<prompt> Bheka isigaba esingezansi bese uphendula umbuzo emva kwalokho ngolimi olufanayo nesigaba: Ukudlula: Umqondo wanamuhla weqembu elingaqondakali lakhiwa emikhakheni eminingana yezibalo. Isisusa sokuqala sokusungulwa kwemfundiso yamaqembu kwakuwukufuna izixazululo zezilinganiso zama-polynomial ezinamazinga aphakeme kuno-4. Isazi sezibalo esingumFulentshi sekhulu le-19 u-Évariste Galois, esandisa umsebenzi wangaphambilini kaPaolo Ruffini noJoseph-Louis Lagrange, wanikeza indlela yokuxazululwa kwe-polynomial equation ethile ngokuya ngeqembu le-symmetry lezimpande zayo izixazululo. Izakhi zeqembu elinjalo likaGalois zihambelana nokuguquguquka okuthile kwezimpande. Ekuqaleni, imibono kaGalois yalahlwa abantu ayephila nabo, futhi yashicilelwa ngemva kokufa kwakhe. Amaqembu okuguquguquka ajwayelekile aphenya ikakhulukazi u-Augustin Louis Cauchy. I-Arthur Cayleys On the theory of groups, as depending on the symbolic equation θn 1 1854 inikeza incazelo yokuqala yeqembu elinemikhawulo. I-Geometry kwakuyinkambu yesibili lapho amaqembu asetshenziswa khona ngokuhlelekile, ikakhulukazi amaqembu we-symmetry njengengxenye yohlelo lukaFelix Klein luka-1872 Erlangen. Ngemva kokuba sekuvele ama-geometry amasha afana ne-hyperbolic ne-projective geometry, uKlein wasebenzisa inkolelo-mbono yamaqembu ukuze awahlele ngendlela ehambisanayo. Eqhubekisela phambili lemibono, uSophus Lie wasungula isifundo samaqembu kaLie ngo-1884. Izakhiwo ezithile zamaqembu ka-Abel zazisetshenziswe ngokungaqondile emsebenzini kaCarl Friedrich Gauss wezinombolo-theoretical Disquisitiones Arithmeticae 1798, futhi ngokucacile nguLeopold Kronecker. Ngo-1847, u-Ernst Kummer wenza imizamo yokuqala yokufakazela i-Fermats Last Theorem ngokuthuthukisa amaqembu achaza ukuhlukaniswa kwezinombolo eziyinhloko. Ukuhlangana kwale mithombo ehlukahlukene emcabangweni ofanayo wamaqembu kwaqala nge-Traité des substitutions et des équations algébriques 1870 kaCamille Jordan. UWalter von Dyck 1882 wethule umqondo wokuchaza iqembu ngokusebenzisa ama-generator kanye nobudlelwano, futhi waba ngowokuqala ukunikeza incazelo ye-axiomatic ye iqembu elingabonakali, ngokusho kwamagama aleso sikhathi. Kusukela ngekhulu lama-20, amaqembu... Umbuzo: Uyini umgomo walolu cwaningo?  <response>: ukwenza lula ukufakazelwa kwalokhu kuhlukaniswa 