Abelya Award

Owerenga ochepa anganene chilichonse chokhudza dzina la Abele. Ayi, zimenezi sizikunena za mnyamata watsoka amene anaphedwa ndi mbale wake weniweni Kaini. Ndikunena za katswiri wa masamu wa ku Norway Niels Henrik Abel (1802–1829) ndi mphoto yotchulidwa pambuyo pake yomwe yangoperekedwa kumene (March 16, 2016) ndi Norwegian Academy of Sciences ndi makalata kwa Sir Andrew J. Wiles. Izi zimalipira akatswiri a masamu chifukwa chosiyidwa ndi Alfred Nobel m'gulu la mphotho yofunika kwambiri padziko lonse lapansi ya sayansi.

Ngakhale masamu amayamikira otchedwa. Fields Mendulo (yomwe imatengedwa kuti ndi yamtengo wapatali kwambiri m'munda wake), imagwirizanitsidwa ndi 15 zikwi zokha. (osati mamiliyoni, masauzande!) a madola aku Canada mpaka wopambana Abel Awards amaika cheke cha 6 miliyoni kroner Norwegian (pafupifupi 750 8 mayuro) m'thumba mwake. Opambana a Nobel alandila SEK 865 miliyoni, kapena pafupifupi XNUMX zikwi. euro - ochepera osewera tennis kuti apambane mpikisano waukulu. Pali zifukwa zingapo zomwe Alfred Nobel sanaphatikizire akatswiri a masamu pakati pa omwe apambana mphotho. Chipangano cha Nobel chinali ndi “zopangidwa ndi zotulukira” zomwe zimabweretsa phindu lalikulu kwa anthu, koma mwina osati zongopeka chabe, koma zothandiza. Masamu sankaonedwa ngati sayansi imene ingathandize anthu.

Chifukwa chiyani Abele

Ndani anali Niels Henrik Abel ndipo adadziwika ndi chiyani? Ayenera kuti anali wanzeru, chifukwa ngakhale kuti anamwalira ndi chifuwa chachikulu ali ndi zaka 27 zokha, adakwanitsa kukhala katswiri wa masamu. Chabwino, kale kusukulu yasekondale amatiphunzitsa kuthetsa ma equation; digiri yoyamba, ndiye lalikulu, ndipo nthawi zina kiyubiki. Zaka mazana anayi zapitazo, asayansi aku Italy adatha kupirira quart equationngakhale amene akuwoneka wosalakwa.

ndi chimodzi mwa zinthu

Inde, asayansi akadatha kuchita izi m'zaka za zana la XNUMX. Sizovuta kulingalira kuti ma equation a madigiri apamwamba adaganiziridwa. Ndipo palibe. Palibe amene wakwanitsa zaka mazana awiri. Niels Abel nayenso analephera. Ndiyeno anazindikira kuti ... mwina sizingatheke nkomwe. Izo zikhoza kutsimikiziridwa kusatheka kuthetsa equation yotere - kapena m'malo, kufotokoza yankho mu masamu osavuta.

Anali oyamba mwa 2. zaka (!) za malingaliro amtunduwu: chinachake sichingatsimikizidwe, chinachake sichingachitike. Kukhazikika pa maumboni oterowo ndi masamu - sayansi yothandiza ikuphwanya zopinga mochulukira. Mu 1888, tcheyamani wa US Patent Commission adanena kuti "zochepa zochepa zomwe ziyenera kuyembekezera m'tsogolomu, chifukwa pafupifupi chirichonse chapangidwa kale." Lero ndizovuta kwa ife ngakhale kuseka izi ... Koma mu masamu, kamodzi kutsimikiziridwa, izo zatayika. Sizingatheke.

Mbiri imagawanitsa zomwe ndafotokozazi Niels Abel i Evarista Galois, onse aŵiri monga “osankhidwa a milungu” anafa asanakwanitse zaka makumi atatu, moŵerengeredwa mopepuka ndi a m’nthaŵi yawo. Niels Abel ndi m'modzi mwa akatswiri a masamu aku Norwegian odziwika bwino (kwenikweni awiri, winayo ali. Sophus Lee, 1842-1899 - mayina samamveka ku Scandinavia, koma onse anali achi Norway).

