Tauākī e pā ana ki te pāngarau o te pāngarau nui. Tauākī o te iwi nui e pā ana ki pāngarau

Ka taea te kite i ngā tauākī e pā ana ki te pāngarau hei pūtaiao waitara i roto i ngā mātāpuna kōrero o mua e kore e anake, engari ano hoki i roto i te taiao kāinga, te wahi e hiahia ana koe ki te tatau me te ine i. Operations whakaahua taonga i roto i ngā o te rōrahi me te āhua hua tatou i nga ra. Tīmata ki te maha o koko o te huka, te āhuatanga i roto i te kawhe, i mua i taua ruritanga o te taurewa auau huamoni tangohia tangohia.

whakamāramatanga

Ko te whakamāramatanga tuatahi me tauākī e pā ana ki te pāngarau taea te kitea i roto i te tangata tohe French Rene Dekarta: "E ti'a ia tatou ki te whakakotahi ki raro i te tawhito, ko katoa e hiahia ana koe ki te whakatika, te ine i mehua ranei te ariā mohiotia katoa o pāngarau ao. Na kahore he mea aha inenga ka kawea i roto i, tau ranei oro, whetu ranei tau. "

Ko te Soviet Union te ngā whakaaro te tauākī A. N. Kolmogorova: "Ko he pūtaiao, te wahi e tata ana te ōwehenga ine ki te āhua tūturu o te ao. Otiia anake i roto i te ariā roa, me te katoa waitara. "

Nikolya Burbaki - he rōpū o pūtaiao i France, e tuhituhi e rave rahi pukapuka e pā ana ki te pūtaiao hou. Waihanga i te rōpū i roto i 1935, ko te tauākī o pāngarau i roto i te epigraph o te putanga tuatahi: "kia huaina ai te ngako o tenei pūtaiao nui te ako o te pānga i runga i ngā pae tahi e te tahi o. e kore ai e mohiotia ētahi āhuatanga o te taonga, engari e taea te tatau ratou te whakamahi i te pai-mohiotia, huru maitatai faufaa. Ko te huinga o ngā tauira waitara tenei. "

German Veyl feaa e i taea katoa ki te hoatu i te whakamāramatanga mārama o pāngarau: "I runga i te pūtake o ngā pātai e taea te whakaaro tuwhera. Ko reira pakeke ki te whakaaro e runga i te wā e kitea e tatou he whakamāramatanga o pāngarau, i te mea e manakohia ana ki te katoa. Mai te mea pea tenei kahore i te pūtaiao, me ngā mahi auaha, rite puoro prosody ranei. "

Quotes e pā ana ki Pūtaiao

Tauākī e pā ana ki te pāngarau o te nui mathematicians me mau faahitiraa poto ui roa pātai atu whakahoki ratou:

• "Ko reira te taputapu katoa pūtaiao rite te scalpel ki te taote" (Apera).
• "I runga i te whenua, i reira he anake ataahua i roto i te ataahua o te matua - te hanga i te āhua pai - ko reira te hanganga pai, te rahi i hanga ki runga o tau Huaputa :. Ataahua - te reira tau" (A. Augustin).
• "Ko te whakamahi matua o pāngarau mo te tangata ke - ko e ko te reira fifi" (Alexandrov).
• "Ko reira te pūtaiao o te nanakia me te mārama. I roto i ngā morare, e taea te whakaaro te reira i te parau mau e te mea mārama, me te kore e rite i te kohu" (melo).
• "Pāngarau - he hanganga aueue ore, me te poropititanga pono" (melo).

Hape me miscalculations

E fakamanatu Tauākī e pā ana ki te pāngarau mathematicians nui e te mea faaore te pūtaiao te taea o hapa i roto i tetahi ruri o mahi:

• "E kore e Pāngarau aro ki hape," (E. Bell).
• "Here reira he kore" kitea "ariā" (E. Bell).
• "Ka mea te Kariki onamata" Pāngarau "a auraa" tohu "o" (Bourbaki).
• "E rima ngā - ira koki, tinana, raina me te mata -. He pāngarau, engari te 'amanaki o toi faaoti e enei ariā" (L. Da Vinci).
• "Ka taea e te pāngarau Hapa utu ora, ki te tangata kotahi e kore e anake, engari ko te katoa o te ao" (Bourbaki).
• "Ko te paraoa whiwhi tatou i roto o te witi. Ko orohina mira e ringihia e ki a ratou. Zasyplesh quinoa, e kore e taro tunua. Na roto i te pāngarau, ki te hanga e koe i te hape i te timatanga, e kore e nga whakatau tika te tiki" (Thomas Huxley).
• "E kore te mea te ngoikore o tenei pūtaiao. Na kei huru whakaarokore noa ki te ako koe" (J. Herbart).

