Georg Feigl attended school in Hamburg then, in 1909, he began his studies at the University of Jena. Due to ill health his studies took longer than expected. He obtained a degree from Jena, then in 1919 he obtained a doctorate there working under Koebe. His doctoral dissertation was on conformal mappings.
In 1919 Feigl became Schmidt's assistant at Berlin and Feigl's later work was to be greatly influenced by him. Feigl later becoming professor at Berlin himself. From 1928 to 1935 Feigl was managing editor of Jahrbuch über Fortschritte der Mathematik, the only reviewing journal at that time.
Feigl worked on geometry, in particular the foundations of geometry and topology. He was also interested in teaching and he introduced many teaching reforms. Through him the modern approach of Hilbert and Klein was introduced into universities and even secondary schools.
In 1935 Feigl became professor of mathematics at Breslau. During World War II he led a computing team working on aeronautical research. In 1945 the advancing Russian army meant that his team had to move and Feigl could not obtain his medication. This caused his death some months later.