Anthu aku Norwegi akutsutsana ndi aku Sweden - mwatsoka, izi ndizofala pakati pa anthu oyandikana nawo. Chimodzi mwazifukwa za kukhazikitsidwa kwa Mphotho ya Abel ndi anthu aku Norway chinali chikhumbo chowonetsa anzawo a Alfred Nobel: chonde, sitiri oipitsitsa.

Kuthamangitsa malo omwe palibe malire

Nayi Niels Henrik Abel kwa inu. Tsopano za wopambana mphothoyo, Mngelezi wazaka 63 (akukhala ku USA). Zomwe anachita mu 1993 zikhoza kuyerekezedwa ndi kukwera Everest, kukwera mwezi, kapena zina zotero. Bwana ndi ndani Andrew Wiles? Ngati muyang'ana mndandanda wa zofalitsa zake ndi zolemba zosiyanasiyana zomwe zingatheke, adzakhala wasayansi wabwino - pali zikwi zambiri. Komabe, amaonedwa kuti ndi mmodzi mwa akatswiri a masamu akuluakulu. Kafukufuku wake amakhudzana ndi chiphunzitso cha manambala ndipo amagwiritsa ntchito ubale ndi algebraic geometry Oraz chiphunzitso choyimira.

Anakhala wotchuka chifukwa chothana ndi vuto lomwe linali losafunikira kwenikweni pamalingaliro a masamu umboni wa Fermat's Last Theorem (Kwa iwo omwe sakudziwa zomwe ndikutanthauza, onani pansipa). Komabe, phindu lenileni silinali yankho lokha, koma kulengedwa kwa njira yatsopano yofufuzira yomwe idagwiritsidwa ntchito kuthetsa mavuto ena ambiri ofunikira.

Sizingatheke kusalingalira tanthauzo la zinthu zina, paulamuliro wa zipambano za anthu. Mazana a zikwi za achinyamata amalota akukankha mpira bwino kuposa ena, zikwi makumi ambiri akufuna kudziwonetsa okha ku mphepo za Himalaya, kudumpha kuchokera ku mphira pa mlatho, kupanga phokoso lomwe amatcha kuyimba, kudya zakudya zopanda thanzi mwa ena ... chiwerengero chosafunikira kwa aliyense. Wogonjetsa woyamba wa Mount Everest, Sir Edward Hillary, anayankha molunjika funso limene anapita kumeneko: “Chifukwa ali, chifukwa Everest ali! Wolemba mawu awa anali katswiri wa masamu moyo wake wonse, chinali njira yanga ya moyo. Cholondola chokhacho! Koma tiyeni tithetse filosofi iyi. Tiyeni tibwererenso panjira yabwino ya masamu. Chifukwa chiyani pali mkangano wonse pa Theorem ya Fermat?

Ine ndikuganiza ife tonse tikudziwa chomwe iwo ali nambala zazikulu. Ndithudi aliyense amamvetsa mawu akuti "kuwola mu zinthu zofunika kwambiri", makamaka pamene mwana wathu atembenuza ulonda kukhala mbali.

Pierre de Fermat (1601-1665) anali loya ku Toulouse, koma iye anachita ndi masamu monga ankachita masewera, ndipo zotsatira zabwino ndithu, chifukwa iye anapita mu mbiri ya masamu monga mlembi wa ziphunzitso zambiri za chiwerengero ndi kusanthula. Anali ndi chizoloŵezi choika ndemanga ndi ndemanga zake m’mphepete mwa mabuku amene amaŵerenga. Ndipo ndiko kulondola - cha m'ma 1660 adalemba m'mphepete mwake:

Nayi Pierre de Fermat kwa inu. Kuyambira nthawi yake (ndipo ndiloleni ndikukumbutseni kuti wolemekezeka Gascon d'Artagnan ankakhala ku France panthawiyo, ndipo Andrzej Kmitsich anamenyana ndi Boguslav Radziwill ku Poland), mazana, ndipo mwinanso masamu akuluakulu ndi ang'onoang'ono anayesetsa kuti akonzenso kuganiza kotayika kwa munthu wanzeru. Ngakhale lero tili otsimikiza kuti umboni wa Fermat sungakhale wolondola, zinali zokhumudwitsa kuti funso losavuta loti equation xⁿ + yⁿ = dⁿ, n> 2 ili ndi mayankho mu manambala achilengedwe? zikhoza kukhala zovuta.

