He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.
His thesis, written under the direction of Max Dehn, was entitled Über unendlich diskontinuierliche Gruppen von einer definierenden Relation (der Freiheitssatz).
He refused to join the Nazi Party and, as a consequence, was not allowed to hold an academic post during World War II.
In 1948, he emigrated to the United States to collaborate on the Bateman Manuscript Project as a co-editor while a visiting professor at the California Institute of Technology.
His doctoral students include Joan Birman, Martin Greendlinger, Edna Grossman, Herbert Keller, Seymour Lipschutz, and Kathryn F.