Ithiyori yigama elinemvelaphi yesiGreki elithi a isiphakamiso esikhombisa iqiniso ngomkhakha othile wesayensi, enokubaluleka kokukhonjiswa ngokuya kwezinye iziphakamiso ezazikhonjiswe ngaphambilini, ezibizwa ngama-axioms. Ngokuvamile theorems asekela isayensi ebizwa ngokuthi ‘ngqo’, ikakhulukazi 'okusemthethweni' (mathematics, logic), okuyilawo asebenzisa izinto ezifanele ukuthola iziphetho ezijwayelekile.
Ukucabanga ngemuva komqondo wethiyori ukuthi, inqobo nje uma lokhu kususelwa kuziphakamiso eziyiqiniso ezichazwe ngokunengqondo nangokunembile, lokho okushiwo yi-theorem kuyiqiniso lobunyoninco ngokuphelele. Lokhu yikho kanye okubavumela ukuthi basebenze njengabasekeli bokuthuthuka kwanoma iyiphi inkolelo-mbono yesayensi, ngaphandle kwesidingo sokukufakazela futhi.
Izinga eliphakathi lama-theorems yisimilo sawo se- okunengqondo. Ngokuvamile, futhi futhi uma kuqhathaniswa nezinye izinhlobo zolwazi lwesayensi (njengalezo ezikhiqizwa ngokubheka noma ngokubheka), imvelaphi yayo ivela ekusebenzeni kwenqubo enengqondo enga-oda kalula. Ngalo mqondo, theorems iqala kusuka ku- a i-hypothesis eyisisekelo, okuyilokho ofuna ukukukhombisa; mqondo, okuyiyona ncamashi ukuboniswa, kanye nokuhambisana, okuyi isiphetho lokho kufinyelelwa lapho ukuboniswa sekuqediwe.
Njengoba kushiwo, umqondo oyinhloko wama-theorems ngumbuzo wokungenzeka njalo nokuthi kungenzeka ukuthi usayinwe futhi wamukelwe futhi ngaso sonke isikhathi. Kodwa-ke, uma kuvela isimo esisodwa lapho i-theorem ilahlekelwa khona jikelele, i-theorem ngokushesha ayisebenzi.
Umqondo we-theorem uthathwe ngu ezinye isayensi (ezomnotho, isayikholoji noma isayensi yezepolitiki, phakathi kokunye) ukuqoka imiqondo ethile ebalulekile noma eyisisekelo elawula leyo mikhakha, noma ngabe lokhu kungaveli ngenqubo echaziwe. Kulezi zimo, ama-axioms awasetshenziswanga kepha kunalokho okucatshangelwa okwenziwe ngezinqubo ezifana nokubuka noma ngisho nesampula lezibalo.
Uhlu olulandelayo luqoqa izibonelo zemibono kanye nencazelo emfushane yalokho okukulandelayo:
- Umbono kaPythagoras: ubudlelwane phakathi kwesilinganiso se-hypotenuse naleso semilenze, esimweni sonxantathu abangakwesokudla.
- Ithiyori yenombolo eyinhloko: Njengoba umugqa wenombolo ukhula, kuzoba nezinombolo ezimbalwa futhi ezimbalwa kulelo qembu.
- Ithiyori ye-Binomial: ifomula yokuxazulula amandla ama-binomials (okungeziwe noma ukukhishwa kwezinto).
- Umbono kaFrobenius: ukuxazulula ifomula yezinhlelo zokulinganisa okulinganayo.
- IThales theorem: izici ngokwama-engeli nezinhlangothi zonxantathu abafanayo, nezinye izakhiwo zazo.
- Umbono ka-Euler: inani lama-vertices kanye nenombolo yobuso ilingana nenombolo yamaphethelo kanye no-2.
- Umbono kaPtolemy: Isamba semikhiqizo ye-diagonals silingana nesamba semikhiqizo yezinhlangothi eziphikisanayo.
- Umbono kaCauchy-HadamardUkusungulwa kobubanzi bokuhlangana kochungechunge lwamandla acishe afane nomsebenzi ozungeze iphoyinti.
- Umbono kaRolle: Esikhaleni lapho ukweqiwa okulinganisiwe emsebenzini ohlukaniswayo kulingana, kuzohlala kunephuzu lapho okususelwa kunyamalala khona.
- Incazelo yenani elisho inani: Uma umsebenzi uqhubeka futhi uhlukaniswa phakathi nesikhathi esithile, kuzoba nephuzu kuleso sikhathi lapho i-tangent izofana ne-secant.
- Umbono kaCauchy Dini: Imibandela yokubalwa kokuphikisanayo esimweni semisebenzi engacacisiwe.
- Umbono we-CalculusUkutholwa nokuhlanganiswa komsebenzi kungukuphambuka komsebenzi.
- Umbono we-Arithmetic: Yonke inombolo ephelele ingamelwa njengomkhiqizo wezinto eziyinhloko.
- I-Bayes theorem (izibalo): Indlela yokuthola amathuba anemibandela.
- I-Cobweb theorem (ezomnotho): Ithiyori yokuchaza ukwakheka kwemikhiqizo eyenziwe ngokususelwa kunani langaphambilini.
- Ithiyori kaMarshall Lerner (ezomnotho): Ukuhlaziywa komthelela wokwehliswa kwemali ngokuya ngamanani nezintengo.
- Coase theorem (ezomnotho): Isixazululo samacala wangaphandle, aqonde ekwehlisweni komthetho.
- Ithiyori yokuvota yaseMedian (isayensi yezepolitiki): Inqubo yokhetho eningi ivame ukuvumela ivoti eliphakathi.
- Ithiyori kaBaglini (isayensi yezepolitiki, i-Argentina): Usopolitiki uvamise ukuletha iziphakamiso zakhe kulesi sikhungo uma esondela ezikhundleni zokuphatha.
- Ithiyori kaThomas (isociology): Uma abantu bezichaza izimo njengezingezangempela, ziba ngokoqobo emiphumeleni yazo.