Kōrero e pā ana ki taurangi

Tauākī e pā ana ki te pāngarau mathematicians nui - he kore noa he ariā whanui o tātaitanga, ko te arotahi kuiti runga taurangi, āhuahanga me te ahupūngao:

• "Algebra - he neke atu i te pūtaiao, ko reira he ara ki te kōrero e pā ana ki te pūtaiao" (Niels Bohr).
• "E kore e taea e te reira i mahi pakeke, te taurangi, hanga hoki te ngahau me te ki te āwhina iwi" (R. Bringherst).
• "Art - he taurangi huna e te reira i atu te wa katoa, me te ora mo te hunga e hiahia ana ki te tomo ona mea ngaro." (E. Bourdelle).
• "Practice whanau i Union taurangi, āhuahanga me te ahupūngao" (R. Bacon).
• "E kore e taea ki te matau pono taurangi, e kore te he punake" (Weitarahāute).
• "I waenganui taurangi, me te pūtaiao Me ki te tāuta mahi tahi hohonu. Kei te maha kite te reira i rite te ako tautoko. Ko he mea e tika ana ki te whakaaro i te take hohonu" (Weitarahāute).
• "Ko te whakatau i runga i raruraru taurangi - kei te tango i te pa hoariri, me te tāuta o nga pourewa o te pa patua o tona haki" (N. Vilenkin).

Geometry rite whakaaroaro ana ataata

Kupu o nga tangata nunui o te pāngarau me te āhuahanga, ka taea e koe te hanga i koe kite i te pono ki a ratou kanohi ake ranei.

• "Ki te titiro koe tata, katoa e haaati nei ia tatou - ko te āhuahanga" (Alexandrov).
• "He i roto i te āhuahanga kahore he whakateka, ngaro me te raruraru?" (Berkeley, D.).
• "Geometry me arorau - he rua merekara konei e mārama nga whakamāramatanga katoa, kahore he totohe i te mau marôraa mana'o, te iriti i mārama whakaaroaro ana ki te tukanga hi'opo'araa ki te tautuhi i te āhuatanga o te ahua, ka ko tonu te ahua i roto i mua o koutou tenei katoa hanga te peu o te whakaaro i ngā wā katoa .." (D. o Berkeley).
• "Hanga āhuahanga Elementary whakamahi o rerekē, ara tinihanga tohunga" (Borel).
• "Ko matou i te puai o te whakaaro pūtaiao Kariki, haere tatou ara Renaissance aito, no te mea e kore e taea e te ao te tīariari, kahore āhuahanga" (Weil).
• "Fokotu'u te āhuahanga te tikanga i roto i te hepohepo o katoa e haaati nei ia tatou" (Wiener).
• "Ka taea te āhuahanga tātai tatou ao" (Wiener).

rorohiko Ataahua

Tauākī e pā ana ki te pāngarau pāngarau nui fakapapau'i e taea te whakaritea te ataahua o ngā tau, me tau ki te toi pono:

• "Tau - ko tenei te tirohanga tuatahi o te pai tino -. I roto i te tikanga e taea etahi tau manako ki wā auau, me te kore ki te tautoko kairautanga" (A. Augustin).
• "Ka taea e pūmanawa ture i roto i te nanakia pāngarau" (Hadamard).
• "Kaiwhakaahua Pūtaiao tätaitanga te huru me te tuakiri o te tangata mārama o te whakaaro, me te whakamatau mau parau mau arorau" (Alexandrov).
• "Ko te tau mo te nanakia waho matauranga ki tonu katoa o te wera ā-" (Alexandrov).
• "Whakapono te Pythagoreans te pūtaiao pāngarau o te timatanga o nga mea katoa" (Aristotle).
• "I roto i te whakaoti i tetahi raruraru ki te tātari o te mahi motuhake e taea te whakatakoto kia rite ki ngā rautaki whānui e ka whai hua mo te taua mahi, te wahi i reira ko te unknown" (M. hu).
• "Science Ko te tukanga o te whanaketanga e taea o teie mahana mohio pakari o te kohatu tahuri ki te tukutuku o te pungawerewere i roto i nga tau i te torutoru" (E. Bell).

