Makai Abela

Kakaikahi ka poe heluhelu e olelo i kekahi mea e pili ana i ka inoa Abela. ʻAʻole, ʻaʻole mākou e kamaʻilio e pili ana i ke kanaka ʻōpio pōʻino i pepehi ʻia e kona kaikaina ponoʻī ʻo Kaina. Ke ʻōlelo nei au i ke kanaka makemakika Norewai ʻo Niels Henrik Abel (1802–1829) a me ka makana i kapa ʻia ma hope ona, i hāʻawi ʻia (16 Malaki 2016) e ka Norwegian Academy of Sciences and Letters to Sir Andrew J. Wiles. Hoʻopiʻi kēia i ka poʻe makemakika no ka haʻalele ʻia ʻana e Alfred Nobel ma ke kūlana o nā ʻāpana o ka makana ʻepekema koʻikoʻi o ka honua.

ʻOiai mahalo ka poʻe makemakika i ka mea i kapa ʻia Medal Fields (i manaʻo ʻia ʻo ka laurel kiʻekiʻe loa ma kāna kula), pili ia me 15 tausani wale nō. (ʻaʻole miliona, kaukani!) Nā kālā Kanada, a hiki i ka lanakila Abel Awards waiho i ka helu no 6 miliona Norwegian kroner (ma kahi o 750 8 euros) i loko o kāna ʻeke. Loaʻa iā Nobel laureates SEK 865 miliona, a ma kahi o XNUMX tausani. euros - emi iho ma mua o nā mea pāʻani tennis no ka lanakila ʻana i kahi hoʻokūkū nui. Aia kekahi mau kumu i hoʻokomo ʻole ʻia ai ʻo Alfred Nobel i nā mea makemakika ma waena o nā mea lanakila o ka makana. ʻO ka makemake o Nobel e pili ana i nā "mea ʻike a me nā ʻike" e lawe mai i ka pōmaikaʻi nui loa i ke kanaka, akā ʻaʻole paha he manaʻo, akā pono. ʻAʻole i manaʻo ʻia ka makemakika he ʻepekema hiki ke lawe mai i ka pono kūpono i ke kanaka.

No ke aha o Abela

ʻO wai Niels Henrik Abel a he aha ka mea i kaulana ai? He akamai paha ʻo ia, no ka mea, ʻoiai ua make ʻo ia i ka maʻi maʻi maʻi i ka makahiki 27 wale nō, ua hoʻokō ʻo ia i kahi māka paʻa ma ka makemakika. ʻAe, aia ma ke kula kiʻekiʻe ke aʻo mai lākou iā mākou pehea e hoʻoponopono ai i nā hoohalike; mua o ka degere mua, a laila huinaha a i kekahi manawa cubic. ʻEhā haneli mau makahiki i hala aku nei, ua hiki i nā ʻepekema Italia ke hoʻokō me ... hoʻohālikelike degere ʻehāʻo ka mea i ʻike ʻole ʻia.

a ʻo ia kekahi o nā mea

ʻAe, ua hiki i nā ʻepekema ke hana i kēia i ke kenekulia XNUMX. ʻAʻole paʻakikī ke koho ʻana ua lawe ʻia nā hoohalike o nā degere kiʻekiʻe. ʻAʻohe mea. No ʻelua haneli makahiki, ʻaʻohe mea i lanakila. Ua hāʻule pū ʻo Niels Abel. A laila ʻike ʻo ia ... hiki ʻole paha kēia. Hiki ke hōʻoia hiki ole ke hooponopono ia hoohalike – a i ʻole, e hōʻike ana i ka hoʻonā ma nā ʻano helu helu maʻalahi.