Akatswiri ambiri a masamu amene anabwera kudzagwira ntchito pa June 23, 1993, anapeza mu e-mail yawo (yomwe panthaŵiyo inali yopangidwa mwatsopano, ikadali yotentha) uthenga wachidule: “Mphekesera zochokera ku Britain: Wiles akutsimikizira Fermat.” Tsiku lotsatira, nyuzipepala ya tsiku ndi tsiku inalemba za izo, ndipo nkhani yomaliza ya Wiles inasonkhanitsa atolankhani, TV ndi photojournalists - monga pa msonkhano wa mpira wotchuka.

Aliyense amene amawerenga "Satana kuchokera m'kalasi lachisanu ndi chiwiri" ndi Kornel Makuszyński amakumbukiradi zomwe Bambo Iwo Gąsowski, m'bale wa pulofesa wa mbiri yakale yemwe dongosolo lake lofunsa mafunso ophunzira linapezedwa ndi Adaś Cisowski, anachita. Iwo Gąsowski anali akungothetsa nkhani ya Fermat, kuwononga nthawi, katundu ndi kunyalanyaza nyumba yake:

Pomaliza, Bambo Iwo adamvetsetsa kuti sangatsimikizire chisangalalo cha banja ndi mawerengedwe amphamvu ndikusiya. Makuszyński sanakonde sayansi, koma ananena zowona za Bambo Gąsowski. Iwo Gąsowski analakwitsa chinthu chimodzi chachikulu. Sanali kuyesera kukhala katswiri m’lingaliro lenileni la mawuwo, iye anali kuchita ngati wosaphunzira. Andrew Wiles ndi pro.

Nkhani yolimbana ndi Fermat's Last Theorem ndiyosangalatsa. Zitha kuwoneka mophweka kuti ndikokwanira kuwathetsa kwa ma exponents omwe ali manambala apamwamba. Kwa n = 3 yankho linaperekedwa mu 1770. Leonard Eulerkwa n = 5 - Peter Gustav Lejeune Dirichlet (1828) ndi Adrienne Marie Legendre mu 1830, ndi n = 7 - Gabriel Lama mu 1840. M'zaka za zana la XNUMX, katswiri wa masamu waku Germany adapereka mphamvu zake zambiri pavuto la Fermat Ernst Eduard Kummer (1810-1893). Ngakhale kuti sanachite bwino kwambiri, adatsimikizira milandu yambiri yapadera ndipo adapeza zinthu zambiri zofunika kwambiri. Zambiri zamakono za algebra, theoretical arithmetic, ndi algebraic number theory zinachokera ku ntchito ya Kummer pa chiphunzitso cha Fermat.

Pothetsa vuto la Fermat ndi njira za chiphunzitso cha nambala yachikale, adagawidwa m'zigawo ziwiri zosiyana za zovuta: yoyamba, pamene tikuganiza kuti xyz ndi coprime ndi exponent n, ndipo yachiwiri, pamene nambala z imagawidwa mofanana ndi exponent. Pachifukwa chachiwiri, zinkadziwika kuti panalibe njira zothetsera n = 150, ndipo poyamba, mpaka n = 000 (Lehmer, 6). Izi zikutanthawuza kuti chitsanzo chofananira sichingakhale chosatheka mulimonse: zingafune ndalama mabiliyoni a manambala kuti mupeze.

