Kwiintsuku ezilishumi elinesihlanu ezidlulileyo, omnye wabafundi bezi zigxeko-ncomo ezithobekileyo wasishiya kumagqabaza ezinye zeengxelo esiye saziva amaxesha amaninzi. Ekuqaleni kwengcinga, njengakwezinye izihlandlo, siphendula kwakwindawo enye ebisenziwa kuyo. Noko ke, ecamngca ngokuthe ngcembe, wacinga ukuba kunokuba mnandi ukunikezela inqaku elipheleleyo kula mabinzana, ekubeni kukho abantu abaninzi abathi, ngokweengxelo zabo, bacinge ngendlela efanayo, nabakholelwa ngokunyanisekileyo ukuba baphosakele. Uyazi, iikhomenti ezithi 'oko ndaphuma esikolweni andizange ndisebenzise imathematika' okanye 'imathematika ayinamsebenzi kum'. Imigca elandelayo ayenzelwanga ukweyisela nabani na. Nangona kunjalo, ndicinga ukuba luvavanyo oluyimfuneko njengesibini esibonakalisa kancinci malunga nokuchaneka 'kweentsomi zasezidolophini' (ndingathi, ngoku ukuba i-anglicism ikwifashoni, 'inkohliso') yohlobo oluchaziweyo. Ndiyaqonda ukuba zichazwa ngokuchubekileyo, kwaye ngaphandle kweenjongo ezimbi, kungoko ndicinga ukuba ngumsebenzi wethu (oochwephesha bemathematika, oososayensi, ootishala okanye abachwepheshile) ukuzama ukuzicacisa, okanye ubuncinane banike izizathu zokungavisisani kwethu. Njengoko, ngaphezu koko, ndiza kuzama ukunika imizekelo ebambekayo, ndicinga ukuba ihambelana ngokugqibeleleyo nobhengezo, oluyintsingiselo yokugqibela yezi ngcinga sizizisa apha ngeveki. Ndiya kubiza bonke abo bathe bafunda baza bagqibezela umsebenzi waseyunivesithi kweso sifundo semathematika; okwangoku isidanga se-bachelor kwimathematika, ngaphambili isidanga se-bachelor kwimathematika. Yinkcazo ebanzi kakhulu, ndiyazi, kuba kuya kubakho abo bathathela ingqalelo iingcali zemathematika kuphela abo benza uphando kwimathematika, hayi abo bazinikele ngokupheleleyo ekufundiseni, ekufikeleleni eluntwini, njl. Ngokwenene, abo bangaphambili ngabo banegunya elingakumbi lokusebenzisa elo nani, kuba bazama ukuqhubela phambili umcimbi ngomsebenzi wabo. Kodwa ekubeni ndiza kuthetha ngokwemigaqo yoqeqesho endilufumeneyo, kungokuba ndizama ukwenza ulwandiso olubonisiweyo. Sesiphi isithandi sobulumko osaziyo esingazange ngandlel’ ithile sikuhlakulele ingqiqo okanye imathematika? Ukuqala ndaweni ithile, ugqabaza ukuba andiqondi ukuba zininzi iingcali zezibalo ezinokufunyanwa ezingabangiyo ifilosofi nembali yefilosofi njengoqeqesho oluyimfuneko kwikharityhulam yakhe nawuphi na ummi onemfundo ephakamileyo, nokuba kuluphi na uhlobo. Kwaye ndiya kuyiphikisa ngombuzo: Yiyiphi intanda-bulumko oyaziyo engazange ihlakulele ingqiqo okanye imathematika ngandlela-thile? Ngaba kuyimfuneko ukwenza uluhlu lweentanda-bulumko ezingezizo ezezibalo? UHáganla uya kufumana inani elisezantsi kakhulu kuneseti yazo zonke iintanda-bulumko. Kwaye isizathu sicacile: imathematika ayicingi nje kuphela imiba yobugcisa esekelwe kwizibalo (leyo yinxalenye kuphela, i-subset esinokuyithetha ngokwemigaqo yesifundo sethu, kunye ne-subset yamaxabiso ekhadinali ngaphantsi kwendawo epheleleyo), kodwa kwakhona ukulandela iNkcazelo kunye nomboniso wawo nawuphi na umba, usebenzisa iilwimi kunye nokuqiqa eyona ifanelekileyo kubume bengxaki. IMathematika ayifuni kuphela isisombululo esibambekayo, njengoko sifundiswa kubomi bethu besikolo, kodwa ngaphezu kwayo yonke ingcamango, uhlalutyo, ukuphuhliswa kweendlela; Emva kokuba ezo buchule zifunyenwe, inxalenye ecacileyo yesisombululo iya kuthengiswa, engasayi kuba yinto eninzi yomatshini yesisombululo sokugqibela. Njengoko ndithetha, le nxalenye yokugqibela kuphela, inxalenye yobugcisa, eyona nto ibalulekileyo kwinyani, kuba into ebalulekileyo kukufumanisa, ukufumana indlela. Apho unomfanekiso wento ethathwa