Ko te rārangi o te ariā tau i tīmataria e Leonhard Euler, ā, i whakawhanakehia e ngā mahi a Gauss i runga i te pāngarau kōwae me ngā rōpū tāpiri me te whakarea e pā ana ki ngā āpure tapawhā. Ko ngā hua tōmua e pā ana ki ngā rōpū whakarōpūtanga i whiwhihia e Lagrange, Ruffini, me Abel i roto i to rātau rapunga mō ngā rongoā whānui o ngā whārite taumaha o te taumata tiketike. I waihangatia e Évariste Galois te kupu "rōpū" me te whakapūmau i tētahi hononga, e mōhiotia ana ināianei ko te ariā a Galois, i waenganui i te ariā o ngā rōpū 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 te āhuahanga kore-Euclidean. I kī te hōtaka a Felix Klein Erlangen ko te kaupapa whakahaere o te ariā o te āhuahanga.
Te ariā o Galois