ʻO kēia ka mua o 2 tausani. makahiki (!) o kēia ʻano noʻonoʻo: ʻaʻole hiki ke hōʻoia ʻia kekahi mea, ʻaʻole hiki ke hana ʻia kekahi mea. Aia ka makemakika ma luna o ia mau hōʻoiaʻiʻo—ʻo ka ʻepekema hoʻomaʻamaʻa ke hoʻomau nei i ka haki ʻana i nā pale. I ka makahiki 1888, ua ʻōlelo ka luna hoʻomalu o ka US Patent Commission "ʻuʻuku nā mea i manaʻo ʻia i ka wā e hiki mai ana, no ka mea, ua hana ʻia nā mea āpau." I kēia lā, he mea paʻakikī iā mākou ke ʻakaʻaka i kēia... Akā i ka makemakika - hoʻāʻo ʻia, nalowale. He mea hiki ole ke hana.

Hoʻokaʻawale ka mōʻaukala i ka ʻike aʻu i wehewehe ai ma waena Niels Abela i Evariste Galois, ua make lāua ʻelua ma ke ʻano he "koho ʻia e nā akua" ma mua o ke kanakolu makahiki, me ka mahalo ʻole ʻia e ko lāua mau hoa. ʻO Niels Abel kekahi o nā mea makemakika Norewai me ka kaulana nui (ʻoiaʻiʻo, ʻelua, ʻo ka lua ... Sophus Lee, 1842-1899 - ʻaʻole kani nā inoa ʻo Scandinavian, akā he poʻe Norewai lāua ʻelua).

ʻAʻole maikaʻi ka poʻe Norewai me nā Swedes - akā naʻe, maʻamau kēia i waena o nā poʻe e pili ana. ʻO kekahi o nā kumu no ka hoʻokumu ʻana i ka makana ʻo Abel e nā Norewai ʻo ia ka makemake e hōʻike i ko lākou mau hoa aloha iā Alfred Nobel: e ʻoluʻolu, ʻaʻole mākou i ʻoi aku ka hewa.

Ke alualu ʻana i kahi komo palena ʻole

Nui no Niels Henrik Abel. I kēia manawa e pili ana i ka mea lanakila, he kanaka Pelekane 63 makahiki (e noho ana ma USA). ʻO kāna hana i ka makahiki 1993 hiki ke hoʻohālikelike ʻia me ka piʻi ʻana iā Everest, e hele ana ma ka mahina a i ʻole kekahi mea like. ʻO wai ka haku Andrew Wiles? Inā ʻoe e nānā i kāna papa inoa o nā mea paʻi a me nā ʻōlelo kuhikuhi like ʻole, he kanaka ʻepekema maikaʻi ʻo ia - he mau tausani o lākou. Eia naʻe, ua manaʻo ʻia ʻo ia kekahi o nā mea makemakika nui loa. Aia kāna noiʻi ʻana i ka ʻepekema helu a hoʻohana i nā pilina me hoʻonaʻauao algebraic ʻO Odraz manaʻo hōʻike.

Ua kaulana ʻo ia no ka hoʻoponopono ʻana i kahi pilikia pili ʻole loa mai ka manaʻo o ka makemakika hōʻoia o Fermat's Last Theorem (ka poʻe ʻike ʻole i kaʻu e kamaʻilio nei - hoʻomanaʻo wau iā ʻoe ma lalo). Eia naʻe, ʻaʻole ʻo ka waiwai maoli ka hopena ponoʻī, akā ʻo ka hana ʻana i kahi ala noiʻi hou i hoʻohana ʻia e hoʻoponopono i nā pilikia koʻikoʻi he nui.

ʻAʻole hiki ke noʻonoʻo i kēia manawa i ke koʻikoʻi o kekahi mau mea, i ka hierarchy o nā hoʻokō kanaka. He mau haneli kaukani o ka poʻe ʻōpio e moeʻuhane ana i ke kiʻi ʻana i ka pōleʻa ʻoi aku ka maikaʻi ma mua o nā mea ʻē aʻe, makemake nā ʻumi kaukani e hōʻike iā lākou iho i ka makani Himalayan, lele mai nā kaula hao ma ke alahaka, hoʻokani i nā leo a lākou e kapa ai he mele, hoʻolei i nā meaʻai maikaʻi ʻole i nā poʻe ʻē aʻe ... e hoʻoponopono i ka hoohalike ʻaʻole pono i kekahi. ʻO ka lanakila mua o ka mauna Everest, Sir Edward Hillary, pane pololei i ka nīnau no ke kumu o kona komo ʻana i laila: "No ka mea, aia nō, no ka mea aia ʻo Everest!" ʻO ka mea kākau o kēia mau ʻōlelo he mea makemakika i kona ola a pau, ʻo ia kaʻu mea ʻai no ke ola. ʻO ka pololei wale nō! Akā, e hoʻopau kākou i kēia manaʻo. E hoʻi kākou i ke ala olakino o ka makemakika. No ke aha e hoʻohauʻoli ai e pili ana i ka theorem a Fermat?

