Nyorai kupfuurira kweiyi ndima - PaYunivhesiti yePalermo, Bagnera akagamuchira "laurea" yake muunyanzvi hwokuvaka muna 1890 uye ipapo "laurea" yake mumasvomhu muna 1895. Vadzidzisi vake vaisanganisira Giovanni Battista Guccia, Francesco Gerbaldi ed Ernesto Cesàro. Muna 1899 akagadzwa kuva "libero docente" (mudzidzisi) mu algebraic analysis paUniversity of Palermo. Akagadzwa purofesa extraordinarius weinfinitesimal calculus muna 1901, ipapo purofesa ordinarius muna 1905, paYunivhesiti yeMessina, kwaakaramba ari kusvikira kudengenyeka kwenyika kwa1908
. Akabva adzidzisa paYunivhesiti yePalermo kusvikira muna 1922 paakazotamira kuSapienza University yeRome, kwaakadzidzisa kusvikira afa.