Tirohia te wāhanga i raro nei, kātahi ka whakautu i te pātai i muri mai i te reo kotahi me te wāhanga:  Passage: E toru ngā pūtake hītori matua o te ariā rōpū: te ariā tau, te ariā o ngā whārite taurangi, me te āhuahanga. I tīmatatia te rārangi tau-ariā e Leonhard Euler, ā, i whakawhanakehia e te mahi a Gauss i runga i te tatauranga kōwae me ngā rōpū tāpiri me te whakarea e pā ana ki ngā āpure tapawhā. I whiwhi Lagrange, Ruffini, me Abel i ngā hua tōmua e pā ana ki ngā rōpū whakarerekētanga i roto i ta rātau rapu i ngā rongoā whānui o ngā whārite taumaha o te taumata tiketike. I hangaia e Évariste Galois te kupu "rōpū" me te whakapumautia he hononga, e mohiotia ana inaianei ko te kaupapa Galois, i waenga i te ariā o nga roopu me te ariā āpure. I roto i te āhuahanga, i hira tuatahi ngā rōpū i roto i te āhuahanga pūwhitinga, ā, i muri mai, i roto i te āhuahanga kore-Euclidean. Ko te kaupapa Erlangen a Felix Klein i kii ko te ariā roopu te kaupapa whakahaere o te ahupūngao.  Pātai: He aha te ariā i hanga e Evariste Galois?
Te ariā o Galois