Manaʻo wau ua ʻike mākou a pau he aha lākou helu nui. ʻOiaʻiʻo, hoʻomaopopo ka poʻe a pau i ka huaʻōlelo "hoʻohui i nā mea nui," ʻoiai ke hoʻololi kā kā mākou keiki liʻiliʻi i ka uaki i mau ʻāpana.

ʻO Pierre de Fermat (1601-1665) he loio mai Toulouse mai, aka, he kamakama no hoi oia i ka makemakika, me na hopena maikai loa, no ka mea, ua iho oia ma ka moolelo o ka makemakika ma ke ano he mea kakau o na theorems he nui no ka helu theory and analysis. Ua maʻa ʻo ia i ke kau ʻana i kāna mau memo a me kāna mau manaʻo ma ka ʻaoʻao o nā puke āna i heluhelu ai. A pololei kēlā - ma kahi o 1660 ua kākau ʻo ia ma kekahi o nā palena:

Nui no Pierre de Fermat. Mai kona manawa (a e hoʻomanaʻo wau iā ʻoe ua noho ke aliʻi koa Gascon d'Artagnan i Farani i kēlā manawa, a ma Polani i hakakā ʻo Andrzej Kmicic me Boguslaw Radziwill), he mau haneli, a he mau tausani o nā mea makemakika nui a me nā mea liʻiliʻi i hoʻāʻo ʻole e hana hou. nā manaʻo nalo o ka mea hoʻokamakama maikaʻi. ʻOiai i kēia lā ua maopopo mākou ʻaʻole hiki ke pololei ka hōʻike a Fermat, he mea hoʻonāukiuki ka nīnau maʻalahi o hoohalike xⁿ + yⁿ = dⁿ, n> 2 loaʻa nā hāʻina ma nā helu kūlohelohe? hiki ke paʻakikī.

He nui nā mea makemakika i hele mai e hana ma Iune 23, 1993, i loaʻa i kā lākou leka uila (ʻo ia ka mea hou a me ka wela hou) he leka laconic: "Rumors from Britain: Wiles proves Fermat." I kekahi lā aʻe, ua kākau pū ka nūpepa i kēlā me kēia lā e pili ana iā ia, a ʻo ka hope o ka moʻolelo haʻiʻōlelo ʻo Wiles i hōʻuluʻulu i ka paʻi, televise a me nā mea paʻi paʻi kiʻi - e like me ka ʻaha kūkā o kahi mea pāʻani pôpeku kaulana.

ʻO ka mea i heluhelu iā "Satan mai ka papa ʻehiku" na Kornel Makuszyński e hoʻomanaʻo maoli i ka mea a Mr. Iwo Gąsowski, ke kaikunāne o ke kumu mōʻaukala nona ka ʻōnaehana nīnau nīnau i ʻike ʻia e Adaś Cisowski. Ua hoʻoponopono ʻo Iwo Gąsowski i ka hoʻohālikelike o Fermat, hoʻopau manawa, kālā a haʻalele i kona home:

ʻO ka hope loa, ua ʻike ʻo Mr. Iwo ʻaʻole ʻo nā bila kiʻekiʻe e hōʻoia i ka hauʻoli o kona ʻohana a haʻalele ʻo ia. ʻAʻole makemake ʻo Makuszyński i ka ʻepekema, akā ua pololei ʻo ia e pili ana iā Mr. Gąsowski. Ua hana hewa ʻo Iwo Gąsowski. ʻAʻole ʻo ia i hoʻāʻo e lilo i loea i ka manaʻo maikaʻi o ka huaʻōlelo, ua hana ʻo ia e like me ka mea amateur. ʻO Andrew Wiles kahi pro.

