Ziziphi iimathematika?

Impendulo engalinganiyo kwimibuzo yokuba zeziphi iimathematika kwanamhlanje azikho, nangona ukuba le nzululwazi yazalwa kudala, phantse ekuqaleni kwempucuko. Kulo lonke ixesha, liye laphucula, ngakumbi, ngelixa liqinisekisa kwaye lihlaziywa njengendlela yokwazi imithetho yehlabathi elijikelezile.

Ngenxa yokunyuselwa kunye nokutshintshwa kwezixhumanisi ezininzi zeemathematika kunye nokusebenza, umntu unikezwa ithuba elikhethekileyo lokufumanisa nokusebenzisa imithetho ethile yemvelo. Ngexesha langoku, liyinjini enamandla kwaye inamandla yetheknoloji kunye nesayensi.

Ziziphi iimathematika? Abantu abaninzi banomdla kule nto, kodwa akulula ukuphendula lo mbuzo. Kakade, wonke umntu uyakwazi ukuphendula yakhe, eya kuxhomekeka kumgangatho wolwazi lwakhe lweemathematika. Kubafundi besikolo esiphakamileyo, eli lizwi eliqhelekileyo le-arithmetic, i-algebra, i-geometry, kunye nokuqala kohlalutyo. Kuba umfundi kwiyunivesithi yobugcisa, le yenzululwazi equkethe amacandelo ambalwa ahlukeneyo.

Kufuneka kuqatshelwe ukuba inani lalo manqaku landa ngexesha, njengoko iimathematika zanamhlanje zilungiswa rhoqo ngolwazi olutsha njengoko lukhula. Ewe, ngomntwana omncinci, le nzu lulwazi lukwazi ukubala. Nangona kunjalo, ubomi bethu bonke buhlanganiswe ngokungahambi kakuhle kunye nesisombululo seengxaki ezahlukeneyo zeemathematika.

Ngokufana neenkcazo zeziphi iimathematika, akukho nto ichazwe ngokucacileyo kwinqaku yale nzululwazi. Kwixesha elidlulileyo bekukholelwa ukuba isisombululo seengxaki ezinjalo kukulinganisa ubungakanani okanye amanani. Kodwa emva kwexeshana inkcazo yeemathematika njengengqungquthela yobungakanani obungapheliyo.

Ihlabathi lamanje lijonga iimathematika njengezenzululwazi zezakhiwo zeemathematika. Eli gama laqaliswa liqela labafundi beFrench abaziwayo kwihlabathi ngaphantsi kwegama elithi Bourbaki.

Le nzu yenzululwazi ayiyiyo yendalo yokucinga. Ibonakalisa iinjongo zehlabathi ngendlela ebonakalayo. Izifundo zayo zisekelwe kwiingcamango ezifunyenwe ngokugqithiseleyo kwizinto ezivela ngqo kwihlabathi langempela kwaye, ngaphezu koko, ukususela kwimimandla yangaphambili.

Ukuvela kwezinto ezinjalo kubandakanyeke ngokusondeleyo. Ngaphezu koko, emva kokuxazulula ingxaki ethile yemathematika, isiphumo sayo sisigxina, kwaye isetyenziswe kwiziganeko ezahlukileyo , imeko ebonakalayo eyahluke kakhulu.

Ngokomzekelo, ukufundiswa kweemathematika kuyancitshiswa ukuze kuxazululwe iingxaki ezithile: indlela yokufumana umlinganiselo wokuzaliswa kweebhaktheriya, ukuba uxinzelelo lwemoya luyahluka njani, okanye indlela yokumisela izinga lokubola kwe- radioactive. Kule meko, isisombululo sazo zonke iingxaki sinciphisa ukulingana okufanayo .

Ukucaca okunjalo kunzima ukuyiqonda kuphela, kodwa ukuziva umntu omdala, nangona kunjalo nangomfundi. Yingakho kubalulekile ukwenza isifundo semathematika sifumaneke kuwo wonke umntu. Kwaye oko kuyadingeka ukuba kugcinwe ibhalansi yeenkcukacha kunye nokuchithwa, intuition kunye nobunzima ngaphandle kokulahlekelwa lula ukuchaza iingcamango ezinzima.

Ewe, namhlanje kunzima ukufumana umntu ongeke abe nengcamango yokuba zeziphi iimathematika. Kodwa, njengomthetho, abaninzi abantu bakholelwa ngokugqithiseleyo ukuba eli li-arithmetic kuphela, oku kuquka ukufunda iinombolo kunye nezenzo ezithile ngoncedo lwabo, njengokuphindaphinda okanye ukwahlukana.

Kodwa ukuba ungena kule nzu lulwazi, uyaqonda ukuba ngokwenene le ngcamango inkulu. Emva koko, imathematika indlela ekhethekileyo yokuchaza ihlabathi kunye nokudibanisa ezinye zeendawo zayo nabanye. Kwiimpawu zemathematika ezichaza indalo, ubudlelwane bamanani buboniswa.

Kodwa njani ukuqonda izibalo? Lo mbandela ohlukeneyo. Le nkqubo idinga umonde, umnqweno kunye nengqalelo. Nangona kunjalo, yonke into ayinzima kakhulu. Wonke umntu unelungelo lokuphumelela kwimathematika, kuba kubonakaliswe ukuba "ukuvakalelwa kwenani" likwazi ukuqonda.

Akukho siphumo sokukhumbula i-axioms, i-theorems, kunye nokukhumbula iifomula, ngelanga, ayiyi kuba. Into ephambili kukuba kuqondwe i-essential theory kunye nemithetho yayo. Yaye ingqwalasela ekhethekileyo ifuna ukufikelela kwizigqibo ezivela kulezo nkcazo ezibekiwe.