ngokuba 'sisithandi sobulumko sokuqala', uThales waseMileto, owathi, njengoko usazi, udume ngethiyori evumele bonke abantu ukuba benze izinto ezinjengokulinganisa imigama ukusuka kwiindawo ezingafikelelekiyo. Ubungenongcoliswa nasekhaya Nokuba yinyani, kuba sivula amehlo rhoqo kusasa, sisebenzisa imathematika. Singatyala umdlalo obizwa ngokuba 'Musa ukwenza into oyifunayo ngandlela ithile ukuze ukwazi ukuyenza'. Ewe, baya kuvuka xa umzimba wabo ubaxelela ukuba benze njalo, kuba iwotshi iya kuthintelwa. Ukulibala malunga neepilisi, iifowuni eziphathwayo, iikhomputha, iithelevishini, ii-microwaves, izitofu, izifudumezi, oomatshini bokuhlamba, njl., nasiphi na isixhobo esinesiphaluka esincinci esidibeneyo, njengoko uyazi, sithobela i-algorithm ethile yemathematika. Ngesizathu esifanayo, awuyi kukwazi ukusebenzisa ukutshintshwa kokukhanya, ngoko ke ukuba ikhaya lakho lingaphakathi, fumana ikhandlela elihle kunye nekhandlela elifakwe kwikhandlela elibandakanyiweyo ukuze ukwazi ukuliphatha ngokukhululekileyo, ngenxa yokuba i-flashlight, efana neyodwa. Kuya kufuneka ukuba ube nee-emele ezilungileyo zokugalela indlu yangasese kuba asinako ukugungxula ityathanga okanye ukuvula itephu kuba uyilo lwemibhobho, ukusebenza kwayo, kufuna izibalo kunye nemilinganiselo eyenziwe ngumntu ukuze isebenze. Ewe kunjalo, yiba namagqabi omthi alungele ukuzicoca, gcina inxalenye, kuba naluphi na uhlobo lwephepha lunemilinganiselo kunye nemilinganiselo ongenakuyisebenzisa, singasathethi ke ngeeveranda zezakhi zokwakheka kwakho (oku kuchaphazela iipilisi zakho kunye namayeza kwaye akanakusela) . Kutheni i-toilet paper roll i-cylindrical kwaye ingabi yi-prismatic, spherical, njl.? Ah, uxolo, asinakusebenzisa amagama ezibalo. IMathematika ayifuni kuphela isisombululo esibambekayo, kodwa ngaphezu kwayo yonke ingcamango, uhlalutyo, ukuphuhliswa kobuchule. Ngendlela efanayo, kufuneka sibe nqunu ngokupheleleyo kwisitrato, kuba imilo yeengubo ayikho nje nayiphi na. Kuye kwafuneka ukuba bayenze ngokomlinganiselo othile, kwaye yenziwe ngeemilo ezinomlinganiselo owaneleyo. Akufanelanga nokuba iinkozo zemali, amatyala (Ngaba ukhe wazibuza ukuba kutheni sisebenzisa amanani u-1, 2 kunye no-5 kunye nophindaphindo lwawo, njengexabiso lemali? Kutheni kungenjalo 1, 3, 7, umzekelo, okanye amanye amaxabiso?), Amakhadi okuthenga ngetyala okanye naluphi na olunye uhlobo (uyazi, ngenxa yeebhakhowudi, iPIN kunye nabanye), kananjalo abayi kuhoya iifrikhwensi zebhasi kunye nezinye iindlela. yezothutho (iiGPS zisekelwe kwi-sphere intersection theorem). Ufumanisa ukuba amanani akakho. Kwaye ukuba uyabazi, awulwazi ucwangco lwabo (Yeka indlela entle ngayo 'iNcwadi yeSanti' nguJorge Luis Borges, ngendlela! umbhalo-ngqangi, kuba iifonti ngoku ziyilwe ngemisebenzi yezibalo kunye neendlela ezithile zokudibanisa; khumbula imithetho yalo mdlalo, ungasebenzisi nantoni na enezibalo kuyo). bafanele bahambe naphi na apho baya khona, kodwa kungekhona ngeyona ndlela imfutshane, kuba kugqitywe ngelithini ngeyona ndlela imfutshane? Kwakhona, kuthetha ukuthini 'mfutshane'? Kucacile ukuba asizukwazi ukutya nantoni na engafunyanwanga ngendlela esetyenziswa ngayo imathematika ethile, ngoko ke, ukuzila oko kunempilo kakhulu, kwaye masiye endle, siyokukha iziqhamo zasendle, kuba ndinoloyiko lokuba singazila ukutya. ayiyi kukwazi ukubamba nantoni na apho igadi inqunyulwe khona, uhlobo lokunkcenkceshela, ilungiselelo lembewu, njl. Kumfanekiso, umyili weleta 'a' kwifonti yeHelvetica, kunye neegophe zeBezier. Ukusebenzisa le ndlela, ngaphezu kwamanqaku apho ukumelwa kokugqibela kudlula khona (ii-nodes), kukho iindawo zokulawula ezichanekileyo ezibonisa