala esibalulekile sokuthola ubufakazi obuphelele. Inganekwane ikhule mayelana nethiyori kaFermat. "Noma mhlawumbe kubi nakakhulu - mhlawumbe awukwazi ngisho nokufakazela ukuthi kungenzeka noma akunakwenzeka ukuxazulula?"

Kodwa kusukela ngawo-80, wonke umuntu wayenomuzwa wokuthi umgomo wawuseduze. Ngikhumbula ukuthi udonga lwaseBerlin lwalumile, futhi ngase ngilalele kakade izinkulumo mayelana "ngokushesha, ngomzuzwana." Nokho, umuntu kwakufanele abe kuqala. U-Andrew Wiles waphetha inkulumo yakhe nge-phlegm yesiNgisi: "Ngicabanga ukuthi u-Fermat uyakufakazela lokho," futhi kwathatha isikhathi ngaphambi kokuba izethameli ezigcwele zibone ukuthi kwenzekeni: inkinga yezibalo eneminyaka engu-330 yasetshenzwa ngokujulile ngamakhulu ochwepheshe bezibalo abavela esikoleni. ibutho uqobo kanye nezimfundamakhwela ezingenakubalwa, njengo-Ivo Gonsovsky ovela kumanoveli kaMakushinsky. Futhi u-Andrew Wiles ube nelungelo lokuxhawula uHarald V, iNkosi yaseNorway. Mhlawumbe akazange anake isabelo nesizotha for Umklomelo Abela, mayelana ngamakhulu ambalwa ezinkulungwane zama-euro - kungani edinga imali engaka?