Nayi nkhani yakale yanu. Kumayambiriro kwa 1988, zidadziwika mu dziko la masamu kuti Yoichi Miyaoka adatsimikizira kusalingana, komwe adatsata zotsatirazi: ngati chowonjezera n chili chokwanira, ndiye kuti equation ya Fermat ilibe mayankho. Poyerekeza ndi zotsatira zoyamba pang'ono za Germany Gerd Faltings (1983) Zotsatira za Miyaoka zimatanthauza kuti ngati pali zothetsera, ndiye (molingana ndi chiwerengero) pali chiwerengero chochepa cha iwo. Chifukwa chake, yankho lavuto la Fermat limachepetsedwa ndikulemba kutha kwa milandu yambiri. Tsoka ilo, ndi angati aiwo omwe sanadziwike: njira zomwe Miyaoka adagwiritsa ntchito sizinalole kuwerengera kuti ndi angati omwe anali kale "mu dongosolo".

Ndikoyenera kudziwa apa kuti kwa zaka zambiri kuphunzira kwa chiphunzitso cha Fermat sikunachitike m'lingaliro la chiphunzitso cha nambala yeniyeni, koma mkati mwa ndondomeko ya algebraic geometry, maphunziro a masamu ochokera ku algebra ndi kuwonjezera kwa Cartesian analytic geometry, ndipo tsopano. kufalikira pafupifupi kulikonse: kuchokera ku maziko a masamu (chiphunzitso topoi mu logic), kudzera kusanthula masamu (njira za cohomological, mitolo yogwira ntchito), classical geometry, mpaka theoretical physics (vector bundles, twistor spaces, solitons).

Pamene ulemu ulibe kanthu

Zimakhalanso zovuta kuti tisakhale achisoni ndi tsogolo la katswiri wa masamu, yemwe thandizo lake pa kuthetsa vuto la Fermat ndilofunika kwambiri. Ndikulankhula za ArakielSuren Yurevich Arakelov, katswiri wa masamu wa ku Ukraine wokhala ndi mizu ya ku Armenian), yemwe kumayambiriro kwa zaka za m'ma 80, ali m'chaka chachinayi, adalenga zomwe zimatchedwa. chiphunzitso cha intersection pa mitundu ya masamu. Malo oterowo ali odzaza ndi mabowo ndi osakwanira, ndipo ma curve pa iwo amatha kutha mwadzidzidzi, ngati titero, kenako kuwonekeranso. Chiphunzitso cha intersection chimalongosola momwe mungawerengere kuchuluka kwa mphambano ya mapindikidwe oterowo. Icho chinali chida chachikulu chogwiritsidwa ntchito ndi Faltings ndi Miyaoka mu ntchito yawo pa vuto la Fermat.

Kamodzi Arakelov anaitanidwa kupereka zotsatira zake pa msonkhano waukulu masamu. Komabe, chifukwa chakuti ankatsutsa dongosolo la Soviet Union, anakanidwa chilolezo chochoka. Posakhalitsa analembedwa usilikali. Iye anasonyeza mwachipongwe kuti sankafuna kulowa usilikali pazifukwa zosagwirizana ndi nkhondo. Monga momwe ndinaphunzirira kuchokera ku magwero okayikitsa, akuti adatumizidwa ku chipatala chotsekedwa cha amisala, komwe adakhala pafupifupi chaka. Monga mukudziwira, mwachiwonekere pazandale, akatswiri amisala aku Soviet adasankha mtundu wapadera wa schizophrenia (mu Chingerezi kuchokera, kutanthauza "ulesi", mu Chirasha. schizophrenia waulesi).

Ndizovuta kunena zana limodzi pa zana momwe zinalili, chifukwa magwero anga a chidziwitso si odalirika kwambiri. Zikuoneka kuti, atatuluka m'chipatala, Arakelov anakhala miyezi ingapo m'nyumba ya amonke ku Zagorsk. Panopa amakhala ku Moscow ndi mkazi wake ndi ana atatu. Sachita masamu. Andrew Wiles ndi wodzaza ndi ulemu ndi ndalama.

