In 1881 Rudio returned to the Eidgenössische Polytechnikum Zürich as a lecturer and, in 1889, he was appointed professor of mathematics there. Rudio was to hold this professorship until he retired in 1928.
Sa 1881 Rudio ibabalik sa Eidgenössische Polytechnikum Zürich bilang isang lektor at, sa 1889, siya ay hihirangin ng mga propesor sa matematika doon. Rudio ay hawakan ito pagkapropesor hanggang siya nagretiro sa 1928.