From 1928 he was editor of the Jahrbuch über die Fortschritte der Mathematik ("Yearbook on the progress of mathematics").

Feigl's main areas of work were the foundations of geometry and topology, where he studied fixed point theorems for n-dimensional manifolds.

Because of the impending siege by the Red Army he was forced to leave Breslau in January 1945 with his family and other members of the Mathematical Institute.

Feigl brought his previously developed materials for the Mathematisches Wörterbuch and asked his students to further refine it in the castle.

Johann Radon (1887–1956) and Feigl were willing and able to continue lectures started in Breslau for one hour a day at Wechselburg castle, without any documents.