Kuchokera ku lingaliro la anthu odyetsedwa bwino a ku Ulaya, sitepeyi ndi yosamvetsetseka Grigory Perelman, amene mu 2002 anathetsa vuto lodziwika kwambiri la zakuthambo m’zaka za m’ma XNUMX,”Poinari kulingaliraNdiyeno iye anakana onse zotheka mphoto. Choyamba Mendulo ya Fields, yotchulidwa pachiyambi, imene akatswiri a masamu amaiona kuti n’njofanana ndi Mphotho ya Nobel, ndiyeno mphoto ya madola milioni imodzi yothetsa limodzi la mavuto asanu ndi awiri ofunika kwambiri a masamu omwe atsala m’zaka za zana la makumi awiri. "Ena anali bwino, sindisamala za ulemu, chifukwa masamu ndizomwe ndimakonda, ndili ndi chakudya ndi ndudu," adauza dziko lodabwa kwambiri.

Kupambana pambuyo pa zaka zoposa 300

Fermat's Last Theorem inalidi vuto lodziwika bwino komanso lochititsa chidwi kwambiri mu masamu. Zinali zotseguka kwa zaka zopitirira mazana atatu, zomwe zinapangidwa momveka bwino komanso zomveka bwino ndipo zinali zotheka kuukiridwa ndi aliyense, ndipo m'zaka zamakompyuta zinali zosavuta kuyesa kuswa mbiri ina ya kuyerekezera njira zothetsera mavuto. M'mbiri ya masamu, nkhaniyi, kupyolera mu ntchito yake yolimbikitsa, idagwira ntchito yofunika kwambiri "kupanga chikhalidwe", zomwe zimathandizira kuti masamu onse awonekere. Ndizodabwitsa chifukwa vuto lenilenilo ndi laling'ono ndipo kungodziwa chabe za kusowa kwa mizu ya equation ya Fermat sikunathandizire kwambiri ku chuma chambiri cha chidziwitso cha masamu.

Mu 1847, Gabriel Lamet (1795-1870) anapereka phunziro ku French Academy of Sciences kulengeza njira yothetsera vuto la Fermat. Komabe, kulakwa kosaonekera polingalira kunazindikirika mwamsanga. Zinachokera ku kugwiritsidwa ntchito kosaloledwa kwa chiphunzitso chapadera cha kuwonongeka. Timakumbukira kuchokera kusukulu kuti nambala iliyonse ili ndi kuwonongeka kwapadera muzinthu zazikulu, mwachitsanzo, 2012 = 2 ∙ 2 ∙ 503. Nambala ya 503 ilibe zogawanitsa (kupatula 1 ndi 503 yokha), kotero sizingatheke kupitirira.

Katundu wapadera wa kugawa ali ndi integers zabwino, koma pakati pa ma seti manambala sikofunikira kuti iwo akhale. Mwachitsanzo, kwa manambala akhalidwe

tili ndi 36 = 2²⋅2³ ,komanso

Posanthula umboni wa Lame, Kummer adatha kutsimikizira kutsimikizika kwa lingaliro la Fermat kwa ena ofotokozera p. Anazitcha kuti zoyambira nthawi zonse. Imeneyi inali sitepe yoyamba yofunikira ku umboni wathunthu. Nthano yakula mozungulira nthano ya Fermat. "Kapena mwina ndizoipitsitsa - mwina simungathe kutsimikizira kuti ndizotheka kapena zosatheka kuzithetsa?"

Koma kuyambira 80s, aliyense ankaona kuti cholinga chinali pafupi. Ndikukumbukira kuti Khoma la Berlin linali litaimabe, ndipo ndinali kumvetsera kale nkhani za "posachedwa, kamphindi." Chabwino, winawake anayenera kukhala woyamba. Andrew Wiles anamaliza nkhani yake ndi phlegm ya Chingerezi: "Ndikuganiza kuti Fermat akutsimikizira," ndipo zinatenga nthawi kuti omvera ambiri azindikire zomwe zinachitika: vuto la masamu la zaka 330 linagwiritsidwa ntchito mozama ndi mazana a masamu ochokera ku bungwe. gulu lokha komanso osawerengeka osawerengeka, monga Ivo Gonsovsky kuchokera m'mabuku a Makushinsky. Ndipo Andrew Wiles anali ndi mwayi wogwirana chanza ndi Harald V, Mfumu ya Norway. Mwina sanali kulabadira malipiro wochepa kwa Mphotho Abele, pafupifupi mayuro zikwi mazana angapo - n'chifukwa chiyani amafuna ndalama zambiri?