He mea hoihoi ka moʻolelo o ka hakakā me Fermat's Last Theorem. Hiki ke ʻike maʻalahi ʻia ua lawa ia e hoʻoponopono iā lākou no nā exponents he helu prima. No ka n = 3 ua hāʻawi ʻia ka hoʻonā i 1770. Leonard Euler, no n = 5 – Peter Gustav Lejeune Dirichlet (Xnumx) a Adrienne Marie Legendre i ka makahiki 1830, a ma n = 7 – Gabriel Lame i ka makahiki 1840. I ke kenekulia XNUMX, ua hāʻawi ka mea makemakika Kelemania i ka hapa nui o kona ikaika i ka pilikia o Fermat Ernst Eduard Kummer (1810-1893). ʻOiai ʻaʻole i loaʻa iā ia ka kūleʻa hope loa, ua hōʻoia ʻo ia i nā hihia kūikawā he nui a ʻike i nā waiwai koʻikoʻi o nā helu prima. ʻO ka hapa nui o ka algebra hou, theoretical arithmetic, a me ka helu algebraic theory no kona kumu i ka hana a Kummer ma ka Fermat's theorem.

I ka hoʻoholo ʻana i ka pilikia o Fermat me ka hoʻohana ʻana i nā ʻano o ke kumumanaʻo helu maʻamau, ua hoʻokaʻawale ʻia lākou i ʻelua mau hihia like ʻole o ka paʻakikī: ʻo ka mua, ke manaʻo mākou ua hui pū ka huahana xyz me ka exponent n, a ʻo ka lua, ke hiki ke puʻunaue like ka helu z e. ka exponent. I ka lua o ka hihia, ua ʻike ʻia ʻaʻohe hopena a hiki i ka n = 150, a ma ka mua, a hiki i ka n = 000 (Lehmer, 6). ʻO ia hoʻi, ʻaʻole hiki ke hoʻohālikelike ʻia i kēlā me kēia hihia: pono e koi ʻia nā helu o nā piliona helu e loaʻa ai.

Eia ka moʻolelo kahiko iā ʻoe. I ka hoʻomaka ʻana o 1988, ua ʻike ʻia ma ka honua makemakika ʻO Yoichi Miyaoka Ua hōʻike ʻia kekahi ʻano like ʻole, kahi i hahai ai kēia mau mea: inā lawa ka nui o ka exponent n, a laila ʻaʻohe hopena o ka hoʻohālikelike o Fermat. Hoʻohālikelike ʻia i ka hopena mua iki o ka Kelemania Gerd Faltings (1983) ʻO ka hopena o Miyaoka i manaʻo ʻia inā loaʻa nā hopena, a laila he helu palena wale nō o lākou (mai ka manaʻo o ka proportionality). No laila, ua hoʻemi ʻia ka hopena o ka pilikia o Fermat i ka helu ʻana i ka hopena o nā hihia he nui. ʻO ka mea pōʻino, ʻehia ka nui o nā mea i ʻike ʻole ʻia: ʻaʻole i ʻae nā ʻano hana i hoʻohana ʻia e Miyaoka i kekahi e koho i ka nui o nā mea i "hoʻonohonoho ʻia."

He mea pono ke hoʻomaopopo ma ʻaneʻi, no nā makahiki he nui, ʻaʻole i hoʻokō ʻia ke aʻo ʻana o ka theorem a Fermat i loko o ke ʻano o ke kumumanaʻo helu maʻemaʻe, akā i loko o ke ʻano o ka geometry algebraic, kahi aʻo makemakika i loaʻa mai ka algebra a ʻo ia ka hoʻonui ʻana o Cartesian analytical geometry. a i kēia manawa ua hoʻolaha kokoke i nā wahi a pau: mai ke kumu o ka makemakika (theory topoi in logic), ma o ka hoʻopalekana makemakika (cohomology method, functional sheaves), classical geometry, to theoretical physics (vector bundles, twistor spaces, solitons).