ukuthambeka kwejika ngalinye. IiSayensi vs. Uluntu Ngezizathu ezicacileyo, asinakwazi yonke into ngayo yonke into ngendlela egqibeleleyo. Ulwazi lomntu lubanzi kangangokuba kufuneka sikhethe. Nangona kunjalo, ukuba nenkcubeko, ukwazi eyona nto isisiseko kuyo yonke into, kuyacetyiswa kwaye kuyatyebisa. Andazi ukuba ngowuphi na umzuzu kwimbali umntu wagqiba ukwenza ukwahlukana phakathi kwenzululwazi kunye noluntu, okanye ngubani na oya kuba lucid 'genius', kodwa ngokuqinisekileyo wenza enye yezona follies ezinkulu ezakha zabakho kwaye ziya kuqhubeka zikhona. Umntu yisethi yeenkalo ezininzi, kwaye awohlulwa. Ifuna kwaye isebenzisa zonke iintlobo zolwazi. Asiyo 'yencwadi', okanye 'yenzululwazi'. Zizo zombini. Isingxengxezo esithandwayo esithi 'Ndingumbhali' liculo lokulula, ukungabi nangqiqo, ukungakwazi. Ukuba ndizifumana ndikwindibano apho bathetha ‘ngobomi liphupha’, ndingaphela njani ndisithi “andicingi, kuba ndiyinzululwazi”? Okanye ukuba uyaphendula, "Loo mboniso bhanyabhanya weQuevedo mkhulu." Ayisebenzi njengengxoxo. Kubukrelekrele ngakumbi ukuba uthi cwaka, okanye ukwamkela ukungazi, kunokuthetha into engekhoyo. Thina oosonzululwazi bezibalo, izazinzulu, asinakuze silindele ukuba wonke umntu asombulule iiequations ezahlukeneyo, okanye ahlengahlengise ukusabela kokunciphisa i-oxidation (phakathi kwezinye izinto, kuba ukuba akunjalo, siya kuba ngaphezulu kakhulu). Kodwa ukukwazi, njengoko incwadi yolwimi kaLázaro Carreter esiyifundileyo yathi, "ukwazi ukutshintsha irejista", ngenjongo yokukwazi ukuva kunye nokuncokola ngokutyibilikayo kunye nonjingalwazi wentlalontle kunye nomsebenzi wokucoca. Kwaye ngokuqinisekileyo ngaphandle kokuhamba ngeenyawo okanye ukucinga okwesibini ukuba eminye imisebenzi i-pluses okanye imbi kunabanye. Bonke bafanelekile ngokulinganayo kuba zonke ziyimfuneko ngokupheleleyo. Ngokomntu, ndingoweqela leencwadi, ndihlala ndihambisana neemuvi ezintsha, ndihlala ndinolwazi olungakumbi okanye olungaphantsi ngeendaba zemihla ngemihla (enye into endiyithandayo), kwaye ndiyingcali yezibalo. Kwaye iincoko nabantwana endifunda nabo ngamanye amaxesha zezemathematika kwaye ezinye ezininzi zimalunga nezihloko 'zobuntu'. Isazi sezibalo okanye nabani na ozinikele 'kwinzululwazi' akaludeleli 'uluntu'. Ngokuchasene noko. Kakade ke, 'ukuba ngumntu', athe umfundi oxhase le migca ayibonisileyo, akuphelelanga kulo naluphi na uqeqesho okanye kuye nabani na ngokukodwa. Endaweni yoko, yinzala yalo lonke ulwazi ebesisoloko sivela, ngcono okanye okubi, kulo lonke ixesha lokuhlala kwethu kule planethi, leyo, ngendlela, ngendlela ekhokelela kuyo, iya kuphela ngaphambi kokuba iLanga libe yinkwenkwezi enkulu ebomvu. La magqabantshintshi okugqibela andikhumbuza ngemiboniso emibini emitsha emangalisayo evela kwiminyaka yamashumi amathandathu enkulungwane edluleyo, andazi ukuba ziseyintsomi yenzululwazi kwakhona, apho kukho neenguqulelo ezisixhenxe zefilimu: 'Iplanethi yeenkawu', nguPierre Boulle, kunye 'Yenza igumbi, Yenza igumbi!' nguHarry Harrison, zombini kunye nomxholo wezibalo. Kuba, njengoko nditshoyo, yonke into inxulumene kwaye isayensi kunye nobuntu aziyonyani eyahlukileyo. Imizekelo iphuphuma kuzo zonke iindidi zemisebenzi, kwanakwinto esiyithathela ingqalelo uncwadi lwamandulo kunye nababhali, abakhoyo nabadlulileyo. Ngaba siya kuze sikwazi ukuyeka ukumamela nabani na othi 'Ndingumntu wenzululwazi' kunye/okanye ngokuphendululekileyo? Kude kube nini bandithemba, ngokungathandabuzekiyo, bafundi abathandekayo. UAlfonso Jesús Población Sáez unguprofesa kwiYunivesithi yaseValladolid kunye nelungu leKomishoni yokusasazwa kweRoyal Spanish Mathematics Society (RSME).
