[1] Gaal received his Ph.D. under Frigyes Riesz and Lipót Fejér in 1947, although at the time, graduate study in Hungary did not exist in the formal way it is thought of today.
Under these conditions, only few higher education faculty could be appointed and students had to learn only from books or one or two old sick professors.
Gaal later went to Paris, where he was employed by the CNRS (Centre National del la Recherche Scientifique) at the rank of attaché de recherché.
Gaal met many leading French mathematicians at the CNRS, including Jean Leray and both Élie and Henri Cartan.
After emigrating to the United States, he held positions at Yale and Princeton before joining the faculty of the School of Mathematics at the University of Minnesota.