Inā ʻaʻohe mea nui ka hanohano

He mea paʻakikī hoʻi ʻaʻole e kaumaha i ka hopena o ka mea makemakika, nona ka hāʻawi ʻana i ka hopena o ka pilikia o Fermat. Ke kamaʻilio nei au no Arakiel (Suren Yurievich Arakelov, Ukrainian mathematician with Armenian roots), ka mea i ka hoʻomaka ʻana o 80s, i kona wā i kona makahiki ʻehā, hana i ka mea i kapa ʻia. ka manaʻo kuʻuna ma nā ʻano helu helu. Ua piha ia mau ʻili i nā lua a me ka piha ʻole, a nalo koke nā pihi ma luna a laila ʻike hou ʻia. Hōʻike ka manaʻo kuʻuna i ka helu ʻana i nā degere o ka hui ʻana o ia mau ʻāpana. ʻO kēia ka mea hana nui i hoʻohana ʻia e Faltings a me Miyaoka i kā lākou hana ma ka pilikia o Fermat.

I kekahi lā ua kono ʻia ʻo Arakelov e hōʻike i kāna mau hopena ma kahi ʻaha ʻōlelo makemakika nui. Eia naʻe, no kona hoʻohewa ʻana i ka ʻōnaehana Soviet, ua hōʻole ʻia ʻo ia e haʻalele. ʻAʻole i liʻuliʻu, ua koho ʻia ʻo ia i ka pūʻali koa. Ua hōʻike pololei ʻo ia i kona kūʻē ʻana i ka ʻoihana koa ma ka laulā no nā kumu pacifist. I koʻu aʻo ʻana mai nā kumu kānalua, ua ʻōlelo ʻia ua hoʻouna ʻia ʻo ia i kahi haukapila psychiatric paʻa, kahi āna i noho ai ma kahi o hoʻokahi makahiki. E like me ka mea i ʻike ʻia, ʻike ʻia no nā kumu politika, ua ʻike nā psychiatrists Soviet i kahi ʻano schizophrenia kūikawā (ma ka ʻōlelo Pelekania mai, ʻo ia hoʻi ka "sluggish", ma ka Lūkini. schizophrenia haʻahaʻa).

He mea paʻakikī ke haʻi i hoʻokahi haneli pākēneka pehea i hana maoli ʻia ai, no ka mea, ʻaʻole hilinaʻi nui koʻu mau kumu ʻike. ʻIke ʻia, ma hope o ka haʻalele ʻana i ka haukapila, ua noho ʻo Arakelov i kekahi mau mahina ma kahi monastery ma Zagorsk. Noho ʻo ia ma Moscow me kāna wahine a me kāna mau keiki ʻekolu. ʻAʻole ʻo ia hana makemakika. Ua piha ʻo Andrew Wiles i ka hanohano a me ke kālā.

Mai ka manaʻo o kahi hui Europa hānai maikaʻi, ʻaʻole hiki ke hoʻomaopopo ʻia ka ʻanuʻu ʻO Grigory Perelman, nāna i hoʻoponopono i ka pilikia topological kaulana loa i ka makahiki 2002,"Manaʻo poinariA laila hōʻole ʻo ia i nā uku kūpono a pau. ʻO ka mua ka Fields Medal i ʻōlelo ʻia ma mua, i manaʻo ʻia e ka makemakika e like me ka Nobel Prize, a laila ka makana hoʻokahi miliona kālā no ka hoʻoponopono ʻana i kekahi o nā pilikia makemakika koʻikoʻi ʻehiku i koe mai ka makahiki iwakālua. "ʻOi aku ka maikaʻi o nā poʻe ʻē aʻe, ʻaʻole wau i manaʻo i ka hanohano no ka mea ʻo ka makemakika kaʻu mea leʻaleʻa, loaʻa iaʻu ka meaʻai a me ka cigakeke," i ʻōlelo ʻo ia i kahi honua kahaha.

