He aha te mea pāngarau?

Ko te whakahoki ta'e ki te pātai o te mea pāngarau ko, ara tenei ra, tonu e kore e te tīariari, ahakoa te meka i whanau tenei pūtaiao i te wa roa i mua, tata ki te ata o te ao. Puta noa i te wa e hua nga reira, te whakanui ake i te whakakoia wa taua, me te whakahoutia ano rite te ara o te mohio ki nga ture o te ao.

Nā ki te hōrapatanga, ngā huringa o hononga matamaha ki te mahi o te pāngarau, homai tangata ko te whai wāhitanga ahurei ki te kitea e me te whakamahi i te hunga tahi atu mau ture o te natura ranei. I te wa nei, ko reira pono he kaha, me te kaha hangarau pūkaha me te pūtaiao.

He aha te mea pāngarau? Paanga i roto i tenei tokomaha, engari e kore te mea ngāwari te whakahoki ki tēnei pātai. O te akoranga, e taea ki te hoatu tona whakahoki ake, e ka whakawhirinaki ki runga ki tona taumata o te matauranga pāngarau katoa ko. Hoki te ākonga kura tiketike ko te ingoa kano o tauhanga, te taurangi, āhuahanga, me te tīmata i te tātari. Hoki ngā ākonga whare wānanga hangarau ko - Pūtaiao arā, o pinepine o ngā wāhanga takitahi.

Me kï reira e tonu faarahi te maha o taua wāhanga ki te wā, ka rite ki, rite ki o ratou whanaketanga o pāngarau hou te tonu taonga ki ngā mōhiohio hou. Well, Ko tenei pūtaiao te kaha ki te kia whakaaro hoki te tamaiti iti. Otiia, He mea paihere to matou ora katoa ki te otinga o ngā raruraru pāngarau.

Waihoki whakatau he aha pāngarau, kahore he whakamāramatanga mārama, me te whänui ana te whakaaetia o te ahanoa o tenei pūtaiao. I roto i te mua i whakapono ai e te otinga ki taua raruraru, ko te ki te ine i te rahinga tau ranei. Otiia i muri i te i reira ko te whakamāramatanga o pāngarau rite te parau haapiiraa rahi mure ore o.

whakaaro te ao hou pāngarau rite te pūtaiao o ngā hanganga pāngarau. I tapa tenei wā i te rōpū o mathematicians French, mohiotia i raro i te ingoa Bourbaki ao.

E kore te mea tenei pūtaiao he hanga noho o te whakaaro. Whakaatu te reira i te ao whāinga i roto i te tahi mau puka waitara. hāngai ana tona ako kei i runga i ngā ariā i takea e abstracting i pānga tika te ao tūturu, me te, i roto i te tua, i te rarahi o mua.

Kei te tata hono te takanga o taua rarahi ki mooni. Ano, i muri i whakaoti i te raruraru pāngarau he Pumau tonu te hua, me te ka tono ki te momo o te ari, te tinana , ko te tino rerekē i ia atu āhua o nei.

Hei tauira, te ako o pāngarau maha whakaiti ki hopanga o ngā raruraru motuhake: me pehea ki te kitea te tere o te tupu kitakita rite huringa pēhanga barometric pehea ki te whakatau i te auau ranei o te mehanga iratuki. iti te otinga o enei raruraru katoa e ki te taua whārite pārōnaki.

he uaua taua oti'a kore anake ki te matau engari ano ki te wheako i te pakeke, kia anake te ākonga. Ko Ko te aha e mea faufaa ki te hanga i te ako o pāngarau wātea ki te katoa. A titau i te reira ki te mau tonu i te pauna o te pū, me te oti'a, pūmanawa me te nanakia, kahore ngaro te humarie o te whakamārama ariā matatini.

O te akoranga, i tenei ra he uaua ki te kitea te tangata nei e kua i kahore whakaaro e pā ana ki te mea he pāngarau. Engari kia rite ki te tikanga, hape whakapono maha iwi e he tauhanga tika tenei, Ko tā te ako o ngā tau, me te mahi motuhake ki a ratou, pērā i te whakarea wehenga ranei.

Otiia, ki te ruku koe ki tenei pūtaiao, e taea e tatou e kite e i roto i te meka tenei ariā ko te nui bulkier. I muri i te katoa, pāngarau ko te ara ahua o te whakaahua i te ao, me te huinga o etahi o ona wahi ki ētahi atu. I roto i te tohu pāngarau e whakaahua te ao, ua faaite i roto i te hononga o ngā tau.

Ko e founga ki te matau i te pāngarau? Ko te take motuhake tenei. titau te tukanga taua manawanui, hiahia me te arotahi. Heoi, e kore te mea pera uaua katoa. ahu ia ki te mahi pai i roto i te pāngarau te mea kua oti te whakamatautau i te reira e "te mana'o o" Ko te kaha hohonu.

No aauraa hua o axioms, theorems me ako ma'uloto tātai, kāore, e kore e. Ko te mea matua - ko ki matau te ngako o te ariā pāngarau, me ona ture. A kia hoatu tokanga makehe te kaha ki te whakatau i te hunga tauākī, i tukua nei.