Tikanga ranei te ora

Tauākī e pā ana ki te pāngarau AV Voloshinova whakamōhio tatou ki pūtaiao nui. Tukua kia kite i te reira rite te wahi o to tatou oraraa:

• "Tonu ka Pāngarau hei te rangatira o ngā wāhi me pekanga katoa. E kore e te viivii ore o te pāngarau i akitū, he hoki he mutunga. Ko te hononga e hono toi me te rorohiko tenei. "
• "Kei te I tangohia tenei te pūtaiao rorohiko anake o te papanga i roto i tona whanaketanga. hanga kaha reira tenei taonga. I teie mahana, e matau ana tangata katoa te tangata kahore hononga ki pāngarau, e ko te reira he ope nui, tona mana kua kahore rohe. "
• "Ka taea e te mau faahitiraa parau pono i roto i te pāngarau utu anake te hunga e e pono i roto i te aroha ki te pūtaiao."
• "Whai me te tono nahanaha o pāngarau ki toi kitea i roto i te waiata, me te i roto i te mahi o Pythagoras me ana kau muimuí."
• "Ko Pāngarau ataahua i roto iho, engari ka hopoi mai ia tenei ataahua ki te whanaketanga o te ao, ko reira te rapu mo te tino."

tauākī Pythagoras e pā ana ki te pāngarau rite timata he pūtaiao

Ko te tino pai-mohiotia kupu o Pythagoras tangi rite te pepeha mo te kau muimui, "he maha katoa."

atu ana tauākī, atu taumauri, e taea te tikanga rite tetahi mea:

• "E he mea nui, engari e kore e fafau i te fakahoko nui."
• "Ki te mohio o nga ture o pāngarau tamata tuatahi o ako katoa te reo o tau."
• "Te tūhura katoa e kite ia koutou, ara, ki te he to koutou hinengaro i roto i te wahi tuatahi."

tauākī Lomonosov e pā ana ki te pāngarau

kihai i pūtaiao Russian Mikhail Vasilyevich anake he aivanaa nui, ako ia manga katoa o te pūtaiao, i te matū ki rotarota. Ko te tauākī tino faahitihia e pā ana ki University pāngarau te whai ake: "Ko e tika ana Pāngarau ki te mohio na anake e ko ia i roto i te raupapa o ahu maramarama."

Hoki, ka taea te kitea i te University tauākī i runga i marau motuhake:

• "Geometry - te kuini o te rangahau katoa duma."
• "Matū Ko ahupūngao ringa me kanohi - pāngarau iho."
• "Ahupūngao matapo kahore rorohiko pūtaiao".
• "Ko nga mea katoa e he pāhekeheke i roto i taua sciences rite aerometry, Hydraulics me optics, hanga mārama, mārama, me te pono tātai pāngarau."

tupato whakaaroaro

Tauākī e pā ana ki te pāngarau titiro maha mathematicians nui rite kupu atamai. Ētahi E taea e ki te matau iwi anake i roto i te matau, engari i reira he korukī e e wātea ana ki te katoa:

• "Ka taea te huaina ētahi atu taonga me nga mea i te ara ano e tika ana ki ngā tātaitanga, me ngā tātai" (Poincaré).
• "Ko te tangata e kore he mōhio ki te taketake o te pūtaiao o tau nei, e kore e taea e manuïa i roto i tetahi take" (R. Bacon).
• "Pāngarau - ko te ako o tātai rerekē, me te ki a ratou, otiia kahore he ihirangi" (Hilbert).
• "Ki te i taea e ki te whakamatau i te ture tauwehe kahore tetahi, huaina ai ko te axiom" (Euclid).
• "Pāngarau Ko te katoa! Just kore te mea e hiahia ana koe tika inaianei" (Albert Einstein).

mea urutau hoki ngā tamariki

Tauākī e pā ana ki te pāngarau mō ngā tamariki e mahara ana tatou i nga ra toku kura, ka i raro i ia pūtaiao portrait faahiti ana whakaaro me te waiaro ki te pūtaiao:

• "Ehara i noa te hinengaro ongó, e hiahia ana koe ki te kitea te whakamahi hoki reira" (Descartes).
• "Ki te mea paari roa'e mohio kita" (Felas).
• "I mua i rutu tatou te raruraru, e hiahia ana koe ki te āta pānui i te ture me ngā here" (Hadamard).

korukī o te nui

kotahi whakamatau ano tauākī o pūtaiao i runga i te pāngarau me te pūtaiao i roto i te whānui e waho nga mea timatanga o te matauranga taketake i roto i te ao hou noa e kore e taea te mahi:

• "I roto i nga pūtaiao e kite i te ōrau o te pono i roto i roto i te Science Computing" (Kant).
• "He Mathematicians rite Itāriana. Mea ratou te tahi mea, te iriti i tonu ratou ki roto ki o ratou reo, a hurihia, whiwhi tatou i te ritenga atu" (Goethe).
• "Rorohiko ture e te hunga whai pānga ki te ao tūturu, he hārakiraki. Ka ko waitara nga ture tino pono" (Albert Einstein).
• "Mai taua wa, ka rite ki te ariā o te ngä ka tatau o te pāngarau, e kore matau e ahau i te reira kua" (Albert Einstein).

e kore te tinihanga i nga wa katoa tauākī o te iwi nui e pā ana ki te pāngarau. Ko to tatou ki te whakaae e waho te pūtaiao o tau, e kore e taea e to tatou ao te tīariari.