Ka lanakila ma hope o 300 makahiki

ʻO Fermat's Last Theorem ka pilikia makemakika kaulana loa. Ua wehe ʻia no ʻekolu haneli mau makahiki, ua hoʻokumu ʻia ma kahi ʻano akaka a hiki ke heluhelu ʻia a hiki ke hoʻouka ʻia e kekahi, a i ke au o ka hoʻohana nui ʻana o nā kamepiula he mea maʻalahi ke hoʻāʻo e wāwahi i kahi moʻolelo ʻē aʻe. koho ana i na mea e hiki ai. I loko o ka moʻolelo o ka makemakika, ua hoʻokani kēia pukana, ma o kāna hana hoʻouluhua, i ka hana "hoʻokumu moʻomeheu" koʻikoʻi, e kōkua ana i ka hoʻokumu ʻana i nā aʻo makemakika holoʻokoʻa. He mea ʻē kēia no ka mea he mea liʻiliʻi ka pilikia ponoʻī a ʻaʻole i kōkua nui ka ʻike e pili ana i ka nele o nā aʻa o ka hoʻohālikelike Fermat i ka waihona nui o ka ʻike makemakika.

I ka makahiki 1847, ua aʻo ʻo Gabriel Lamé (1795-1870) ma ka French Academy of Sciences, e hoʻolaha ana i ka hopena o ka pilikia o Fermat. Eia naʻe, ua ʻike koke ʻia kahi kuhi hewa ma ka noʻonoʻo. Hoʻokumu ʻia ia ma ka hoʻohana ʻole ʻia o ka theorem decomposition kū hoʻokahi. Ke hoʻomanaʻo nei mākou mai ke kula mai, ʻo kēlā me kēia helu he haʻihaʻi maopopo ʻole i loko o nā kumu kumu, no ka laʻana, 2012 = 2 ∙ 2 ∙ 503. ʻAʻohe mea mahele o ka helu 503 (koe wale nō 1 a me 503 ponoʻī), no laila ʻaʻole hiki ke hoʻonui ʻia.

Loaʻa i nā integer maikaʻi ka māhele kūʻokoʻa, akā ʻaʻole pono lākou i waena o nā pūʻulu helu ʻē aʻe. No ka laʻana, no nā helu kiko

loaʻa iā mākou 36 = 2²⋅2³ , aka hoi

Ma ke kālailai ʻana i ka hōʻike a Lame, ua hiki iā Kummer ke hōʻoia i ka ʻoiaʻiʻo o ka manaʻo kuhi a Fermat no kekahi mau mea hoʻolaha o ka helu p. Ua kapa ʻo ia iā lākou i nā helu kumu maʻamau. ʻO kēia ka hana koʻikoʻi mua i kahi hōʻoia piha. Ua ulu aʻe kekahi moʻolelo a puni ka theorem a Fermat. "A i ʻole ʻoi aku ka ʻino - ʻaʻole hiki iā ʻoe ke hōʻoia he hiki a hiki ʻole paha ke hoʻoponopono?"

Akā mai ka 80s, ua manaʻo nā mea a pau ua kokoke ka pahuhopu. Ke hoʻomanaʻo nei au i ke kū ʻana o ka Wall Berlin, a ke hoʻolohe nei au i nā haʻi'ōlelo e pili ana i "koke koke, i kahi manawa." ʻAe, pono kekahi i mua. Ua hoʻopau ʻo Andrew Wiles i kāna haʻiʻōlelo me ka phlegm English, "Manaʻo wau ua hōʻoia ʻo Fermat," a ua lōʻihi ka manawa ma mua o ka ʻike ʻana o ka lehulehu i ka mea i hana ʻia: he pilikia makemakika 330 makahiki i hana ikaika ʻia e nā haneli o ka regimental matematika. a me ka helu ʻana o nā poʻe hoʻomaka, e like me Ivo Gonsovski mai nā puke moʻolelo a Makuszynski. A ua loaʻa iā Andrew Wiles ka hanohano o ka lulu lima me Harald V, ke Aliʻi o Norewai. ʻAʻole paha ʻo ia i hoʻolohe i ka hoʻohui haʻahaʻa i ka makana ʻo Abel, ma kahi o nā haneli haneli - no ke aha ʻo ia e makemake ai i ke kālā nui?