The Greek government had asked Carathéodory to establish a second university in Smyrna. However, he also required a university post so he was appointed as Professor of Analytical and Higher Geometry at the University of Athens on 2 June 1920.
Ang Greek pamahalaan ay nagtanong Carathéodory na magtatag ng isang pangalawang unibersidad sa Smyrna. Gayunman, siya din ang kinakailangan ng isang unibersidad-post kaya siya ay hinirang bilang Professor ng Analytical at mas mataas na geometry sa University of Athens sa 2 Hunyo 1920.